TY - JOUR
T1 - Multiparty quantum data hiding with enhanced security and remote deletion
Y1 - 2018
A1 - Xingyao Wu
A1 - Jianxin Chen
AB -
One of the applications of quantum technology is to use quantum states and measurements to communicate which offers more reliable security promises. Quantum data hiding, which gives the source party the ability of sharing data among multiple receivers and revealing it at a later time depending on his/her will, is one of the promising information sharing schemes which may address practical security issues. In this work, we propose a novel quantum data hiding protocol. By concatenating different subprotocols which apply to rather symmetric hiding scenarios, we cover a variety of more general hiding scenarios. We provide the general requirements for constructing such protocols and give explicit examples of encoding states for five parties. We also proved the security of the protocol in sense that the achievable information by unauthorized operations asymptotically goes to zero. In addition, due to the capability of the sender to manipulate his/her subsystem, the sender is able to abort the protocol remotely at any time before he/she reveals the information.
U4 - 5
UR - https://arxiv.org/abs/1804.01982
ER -
TY - JOUR
T1 - Quantum algorithm for multivariate polynomial interpolation
JF - Proceedings of The Royal Society A
Y1 - 2018
A1 - Jianxin Chen
A1 - Andrew M. Childs
A1 - Shih-Han Hung
AB - How many quantum queries are required to determine the coefficients of a degree-d polynomial in n variables? We present and analyze quantum algorithms for this multivariate polynomial interpolation problem over the fields Fq, R, and C. We show that kC and 2kC queries suffice to achieve probability 1 for C and R, respectively, where kC = ⌈ 1 n+1 ( n+d d )⌉ except for d = 2 and four other special cases. For Fq, we show that ⌈ d n+d ( n+d d )⌉ queries suffice to achieve probability approaching 1 for large field order q. The classical query complexity of this problem is ( n+d d ), so our result provides a speedup by a factor of n + 1, n+1 2 , and n+d d for C, R, and Fq, respectively. Thus we find a much larger gap between classical and quantum algorithms than the univariate case, where the speedup is by a factor of 2. For the case of Fq, we conjecture that 2kC queries also suffice to achieve probability approaching 1 for large field order q, although we leave this as an open problem.
VL - 474
UR - http://rspa.royalsocietypublishing.org/content/474/2209/20170480
CP - 2209
U5 - 10.1098/rspa.2017.0480
ER -
TY - JOUR
T1 - Quantum state tomography via reduced density matrices
JF - Physical Review Letters
Y1 - 2017
A1 - Tao Xin
A1 - Dawei Lu
A1 - Joel Klassen
A1 - Nengkun Yu
A1 - Zhengfeng Ji
A1 - Jianxin Chen
A1 - Xian Ma
A1 - Guilu Long
A1 - Bei Zeng
A1 - Raymond Laflamme
AB - Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.
VL - 118
U4 - 020401
UR - http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.020401
U5 - 10.1103/PhysRevLett.118.020401
ER -
TY - JOUR
T1 - Detecting Consistency of Overlapping Quantum Marginals by Separability
JF - Physical Review A
Y1 - 2016
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - Nengkun Yu
A1 - Bei Zeng
AB - The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability.
VL - 93
U4 - 032105
UR - http://arxiv.org/abs/1509.06591
CP - 3
U5 - 10.1103/PhysRevA.93.032105
ER -
TY - JOUR
T1 - A finite presentation of CNOT-dihedral operators
Y1 - 2016
A1 - Matthew Amy
A1 - Jianxin Chen
A1 - Neil J. Ross
AB - We give a finite presentation by generators and relations of unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOT-dihedral operators. To this end, we introduce a notion of normal form for CNOT-dihedral circuits and prove that every CNOT-dihedral operator admits a unique normal form. Moreover, we show that in the presence of certain structural rules only finitely many circuit identities are required to reduce an arbitrary CNOT-dihedral circuit to its normal form. By appropriately restricting our relations, we obtain a finite presentation of unitary operators expressible over the {CNOT, T } gate set as a corollary.
UR - https://arxiv.org/abs/1701.00140
ER -
TY - JOUR
T1 - Joint product numerical range and geometry of reduced density matrices
Y1 - 2016
A1 - Jianxin Chen
A1 - Cheng Guo
A1 - Zhengfeng Ji
A1 - Yiu-Tung Poon
A1 - Nengkun Yu
A1 - Bei Zeng
A1 - Jie Zhou
AB - The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection Θ is convex in R3. The boundary ∂Θ of Θ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti's theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range Π of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that ruled surface emerge naturally when taking a convex hull of Π. We show that, a ruled surface on ∂Θ sitting in Π has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of Θ, with two boundary pieces of symmetry breaking origin separated by two gapless lines.
UR - http://arxiv.org/abs/1606.07422
ER -
TY - JOUR
T1 - Pure-state tomography with the expectation value of Pauli operators
JF - Physical Review A
Y1 - 2016
A1 - Xian Ma
A1 - Tyler Jackson
A1 - Hui Zhou
A1 - Jianxin Chen
A1 - Dawei Lu
A1 - Michael D. Mazurek
A1 - Kent A.G. Fisher
A1 - Xinhua Peng
A1 - David Kribs
A1 - Kevin J. Resch
A1 - Zhengfeng Ji
A1 - Bei Zeng
A1 - Raymond Laflamme
AB - We examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary n-qubit pure state among all quantum states. We show that only 11 Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with 16 measurements, and only 31 Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with 64 measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.
VL - 93
U4 - 032140
UR - http://arxiv.org/abs/1601.05379
CP - 3
U5 - http://dx.doi.org/10.1103/PhysRevA.93.032140
ER -
TY - JOUR
T1 - Quantifying the coherence of pure quantum states
JF - Physical Review A
Y1 - 2016
A1 - Jianxin Chen
A1 - Nathaniel Johnston
A1 - Chi-Kwong Li
A1 - Sarah Plosker
AB - In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an explicit characterization of the closest incoherent state to a given pure state under the trace distance measure of coherence, and we affirm a recent conjecture that the ℓ1 measure of coherence of a pure state is never smaller than its relative entropy of coherence. We then use our result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states, and we derive a new inequality relating the negativity and distillable entanglement of pure states.
VL - 94
U4 - 042313
UR - https://doi.org/10.1103/PhysRevA.94.042313
CP - 4
U5 - 10.1103/PhysRevA.94.042313
ER -
TY - JOUR
T1 - Tomography is necessary for universal entanglement detection with single-copy observables
JF - Physical Review Letters
Y1 - 2016
A1 - Dawei Lu
A1 - Tao Xin
A1 - Nengkun Yu
A1 - Zhengfeng Ji
A1 - Jianxin Chen
A1 - Guilu Long
A1 - Jonathan Baugh
A1 - Xinhua Peng
A1 - Bei Zeng
A1 - Raymond Laflamme
AB - Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.
VL - 116
U4 - 230501
UR - http://arxiv.org/abs/1511.00581
CP - 23
U5 - 10.1103/PhysRevLett.116.230501
ER -
TY - JOUR
T1 - Discontinuity of Maximum Entropy Inference and Quantum Phase Transitions
JF - New Journal of Physics
Y1 - 2015
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - Chi-Kwong Li
A1 - Yiu-Tung Poon
A1 - Yi Shen
A1 - Nengkun Yu
A1 - Bei Zeng
A1 - Duanlu Zhou
AB - In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit.
VL - 17
U4 - 083019
UR - http://arxiv.org/abs/1406.5046v2
CP - 8
J1 - New J. Phys.
U5 - 10.1088/1367-2630/17/8/083019
ER -
TY - JOUR
T1 - The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases)
JF - Communications in Mathematical Physics
Y1 - 2015
A1 - Jianxin Chen
A1 - Nathaniel Johnston
AB - A long-standing open question asks for the minimum number of vectors needed to form an unextendible product basis in a given bipartite or multipartite Hilbert space. A partial solution was found by Alon and Lovasz in 2001, but since then only a few other cases have been solved. We solve all remaining bipartite cases, as well as a large family of multipartite cases.
VL - 333
U4 - 351 - 365
UR - http://arxiv.org/abs/1301.1406v1
CP - 1
J1 - Commun. Math. Phys.
U5 - 10.1007/s00220-014-2186-7
ER -
TY - JOUR
T1 - Universal Subspaces for Local Unitary Groups of Fermionic Systems
JF - Communications in Mathematical Physics
Y1 - 2015
A1 - Lin Chen
A1 - Jianxin Chen
A1 - Dragomir Z. Djokovic
A1 - Bei Zeng
AB - Let $\mathcal{V}=\wedge^N V$ be the $N$-fermion Hilbert space with $M$-dimensional single particle space $V$ and $2N\le M$. We refer to the unitary group $G$ of $V$ as the local unitary (LU) group. We fix an orthonormal (o.n.) basis $\ket{v_1},...,\ket{v_M}$ of $V$. Then the Slater determinants $e_{i_1,...,i_N}:= \ket{v_{i_1}\we v_{i_2}\we...\we v_{i_N}}$ with $i_1<...3. If $M$ is even, the well known BCS states are not LU-equivalent to any single occupancy state. Our main result is that for N=3 and $M$ even there is a universal subspace $\cW\subseteq\cS$ spanned by $M(M-1)(M-5)/6$ states $e_{i_1,...,i_N}$. Moreover the number $M(M-1)(M-5)/6$ is minimal.
VL - 333
U4 - 541 - 563
UR - http://arxiv.org/abs/1301.3421v2
CP - 2
J1 - Commun. Math. Phys.
U5 - 10.1007/s00220-014-2187-6
ER -
TY - JOUR
T1 - Symmetric Extension of Two-Qubit States
JF - Physical Review A
Y1 - 2014
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - David Kribs
A1 - Norbert Lütkenhaus
A1 - Bei Zeng
AB - Quantum key distribution uses public discussion protocols to establish shared secret keys. In the exploration of ultimate limits to such protocols, the property of symmetric extendibility of underlying bipartite states $\rho_{AB}$ plays an important role. A bipartite state $\rho_{AB}$ is symmetric extendible if there exits a tripartite state $\rho_{ABB'}$, such that the $AB$ marginal state is identical to the $AB'$ marginal state, i.e. $\rho_{AB'}=\rho_{AB}$. For a symmetric extendible state $\rho_{AB}$, the first task of the public discussion protocol is to break this symmetric extendibility. Therefore to characterize all bi-partite quantum states that possess symmetric extensions is of vital importance. We prove a simple analytical formula that a two-qubit state $\rho_{AB}$ admits a symmetric extension if and only if $\tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}$. Given the intimate relationship between the symmetric extension problem and the quantum marginal problem, our result also provides the first analytical necessary and sufficient condition for the quantum marginal problem with overlapping marginals.
VL - 90
UR - http://arxiv.org/abs/1310.3530v2
CP - 3
J1 - Phys. Rev. A
U5 - 10.1103/PhysRevA.90.032318
ER -
TY - JOUR
T1 - Unextendible Product Basis for Fermionic Systems
JF - Journal of Mathematical Physics
Y1 - 2014
A1 - Jianxin Chen
A1 - Lin Chen
A1 - Bei Zeng
AB - We discuss the concept of unextendible product basis (UPB) and generalized UPB for fermionic systems, using Slater determinants as an analogue of product states, in the antisymmetric subspace $\wedge^ N \bC^M$. We construct an explicit example of generalized fermionic unextendible product basis (FUPB) of minimum cardinality $N(M-N)+1$ for any $N\ge2,M\ge4$. We also show that any bipartite antisymmetric space $\wedge^ 2 \bC^M$ of codimension two is spanned by Slater determinants, and the spaces of higher codimension may not be spanned by Slater determinants. Furthermore, we construct an example of complex FUPB of $N=2,M=4$ with minimum cardinality $5$. In contrast, we show that a real FUPB does not exist for $N=2,M=4$ . Finally we provide a systematic construction for FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions.
VL - 55
U4 - 082207
UR - http://arxiv.org/abs/1312.4218v1
CP - 8
J1 - J. Math. Phys.
U5 - 10.1063/1.4893358
ER -
TY - JOUR
T1 - Symmetries of Codeword Stabilized Quantum Codes
JF - 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)
Y1 - 2013
A1 - Salman Beigi
A1 - Jianxin Chen
A1 - Markus Grassl
A1 - Zhengfeng Ji
A1 - Qiang Wang
A1 - Bei Zeng
AB - Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general framework for constructing quantum error-correcting codes known to date. A CWS code Q can be represented by a self-dual additive code S and a classical code C, i.,e., Q=(S,C), however this representation is in general not unique. We show that for any CWS code Q with certain permutation symmetry, one can always find a self-dual additive code S with the same permutation symmetry as Q such that Q=(S,C). As many good CWS codes have been found by starting from a chosen S, this ensures that when trying to find CWS codes with certain permutation symmetry, the choice of S with the same symmetry will suffice. A key step for this result is a new canonical representation for CWS codes, which is given in terms of a unique decomposition as union stabilizer codes. For CWS codes, so far mainly the standard form (G,C) has been considered, where G is a graph state. We analyze the symmetry of the corresponding graph of G, which in general cannot possess the same permutation symmetry as Q. We show that it is indeed the case for the toric code on a square lattice with translational symmetry, even if its encoding graph can be chosen to be translational invariant.
VL - 22
U4 - 192-206
UR - http://arxiv.org/abs/1303.7020v2
U5 - 10.4230/LIPIcs.TQC.2013.192
ER -
TY - JOUR
T1 - Uniqueness of Quantum States Compatible with Given Measurement Results
JF - Physical Review A
Y1 - 2013
A1 - Jianxin Chen
A1 - Hillary Dawkins
A1 - Zhengfeng Ji
A1 - Nathaniel Johnston
A1 - David Kribs
A1 - Frederic Shultz
A1 - Bei Zeng
AB - We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it is known that for a d-dimensional Hilbert space, there exists a set of 4d-5 observables that uniquely determines any pure state. We show that for case (2), 5d-7 observables suffice to uniquely determine any pure state. Thus there is a gap between the results for (1) and (2), and we give some examples to illustrate this. The case of observables corresponding to reduced density matrices (RDMs) of a multipartite system is also discussed, where we improve known bounds on local dimensions for case (2) in which almost all pure states are uniquely determined by their RDMs. We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low rank quantum states.
VL - 88
UR - http://arxiv.org/abs/1212.3503v2
CP - 1
J1 - Phys. Rev. A
U5 - 10.1103/PhysRevA.88.012109
ER -
TY - JOUR
T1 - Universal Entanglers for Bosonic and Fermionic Systems
Y1 - 2013
A1 - Joel Klassen
A1 - Jianxin Chen
A1 - Bei Zeng
AB - A universal entangler (UE) is a unitary operation which maps all pure product states to entangled states. It is known that for a bipartite system of particles $1,2$ with a Hilbert space $\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}$, a UE exists when $\min{(d_1,d_2)}\geq 3$ and $(d_1,d_2)\neq (3,3)$. It is also known that whenever a UE exists, almost all unitaries are UEs; however to verify whether a given unitary is a UE is very difficult since solving a quadratic system of equations is NP-hard in general. This work examines the existence and construction of UEs of bipartite bosonic/fermionic systems whose wave functions sit in the symmetric/antisymmetric subspace of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$. The development of a theory of UEs for these types of systems needs considerably different approaches from that used for UEs of distinguishable systems. This is because the general entanglement of identical particle systems cannot be discussed in the usual way due to the effect of (anti)-symmetrization which introduces "pseudo entanglement" that is inaccessible in practice. We show that, unlike the distinguishable particle case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are symmetric (resp. antisymmetric) subspaces of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ if and only if $d\geq 3$ (resp. $d\geq 8$). To prove this we employ algebraic geometry to reason about the different algebraic structures of the bosonic/fermionic systems. Additionally, due to the relatively simple coherent state form of unentangled bosonic states, we are able to give the explicit constructions of two bosonic UEs. Our investigation provides insight into the entanglement properties of systems of indisitinguishable particles, and in particular underscores the difference between the entanglement structures of bosonic, fermionic and distinguishable particle systems.
UR - http://arxiv.org/abs/1305.7489v1
ER -
TY - JOUR
T1 - Comment on some results of Erdahl and the convex structure of reduced density matrices
JF - Journal of Mathematical Physics
Y1 - 2012
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - Mary Beth Ruskai
A1 - Bei Zeng
A1 - Duan-Lu Zhou
AB - In J. Math. Phys. 13, 1608-1621 (1972), Erdahl considered the convex structure of the set of $N$-representable 2-body reduced density matrices in the case of fermions. Some of these results have a straightforward extension to the $m$-body setting and to the more general quantum marginal problem. We describe these extensions, but can not resolve a problem in the proof of Erdahl's claim that every extreme point is exposed in finite dimensions. Nevertheless, we can show that when $2m \geq N$ every extreme point of the set of $N$-representable $m$-body reduced density matrices has a unique pre-image in both the symmetric and anti-symmetric setting. Moreover, this extends to the quantum marginal setting for a pair of complementary $m$-body and $(N-m)$-body reduced density matrices.
VL - 53
U4 - 072203
UR - http://arxiv.org/abs/1205.3682v1
CP - 7
J1 - J. Math. Phys.
U5 - 10.1063/1.4736842
ER -
TY - JOUR
T1 - Correlations in excited states of local Hamiltonians
JF - Physical Review A
Y1 - 2012
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - Zhaohui Wei
A1 - Bei Zeng
AB - Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix).
VL - 85
UR - http://arxiv.org/abs/1106.1373v2
CP - 4
J1 - Phys. Rev. A
U5 - 10.1103/PhysRevA.85.040303
ER -
TY - JOUR
T1 - From Ground States to Local Hamiltonians
JF - Physical Review A
Y1 - 2012
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - Bei Zeng
A1 - D. L. Zhou
AB - Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices. A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern, is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have $V$ satisfying the necessary condition mentioned above as its ground-state space, by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles.
VL - 86
UR - http://arxiv.org/abs/1110.6583v4
CP - 2
J1 - Phys. Rev. A
U5 - 10.1103/PhysRevA.86.022339
ER -
TY - JOUR
T1 - Ground-State Spaces of Frustration-Free Hamiltonians
JF - Journal of Mathematical Physics
Y1 - 2012
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - David Kribs
A1 - Zhaohui Wei
A1 - Bei Zeng
AB - We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of `reduced spaces' to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set $\Theta_k$ of all the $k$-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in $\Theta_k$, called atoms, are analogs of extreme points. We study the properties of atoms in $\Theta_k$ and discuss its relationship with ground states of $k$-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in $\Theta_2$ are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in $\Theta_k$ may not be the join of atoms, indicating a richer structure for $\Theta_k$ beyond the convex structure. Our study of $\Theta_k$ deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from a new angle of reduced spaces.
VL - 53
U4 - 102201
UR - http://arxiv.org/abs/1112.0762v1
CP - 10
J1 - J. Math. Phys.
U5 - 10.1063/1.4748527
ER -
TY - JOUR
T1 - Minimum Entangling Power is Close to Its Maximum
Y1 - 2012
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - David W Kribs
A1 - Bei Zeng
AB - Given a quantum gate $U$ acting on a bipartite quantum system, its maximum (average, minimum) entangling power is the maximum (average, minimum) entanglement generation with respect to certain entanglement measure when the inputs are restricted to be product states. In this paper, we mainly focus on the 'weakest' one, i.e., the minimum entangling power, among all these entangling powers. We show that, by choosing von Neumann entropy of reduced density operator or Schmidt rank as entanglement measure, even the 'weakest' entangling power is generically very close to its maximal possible entanglement generation. In other words, maximum, average and minimum entangling powers are generically close. We then study minimum entangling power with respect to other Lipschitiz-continuous entanglement measures and generalize our results to multipartite quantum systems. As a straightforward application, a random quantum gate will almost surely be an intrinsically fault-tolerant entangling device that will always transform every low-entangled state to near-maximally entangled state.
UR - http://arxiv.org/abs/1210.1296v1
ER -
TY - JOUR
T1 - Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt)
Y1 - 2012
A1 - Jianxin Chen
A1 - Andreas Winter
AB - We demonstrate the convexity of the difference between the regularized entanglement of purification and the entropy, as a function of the state. This is proved by means of a new asymptotic protocol to prepare a state from pre-shared entanglement and by local operations only. We go on to employ this convexity property in an investigation of the additivity of the (single-copy) entanglement of purification: using numerical results for two-qubit Werner states we find strong evidence that the entanglement of purification is different from its regularization, hence that entanglement of purification is not additive.
UR - http://arxiv.org/abs/1206.1307v1
ER -
TY - JOUR
T1 - Rank Reduction for the Local Consistency Problem
JF - Journal of Mathematical Physics
Y1 - 2012
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - Alexander Klyachko
A1 - David W. Kribs
A1 - Bei Zeng
AB - We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be compatible. We prove that any compatible local density operators can be satisfied by a low rank global density operator. Then we study both fermionic and bosonic versions of the N-representability problem as applications. After applying the channel-state duality, we prove that any compatible local channels can be obtained through a global quantum channel with small Kraus rank.
VL - 53
U4 - 022202
UR - http://arxiv.org/abs/1106.3235v2
CP - 2
J1 - J. Math. Phys.
U5 - 10.1063/1.3685644
ER -
TY - JOUR
T1 - Entanglement can completely defeat quantum noise
JF - Physical Review Letters
Y1 - 2011
A1 - Jianxin Chen
A1 - Toby S. Cubitt
A1 - Aram W. Harrow
A1 - Graeme Smith
AB - We describe two quantum channels that individually cannot send any information, even classical, without some chance of decoding error. But together a single use of each channel can send quantum information perfectly reliably. This proves that the zero-error classical capacity exhibits superactivation, the extreme form of the superadditivity phenomenon in which entangled inputs allow communication over zero capacity channels. But our result is stronger still, as it even allows zero-error quantum communication when the two channels are combined. Thus our result shows a new remarkable way in which entanglement across two systems can be used to resist noise, in this case perfectly. We also show a new form of superactivation by entanglement shared between sender and receiver.
VL - 107
UR - http://arxiv.org/abs/1109.0540v1
CP - 25
J1 - Phys. Rev. Lett.
U5 - 10.1103/PhysRevLett.107.250504
ER -
TY - JOUR
T1 - No-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems
JF - Physical Review A
Y1 - 2011
A1 - Jianxin Chen
A1 - Xie Chen
A1 - Runyao Duan
A1 - Zhengfeng Ji
A1 - Bei Zeng
AB - One-way quantum computing achieves the full power of quantum computation by performing single particle measurements on some many-body entangled state, known as the resource state. As single particle measurements are relatively easy to implement, the preparation of the resource state becomes a crucial task. An appealing approach is simply to cool a strongly correlated quantum many-body system to its ground state. In addition to requiring the ground state of the system to be universal for one-way quantum computing, we also want the Hamiltonian to have non-degenerate ground state protected by a fixed energy gap, to involve only two-body interactions, and to be frustration-free so that measurements in the course of the computation leave the remaining particles in the ground space. Recently, significant efforts have been made to the search of resource states that appear naturally as ground states in spin lattice systems. The approach is proved to be successful in spin-5/2 and spin-3/2 systems. Yet, it remains an open question whether there could be such a natural resource state in a spin-1/2, i.e., qubit system. Here, we give a negative answer to this question by proving that it is impossible for a genuinely entangled qubit states to be a non-degenerate ground state of any two-body frustration-free Hamiltonian. What is more, we prove that every spin-1/2 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states, a stronger result that is interesting independent of the context of one-way quantum computing.
VL - 83
UR - http://arxiv.org/abs/1004.3787v1
CP - 5
J1 - Phys. Rev. A
U5 - 10.1103/PhysRevA.83.050301
ER -
TY - JOUR
T1 - Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel
JF - IEEE Transactions on Information Theory
Y1 - 2011
A1 - Toby S. Cubitt
A1 - Jianxin Chen
A1 - Aram W. Harrow
AB - The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly, so that they can be decoded with zero probability of error. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the channels are available), but such that access to even a single copy of both channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a quantum channel.
VL - 57
U4 - 8114 - 8126
UR - http://arxiv.org/abs/0906.2547v3
CP - 12
J1 - IEEE Trans. Inform. Theory
U5 - 10.1109/TIT.2011.2169109
ER -
TY - JOUR
T1 - Optimal Perfect Distinguishability between Unitaries and Quantum Operations
Y1 - 2010
A1 - Cheng Lu
A1 - Jianxin Chen
A1 - Runyao Duan
AB - We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula of optimal query time. We extend the sequential condition to general d-dimensional case. Meanwhile, we provide an upper bound and a lower bound for optimal sequential query time. In the process a new iterative method is given, the most notable innovation of which is its independence to auxiliary systems or entanglement. Following the idea, we further obtain an upper bound and a lower bound of (entanglement-assisted) q-maximal fidelities between a unitary and a quantum operation. Thus by the recursion in [1] an upper bound and a lower bound for optimal general perfect discrimination are achieved. Finally our lower bound result can be extended to the case of arbitrary two quantum operations.
UR - http://arxiv.org/abs/1010.2298v1
ER -
TY - JOUR
T1 - Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians
Y1 - 2010
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - Mary Beth Ruskai
A1 - Bei Zeng
A1 - Duanlu Zhou
AB - The structure of the ground spaces of quantum systems consisting of local interactions is of fundamental importance to different areas of physics. In this Letter, we present a necessary and sufficient condition for a subspace to be the ground space of a k-local Hamiltonian. Our analysis are motivated by the concept of irreducible correlations studied by [Linden et al., PRL 89, 277906] and [Zhou, PRL 101, 180505], which is in turn based on the principle of maximum entropy. It establishes a better understanding of the ground spaces of local Hamiltonians and builds an intimate link of ground spaces to the correlations of quantum states.
UR - http://arxiv.org/abs/1010.2739v4
ER -
TY - JOUR
T1 - Ancilla-Assisted Discrimination of Quantum Gates
Y1 - 2008
A1 - Jianxin Chen
A1 - Mingsheng Ying
AB - The intrinsic idea of superdense coding is to find as many gates as possible such that they can be perfectly discriminated. In this paper, we consider a new scheme of discrimination of quantum gates, called ancilla-assisted discrimination, in which a set of quantum gates on a $d-$dimensional system are perfectly discriminated with assistance from an $r-$dimensional ancilla system. The main contribution of the present paper is two-fold: (1) The number of quantum gates that can be discriminated in this scheme is evaluated. We prove that any $rd+1$ quantum gates cannot be perfectly discriminated with assistance from the ancilla, and there exist $rd$ quantum gates which can be perfectly discriminated with assistance from the ancilla. (2) The dimensionality of the minimal ancilla system is estimated. We prove that there exists a constant positive number $c$ such that for any $k\leq cr$ quantum gates, if they are $d$-assisted discriminable, then they are also $r$-assisted discriminable, and there are $c^{\prime}r\textrm{}(c^{\prime}>c)$ different quantum gates which can be discriminated with a $d-$dimensional ancilla, but they cannot be discriminated if the ancilla is reduced to an $r-$dimensional system. Thus, the order $O(r)$ of the number of quantum gates that can be discriminated with assistance from an $r-$dimensional ancilla is optimal. The results reported in this paper represent a preliminary step toward understanding the role ancilla system plays in discrimination of quantum gates as well as the power and limit of superdense coding.
UR - http://arxiv.org/abs/0809.0336v1
ER -
TY - JOUR
T1 - Existence of Universal Entangler
JF - Journal of Mathematical Physics
Y1 - 2008
A1 - Jianxin Chen
A1 - Runyao Duan
A1 - Zhengfeng Ji
A1 - Mingsheng Ying
A1 - Jun Yu
AB - A gate is called entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for generating entanglements, and thus provides important physical resources for accomplishing many tasks in quantum computing and quantum information. This Letter demonstrates that a universal entangler always exists except for a degenerated case. Nevertheless, the problem how to find a universal entangler remains open.
VL - 49
U4 - 012103
UR - http://arxiv.org/abs/0704.1473v2
CP - 1
J1 - J. Math. Phys.
U5 - 10.1063/1.2829895
ER -
TY - JOUR
T1 - The LU-LC conjecture is false
Y1 - 2007
A1 - Zhengfeng Ji
A1 - Jianxin Chen
A1 - Zhaohui Wei
A1 - Mingsheng Ying
AB - The LU-LC conjecture is an important open problem concerning the structure of entanglement of states described in the stabilizer formalism. It states that two local unitary equivalent stabilizer states are also local Clifford equivalent. If this conjecture were true, the local equivalence of stabilizer states would be extremely easy to characterize. Unfortunately, however, based on the recent progress made by Gross and Van den Nest, we find that the conjecture is false.
UR - http://arxiv.org/abs/0709.1266v2
J1 - Quantum Inf. Comput.
ER -