



01598nas a2200241   4500008004100000245005800041210005800099260001500157300001100172490000800183520093100191100001301122700001401135700001801149700001601167700001801183700001801201700001301219700001601232700001401248700002201262856007201284       2017                        eng d00aQuantum state tomography via reduced density matrices0 aQuantum state tomography via reduced density matrices  c2017/01/09  a0204010 v1183 a<p>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.</p>1 aXin, Tao1 aLu, Dawei1 aKlassen, Joel1 aYu, Nengkun1 aJi, Zhengfeng1 aChen, Jianxin1 aMa, Xian1 aLong, Guilu1 aZeng, Bei1 aLaflamme, Raymond  uhttp://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.02040101164nas a2200169   4500008004100000245007500041210006900116260001500185300001100200490000700211520067400218100001800892700001800910700001600928700001400944856003600958       2016                        eng d00aDetecting Consistency of Overlapping Quantum Marginals by Separability0 aDetecting Consistency of Overlapping Quantum Marginals by Separa  c2016/03/03  a0321050 v933 a  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.
1 aChen, Jianxin1 aJi, Zhengfeng1 aYu, Nengkun1 aZeng, Bei  uhttp://arxiv.org/abs/1509.0659101692nas a2200181   4500008004100000245007500041210006900116260001500185520116000200100001801360700001501378700001801393700001901411700001601430700001401446700001401460856003601474       2016                        eng d00aJoint product numerical range and geometry of reduced density matrices0 aJoint product numerical range and geometry of reduced density ma  c2016/06/233 aThe 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.1 aChen, Jianxin1 aGuo, Cheng1 aJi, Zhengfeng1 aPoon, Yiu-Tung1 aYu, Nengkun1 aZeng, Bei1 aZhou, Jie  uhttp://arxiv.org/abs/1606.0742201933nas a2200277   4500008004100000245007200041210006900113260001500182300001100197490000700208520116900215100001301384700001901397700001401416700001801430700001401448700002501462700002301487700001701510700001701527700002101544700001801565700001401583700002201597856003601619       2016                        eng d00aPure-state tomography with the expectation value of Pauli operators0 aPurestate tomography with the expectation value of Pauli operato  c2016/03/31  a0321400 v933 a<p>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.</p>1 aMa, Xian1 aJackson, Tyler1 aZhou, Hui1 aChen, Jianxin1 aLu, Dawei1 aMazurek, Michael, D.1 aFisher, Kent, A.G.1 aPeng, Xinhua1 aKribs, David1 aResch, Kevin, J.1 aJi, Zhengfeng1 aZeng, Bei1 aLaflamme, Raymond  uhttp://arxiv.org/abs/1601.0537901747nas a2200241   4500008004100000245009400041210006900135260001500204300001100219490000800230520106300238100001401301700001301315700001601328700001801344700001801362700001601380700002001396700001701416700001401433700002201447856003601469       2016                        eng d00aTomography is necessary for universal entanglement detection with single-copy observables0 aTomography is necessary for universal entanglement detection wit  c2016/06/07  a2305010 v1163 aEntanglement, 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.1 aLu, Dawei1 aXin, Tao1 aYu, Nengkun1 aJi, Zhengfeng1 aChen, Jianxin1 aLong, Guilu1 aBaugh, Jonathan1 aPeng, Xinhua1 aZeng, Bei1 aLaflamme, Raymond  uhttp://arxiv.org/abs/1511.0058101250nas a2200217   4500008004100000245007700041210006900118260001500187300001100202490000700213520064200220100001800862700001800880700001800898700001900916700001300935700001600948700001400964700001700978856003700995       2015                        eng d00aDiscontinuity of Maximum Entropy Inference and Quantum Phase Transitions0 aDiscontinuity of Maximum Entropy Inference and Quantum Phase Tra  c2015/08/10  a0830190 v173 a  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.
1 aChen, Jianxin1 aJi, Zhengfeng1 aLi, Chi-Kwong1 aPoon, Yiu-Tung1 aShen, Yi1 aYu, Nengkun1 aZeng, Bei1 aZhou, Duanlu  uhttp://arxiv.org/abs/1406.5046v201602nas a2200169   4500008004100000245007000041210006900111260001500180300001400195490000800209520110500217100001401322700001801336700002701354700001401381856003701395       2015                        eng d00aUniversal Subspaces for Local Unitary Groups of Fermionic Systems0 aUniversal Subspaces for Local Unitary Groups of Fermionic System  c2014/10/10  a541 - 5630 v3333 a  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
$i_1<...<i_N$ form an o.n. basis of $\cV$. Let $\cS\subseteq\cV$ be the
subspace spanned by all $e_{i_1,...,i_N}$ such that the set $\{i_1,...,i_N\}$
contains no pair $\{2k-1,2k\}$, $k$ an integer. We say that the
$\ket{\psi}\in\cS$ are single occupancy states (with respect to the basis
$\ket{v_1},...,\ket{v_M}$). We prove that for N=3 the subspace $\cS$ is
universal, i.e., each $G$-orbit in $\cV$ meets $\cS$, and that this is false
for N>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.
1 aChen, Lin1 aChen, Jianxin1 aDjokovic, Dragomir, Z.1 aZeng, Bei  uhttp://arxiv.org/abs/1301.3421v201596nas a2200169   4500008004100000245004400041210004300085260001400128490000700142520114800149100001801297700001801315700001701333700002501350700001401375856003701389       2014                        eng d00aSymmetric Extension of Two-Qubit States0 aSymmetric Extension of TwoQubit States  c2014/9/170 v903 a  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.
1 aChen, Jianxin1 aJi, Zhengfeng1 aKribs, David1 aLütkenhaus, Norbert1 aZeng, Bei  uhttp://arxiv.org/abs/1310.3530v201286nas a2200157   4500008004100000245005300041210005300094260001500147300001100162490000700173520086500180100001801045700001401063700001401077856003701091       2014                        eng d00aUnextendible Product Basis for Fermionic Systems0 aUnextendible Product Basis for Fermionic Systems  c2014/01/01  a0822070 v553 a  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.
1 aChen, Jianxin1 aChen, Lin1 aZeng, Bei  uhttp://arxiv.org/abs/1312.4218v101999nas a2200193   4500008004100000245005200041210005200093260001500145300001200160490000700172520148600179100001801665700001801683700001901701700001801720700001601738700001401754856003701768       2013                        eng d00aSymmetries of Codeword Stabilized Quantum Codes0 aSymmetries of Codeword Stabilized Quantum Codes  c2013/03/28  a192-2060 v223 a  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.
1 aBeigi, Salman1 aChen, Jianxin1 aGrassl, Markus1 aJi, Zhengfeng1 aWang, Qiang1 aZeng, Bei  uhttp://arxiv.org/abs/1303.7020v202008nas a2200193   4500008004100000245007500041210006900116260001400185490000700199520143800206100001801644700002101662700001801683700002401701700001701725700002101742700001401763856003701777       2013                        eng d00aUniqueness of Quantum States Compatible with Given Measurement Results0 aUniqueness of Quantum States Compatible with Given Measurement R  c2013/7/110 v883 a  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.
1 aChen, Jianxin1 aDawkins, Hillary1 aJi, Zhengfeng1 aJohnston, Nathaniel1 aKribs, David1 aShultz, Frederic1 aZeng, Bei  uhttp://arxiv.org/abs/1212.3503v202285nas a2200133   4500008004100000245005900041210005900100260001500159520189000174100001802064700001802082700001402100856003702114       2013                        eng d00aUniversal Entanglers for Bosonic and Fermionic Systems0 aUniversal Entanglers for Bosonic and Fermionic Systems  c2013/05/313 a  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.
1 aKlassen, Joel1 aChen, Jianxin1 aZeng, Bei  uhttp://arxiv.org/abs/1305.7489v101351nas a2200181   4500008004100000245009200041210006900133260001500202300001100217490000700228520080600235100001801041700001801059700002301077700001401100700001801114856003701132       2012                        eng d00aComment on some results of Erdahl and the convex structure of reduced  density matrices0 aComment on some results of Erdahl and the convex structure of re  c2012/05/16  a0722030 v533 a  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.
1 aChen, Jianxin1 aJi, Zhengfeng1 aRuskai, Mary, Beth1 aZeng, Bei1 aZhou, Duan-Lu  uhttp://arxiv.org/abs/1205.3682v101936nas a2200157   4500008004100000245005700041210005700098260001300155490000700168520149900175100001801674700001801692700001701710700001401727856003701741       2012                        eng d00aCorrelations in excited states of local Hamiltonians0 aCorrelations in excited states of local Hamiltonians  c2012/4/90 v853 a  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).
1 aChen, Jianxin1 aJi, Zhengfeng1 aWei, Zhaohui1 aZeng, Bei  uhttp://arxiv.org/abs/1106.1373v201702nas a2200157   4500008004100000245004500041210004500086260001400131490000700145520128800152100001801440700001801458700001401476700001701490856003701507       2012                        eng d00aFrom Ground States to Local Hamiltonians0 aFrom Ground States to Local Hamiltonians  c2012/8/300 v863 a  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.
1 aChen, Jianxin1 aJi, Zhengfeng1 aZeng, Bei1 aZhou, D., L.  uhttp://arxiv.org/abs/1110.6583v401607nas a2200181   4500008004100000245005700041210005500098260001500153300001100168490000700179520111800186100001801304700001801322700001701340700001701357700001401374856003701388       2012                        eng d00aGround-State Spaces of Frustration-Free Hamiltonians0 aGroundState Spaces of FrustrationFree Hamiltonians  c2012/01/01  a1022010 v533 a  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.
1 aChen, Jianxin1 aJi, Zhengfeng1 aKribs, David1 aWei, Zhaohui1 aZeng, Bei  uhttp://arxiv.org/abs/1112.0762v101508nas a2200145   4500008004100000245005300041210005300094260001500147520109300162100001801255700001801273700002001291700001401311856003701325       2012                        eng d00aMinimum Entangling Power is Close to Its Maximum0 aMinimum Entangling Power is Close to Its Maximum  c2012/10/043 a  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.
1 aChen, Jianxin1 aJi, Zhengfeng1 aKribs, David, W1 aZeng, Bei  uhttp://arxiv.org/abs/1210.1296v101124nas a2200181   4500008004100000245005300041210005300094260001500147300001100162490000700173520063000180100001800810700001800828700002400846700002100870700001400891856003700905       2012                        eng d00aRank Reduction for the Local Consistency Problem0 aRank Reduction for the Local Consistency Problem  c2012/02/09  a0222020 v533 a  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.
1 aChen, Jianxin1 aJi, Zhengfeng1 aKlyachko, Alexander1 aKribs, David, W.1 aZeng, Bei  uhttp://arxiv.org/abs/1106.3235v202114nas a2200169   4500008004100000245009200041210006900133260001300202490000700215520160400222100001801826700001401844700001701858700001801875700001401893856003701907       2011                        eng d00aNo-go Theorem for One-way Quantum Computing on Naturally Occurring  Two-level Systems
0 aNogo Theorem for Oneway Quantum Computing on Naturally Occurring  c2011/5/90 v833 a  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.
1 aChen, Jianxin1 aChen, Xie1 aDuan, Runyao1 aJi, Zhengfeng1 aZeng, Bei  uhttp://arxiv.org/abs/1004.3787v101132nas a2200157   4500008004100000245007300041210006900114260001500183520064900198100001800847700001800865700002300883700001400906700001700920856003700937       2010                        eng d00aPrinciple of Maximum Entropy and Ground Spaces of Local Hamiltonians0 aPrinciple of Maximum Entropy and Ground Spaces of Local Hamilton  c2010/10/133 a  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.
1 aChen, Jianxin1 aJi, Zhengfeng1 aRuskai, Mary, Beth1 aZeng, Bei1 aZhou, Duanlu  uhttp://arxiv.org/abs/1010.2739v4