



01933nas 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/1601.0537901596nas 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/1310.3530v202008nas 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/1212.3503v201607nas 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/1112.0762v1