Bipartite Subspaces Having No Bases Distinguishable by Local Operations and Classical Communication

Watrous, John

doi:10.1103/physrevlett.95.080505

Cited by 112 publications

(75 citation statements)

References 13 publications

(21 reference statements)

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“…Thus it follows from Theorem 1 that any basis for S is unambiguously distinguishable by LOCC. Interestingly, recently Watrous found another kind of special bipartite subspace having no basis exactly distinguishable by LOCC [14].…”

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confidence: 99%

Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication

Duan

Feng

et al. 2007

Phys. Rev. Lett.

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We show that an arbitrary basis of a multipartite quantum state space consisting of K distant parties such that the kth party has local dimension d k always contains at least N = P K k=1 (d k −1)+1 members that are unambiguously distinguishable using local operations and classical communication (LOCC). We further show this lower bound is optimal by analytically constructing a special product basis having only N members unambiguously distinguishable by LOCC. Interestingly, such a special product basis not only gives a stronger form of the weird phenomenon "nonlocality without entanglement", but also implies the existence of locally distinguishable entangled basis.

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confidence: 99%

Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication

Duan

Feng

et al. 2007

Phys. Rev. Lett.

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“…Local distinguishability of a finite set of orthogonal multipartite states has become an increasingly interesting topic in quantum information partly due to its important applications in classical data hiding [1] and quantum channel capacity [2][3][4][5]. It is well known that orthogonal quantum states can always be perfectly distinguished if there are no restrictions on the measurements one can perform on the system.…”

Section: Introductionmentioning

confidence: 99%

“…In 2005 Watrous demonstrated that there exists a class of m ⊗ m subspaces having no orthonormal bases locally distinguishable if m > 2 [4]. Such subspaces are said to be locally indistinguishable; otherwise, they are said to be locally distinguishable.…”

Section: Introductionmentioning

confidence: 99%

Any2⊗nsubspace is locally distinguishable

Duan

Ying

2011

Phys. Rev. A

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A subspace of a multipartite Hilbert space is said to be locally indistinguishable if any orthonormal basis of this subspace cannot be perfectly distinguished by local operations and classical communication. Previously it was shown that any m ⊗ n bipartite system with m > 2 and n > 2 has a locally indistinguishable subspace. However, it has been an open problem since 2005 whether there is a locally indistinguishable bipartite subspace with a qubit subsystem. We settle this problem in negative by showing that any 2 ⊗ n bipartite subspace contains a basis that is locally distinguishable. As an interesting application, we show that any quantum channel with two Kraus operators has optimal environment-assisted classical capacity.

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“…The effect of restrictions on the measurement on the ability to discriminate-either ambiguously or unambiguously-between quantum states has also recently attracted much attention. In particular, the limits of LOCC discrimination have been investigated in [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], for instance. Such limits are at the base of the existence of hiding states [34][35][36][37], which are orthogonal and therefore perfectly distinguishable by global operations, but hardly distinguishable by LOCC measurements.…”

Section: Introductionmentioning

confidence: 99%

Entanglement in channel discrimination with restricted measurements

2010

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We study the power of measurements implementable with local quantum operations and classical communication (or LOCC measurements for short) in the setting of quantum channel discrimination. More precisely, we consider discrimination procedures that attempt to identify an unknown channel, chosen uniformly from two known alternatives, that take the following form: (i) the input to the unknown channel is prepared in a possibly entangled state with an ancillary system, (ii) the unknown channel is applied to the input system, and (iii) an LOCC measurement is performed on the output and ancillary systems, resulting in a guess for which of the two channels was given. The restriction of the measurement in such a procedure to be an LOCC measurement is of interest because it isolates the entanglement in the initial input/ancillary systems as a resource in the setting of channel discrimination. We prove that there exist channel discrimination problems for which restricted procedures of this sort can be at either of the two extremes: they may be optimal within the set of all discrimination procedures (and simultaneously outperform all strategies that make no use of entanglement), or they may be no better than unentangled strategies (and simultaneously sub-optimal within the set of all discrimination procedures).Comment: 17 pages, 4 figure

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Bipartite Subspaces Having No Bases Distinguishable by Local Operations and Classical Communication

Cited by 112 publications

References 13 publications

Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication

Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication

Any2⊗nsubspace is locally distinguishable

Entanglement in channel discrimination with restricted measurements

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