LOCC distinguishability of unilaterally transformable quantum states

Abstract

We consider the question of perfect local distinguishability of mutually orthogonal bipartite quantum states, with the property that every state can be specified by a unitary operator acting on the local Hilbert space of Bob. We show that if the states can be exactly discriminated by one-way LOCC where Alice goes first, then the unitary operators can also be perfectly distinguished by an orthogonal measurement on Bob's Hilbert space. We give examples of sets of N<=d maximally entangled states in $d\otimes d$ for d=4,5,6 that are not perfectly distinguishable by one-way LOCC. Interestingly for d=5,6 our examples consist of four and five states respectively. We conjecture that these states cannot be perfectly discriminated by two-way LOCC.

Revised version, new proofs added; to appear in New Journal of Physics

References in corpus (3)

• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Distinguishability of Quantum States by Separable Operations
• Local distinguishability with preservation of entanglement

Cited by in corpus (45)

• Strong Quantum Nonlocality without Entanglement
• Quantum secret sharing based on local distinguishability
• Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States
• Nonlocality of orthogonal product basis quantum states
• Local indistinguishability of orthogonal product states
• PPT-indistinguishable states via semidefinite programming
• Limitations on separable measurements by convex optimization
• Distinguishability of Quantum States by Positive Operator-Valued Measures with Positive Partial Transpose
• Three maximally entangled states can require two-way LOCC for local discrimination
• Entanglement as a resource for local state discrimination in multipartite systems
• Strong quantum nonlocality with entanglement
• Strongly nonlocal unextendible product bases do exist
• Optimal resource states for local state discrimination
• Strong quantum nonlocality in $N$-partite systems
• $d$ locally indistinguishable maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Local distinguishability based genuinely quantum nonlocality without entanglement
• Tight bounds on the distinguishability of quantum states under separable measurements
• The local distinguishability of any three generalized Bell states
• Bounds on the smallest sets of quantum states with special quantum nonlocality
• On small set of one-way LOCC indistinguishability of maximally entangled states
• Indistinguishability of bipartite states by positive-partial-transpose operations in the many-copy scenario
• Genuine activation of nonlocality: From locally available to locally hidden information
• Twist-teleportation based local discrimination of maximally entangled states
• Genuine hidden nonlocality without entanglement: from the perspective of local discrimination
• Alternative method for deriving nonlocal multipartite product states
• Entanglement cost of discriminating noisy Bell states by local operations and classical communication
• Measurement-based universal blind quantum computation with minor resources
• Local discrimination of generalized Bell states via commutativity
• Small set of orthogonal product states with nonlocality
• Local Quantum State Marking
• Genuine Activation of Quantum Nonlocality: Stronger Than Local Indistinguishability
• Positive-partial-transpose distinguishability for lattice-type maximally entangled states
• Finding out all locally indistinguishable sets of generalized Bell states
• LOCC protocols with bounded width per round optimize convex functions
• Generalized bipartite quantum state discrimination problems with sequential measurements
• Detectors for local discrimination of sets of generalized Bell states
• Strongest quantum nonlocality in $N$-partite systems
• Locally distinguishing a maximally entangled basis using shared entanglement
• Local unitary classification of sets of generalized Bell states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$
• Conclusive Local State Marking: More Nonlocality With No Entanglement
• Application of Ramsey theory to localization of set of product states via multicopies
• Conditions for local transformations between sets of quantum states
• Global versus Local Discrimination of Locally Implementable Multipartite Unitaries
• Graph connectivity based strong quantum nonlocality with genuine entanglement