Bipartite subspaces having no LOCC-distinguishable bases

Abstract

It is proved that there exist subspaces of bipartite tensor product spaces that have no orthonormal bases that can be perfectly distinguished by means of LOCC protocols. A corollary of this fact is that there exist quantum channels having sub-optimal classical capacity even when the receiver may communicate classically with a third party that represents the channel's environment.

12 pages. Two references added in version 2

References in corpus (6)

• Distinguishability and indistinguishability by LOCC
• Local indistinguishability: more nonlocality with less entanglement
• Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
• On quantum error-correction by classical feedback in discrete time
• On environment-assisted capacities of quantum channels
• Correcting quantum channels by measuring the environment

Cited by in corpus (79)

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• Local indistinguishability of orthogonal product states
• LOCC distinguishability of unilaterally transformable quantum states
• Limitations on separable measurements by convex optimization
• Distinguishability of Quantum States by Positive Operator-Valued Measures with Positive Partial Transpose
• Genuinely Nonlocal Product Bases: Classification and Entanglement Assisted Discrimination
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• Entanglement as a resource for local state discrimination in multipartite systems
• Any $2\otimes n$ subspace is locally distinguishable
• When do Local Operations and Classical Communication Suffice for Two-Qubit State Discrimination?
• Entanglement Cost of Nonlocal Measurements
• Asymptotically perfect discrimination in the LOCC paradigm
• Nonlocal Entanglement Transformations Achievable by Separable Operations
• Optimal resource states for local state discrimination
• Local distinguishability of orthogonal 2\otimes3 pure states
• Entanglement, mixedness and perfect local discrimination of orthogonal quantum states
• Multiparty orthogonal product states with minimal genuine nonlocality
• Entanglement in channel discrimination with restricted measurements
• $d$ locally indistinguishable maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$
• Local Distinguishability of Orthogonal Quantum States and Generators of SU(N)
• Distinguishability classes, resource sharing, and bound entanglement distribution
• Multi-copy adaptive local discrimination: Strongest possible two-qubit nonlocal bases
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• Tight bounds on the distinguishability of quantum states under separable measurements
• On the Chernoff distance for asymptotic LOCC discrimination of bipartite quantum states
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• Genuine activation of nonlocality: From locally available to locally hidden information
• Nonlocality of tripartite orthogonal product states
• Genuine hidden nonlocality without entanglement: from the perspective of local discrimination
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• Asymptotic local hypothesis testing between a pure bipartite state and the completely mixed state
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Nonlocality without entanglement: Party asymmetric case
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
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• Separability and entanglement in superpositions of quantum states
• Local hypothesis testing between a pure bipartite state and the white noise state
• When asymptotic LOCC offers no advantage over finite LOCC
• Unextendible entangled bases and more nonlocality with less entanglement
• Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis
• Entangled state distillation from single copy mixed states beyond LOCC
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• Incompatibility of local measurements provide advantage in local quantum state discrimination
• Quantum Error Correction and One-Way LOCC State Distinguishability
• More assistance of entanglement, less rounds of classical communication
• Local distinguishability of quantum states in multipartite System
• Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination
• Locally unidentifiable subset of quantum states and its resourcefulness in secret password distribution
• LOCC protocols with bounded width per round optimize convex functions
• Exploring strong locality : Quantum state discrimination regime and beyond
• When is the Chernoff Exponent for Quantum Operations finite?
• Information locking and its resource efficient extraction
• Local cloning of genuine entangled states of three qubit
• Classifying locally distinguishable sets: No activation across bipartitions
• Locally distinguishing a maximally entangled basis using shared entanglement
• Exploration of nonlocalities in ensembles consisting of bipartite quantum states
• Any four orthogonal ququad-ququad maximally entangled states are locally markable
• Multi-partite subspaces containing no locally inaccessible information
• Reliably distinguishing states in qutrit channels using one-way LOCC
• Small sets of locally indistinguishable orthogonal maximally entangled states
• The existence of distinguishable bases in three-dimensional subspaces of qutrit-qudit systems under one-way local operations and classical communication
• Quantum change point and entanglement distillation
• Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
• Single-shot antidistinguishability of unitary operations
• Global versus Local Discrimination of Locally Implementable Multipartite Unitaries
• Conclusive Local State Marking: More Nonlocality With No Entanglement
• Strong quantum nonlocality for multipartite entangled states
• Conditions for local transformations between sets of quantum states
• Entanglement - A Queer In The World Of Quantum : Some Perspectives