Entanglement Cost of Nonlocal Measurements

Abstract

For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled eigenstates, we present upper and lower bounds on the entanglement cost. The upper bound is based on a recent result by D. Berry [Phys. Rev. A 75, 032349 (2007)]. The lower bound, based on the entanglement production capacity of the measurement, implies that for almost all measurements in the class we consider, the entanglement required to perform the measurement is strictly greater than the average entanglement of its eigenstates. On the other hand, we show that for any complete measurement in d x d dimensions that is invariant under all local Pauli operations, the cost of the measurement is exactly equal to the average entanglement of the states associated with the outcomes.

14 pages; new result in v4: cost of an arbitrary measurement invariant under local Pauli operations

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• Entanglement cost of two-qubit orthogonal measurements
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• Locally distinguish unextendible product bases by efficiently using entanglement resource
• Measurements of nonlocal variables and demonstration of the failure of the product rule for a pre- and postselected pair of photons
• Practical measurement-device-independent entanglement quantification
• Locally distinguishing quantum states with limited classical communication
• Optimizing local protocols implementing nonlocal quantum gates
• Nonlocality without entanglement: Party asymmetric case
• Distillation of free entanglement from bound entangled states using weak measurements
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• Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis
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• Distributed Encoding and Decoding of Quantum Information over Networks
• Classifying locally distinguishable sets: No activation across bipartitions
• Exploration of nonlocalities in ensembles consisting of bipartite quantum states
• Locally distinguishing a maximally entangled basis using shared entanglement
• Quantum Coherence and Distinguishability as Complementary Resources: A Resource-Theoretic Perspective from Wave-Particle Duality
• Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
• Non-locality of conjugation symmetry: characterization and examples in quantum network sensing
• Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States
• Discrimination of Quantum States under Local Operations and Classical Communication