Tight bounds on the distinguishability of quantum states under separable measurements

Abstract

One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this work, we characterize the distinguishability of sets of multipartite quantum states when restricted to separable measurements -- those which contain the class of local measurements but nevertheless are free of entanglement between the component systems. We consider two quantities: The separable fidelity -- a truly quantum quantity -- which measures how well we can "clone" the input state, and the classical probability of success, which simply gives the optimal probability of identifying the state correctly. We obtain lower and upper bounds on the separable fidelity and give several examples in the bipartite and multipartite settings where these bounds are optimal. Moreover the optimal values in these cases can be attained by local measurements. We further show that for distinguishing orthogonal states under separable measurements, a strategy that maximizes the probability of success is also optimal for separable fidelity. We point out that the equality of fidelity and success probability does not depend on an using optimal strategy, only on the orthogonality of the states. To illustrate this, we present an example where two sets (one consisting of orthogonal states, and the other non-orthogonal states) are shown to have the same separable fidelity even though the success probabilities are different.

19 pages; published version

References in corpus (5)

• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Distinguishability of Quantum States by Separable Operations
• PPT-indistinguishable states via semidefinite programming
• Local discrimination of mixed states
• Distinguishability of Quantum States by Positive Operator-Valued Measures with Positive Partial Transpose

Cited by in corpus (21)

• Strong Quantum Nonlocality without Entanglement
• Operational relevance of resource theories of quantum measurements
• Limitations on separable measurements by convex optimization
• Three maximally entangled states can require two-way LOCC for local discrimination
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• Optimal resource states for local state discrimination
• Twist-teleportation based local discrimination of maximally entangled states
• Genuine activation of nonlocality: From locally available to locally hidden information
• Genuine hidden nonlocality without entanglement: from the perspective of local discrimination
• Entanglement cost of discriminating noisy Bell states by local operations and classical communication
• Operator Structures and Quantum One-Way LOCC Conditions
• Local discrimination of generalized Bell states via commutativity
• Bipartite discrimination of independently prepared quantum states as a counterexample to a parallel repetition conjecture
• Single-shot Distinguishability and Anti-distinguishability of Quantum Measurements
• Limitation of maximally entangled probes for single-shot distinguishability of unitaries
• Non-projective Bell state measurements
• Locally distinguishing a maximally entangled basis using shared entanglement
• Small sets of locally indistinguishable orthogonal maximally entangled states
• Conclusive Local State Marking: More Nonlocality With No Entanglement
• Conditions for local transformations between sets of quantum states
• Application of Ramsey theory to localization of set of product states via multicopies