Separable Operations on Pure States

Abstract

We show that the possible ensembles produced when a separable operation acts on a single pure bipartite entangled state are completely characterized by a majorization condition, a collection of inequalities for Schmidt coefficients, which is identical to that already known for the particular case of local operations and classical communication (LOCC). As a consequence, various known results for LOCC, including some involving monotonicity of entanglement, can be extended to the class of all separable operations.

Typo corrected in the abstract

References in corpus (6)

• Quantum Nonlocality without Entanglement
• Conditions for a class of entanglement transformations
• Entanglement of pure states for a single copy
• Minimal conditions for local pure-state entanglement manipulation
• Atemporal diagrams for quantum circuits
• Entanglement transformations using separable operations

Cited by in corpus (28)

• Open-System Dynamics of Entanglement
• Nonlocality of orthogonal product basis quantum states
• Local indistinguishability of orthogonal product states
• Transformations among Pure Multipartite Entangled States via Local Operations Are Almost Never Possible
• Entangled pure state transformations via local operations assisted by finitely many rounds of classical communication
• Entanglement manipulation of multipartite pure states with finite rounds of classical communication
• Necessary and sufficient conditions for local manipulation of multipartite pure quantum states
• Efficient implementation of bipartite nonlocal unitary gates using prior entanglement and classical communication
• Noisy entanglement evolution for graph states
• Nonlocal Entanglement Transformations Achievable by Separable Operations
• Entanglement requirements for implementing bipartite unitary operations
• Equivalence of qubit-environment entanglement and discord generation via pure dephasing interactions and the consequences thereof
• When a quantum measurement can be implemented locally ... and when it cannot
• Norms and Cones in the Theory of Quantum Entanglement
• Local cloning of entangled states
• Entanglement monotones and transformations of symmetric bipartite states
• Measurement outcomes that do not occur and their role in entanglement transformations
• Bounds On Entanglement Catalysts
• Local quantum protocols for separable measurements with many parties
• Deterministic transformations of three-qubit entangled pure states
• Entanglement cost for infinite-dimensional physical systems
• Entanglement transformation between sets of bipartite pure quantum states using local operations
• Comment on "Entanglement transformation between two-qubit mixed states by LOCC" [Phys. Lett. A 373 (2009) 3610]
• Conditions for degradability of tripartite quantum states
• Nonexistence of maximally entangled mixed states for a fixed spectrum
• Separable Operations, Graph Codes and the Location of Quantum Information
• Insufficiency of Pure-State Ensembles in Characterizing Transformations of Entangled States under LOCC
• Entanglement concentration via measurement:- role of imaginarity