Entanglement transformations using separable operations

Abstract

We study conditions for the deterministic transformation $|\psi ⟩⟶|\varphi ⟩$ of a bipartite entangled state by a separable operation. If the separable operation is a local operation with classical communication (LOCC), Nielsen's majorization theorem provides necessary and sufficient conditions. For the general case we derive a necessary condition in terms of products of Schmidt coefficients, which is equivalent to the Nielsen condition when either of the two factor spaces is of dimension 2, but is otherwise weaker. One implication is that no separable operation can reverse a deterministic map produced by another separable operation, if one excludes the case where the Schmidt coefficients of $|\psi ⟩$ and are the same as those of $|\varphi ⟩$. The question of sufficient conditions in the general separable case remains open. When the Schmidt coefficients of $|\psi ⟩$ are the same as those of $|\varphi ⟩$, we show that the Kraus operators of the separable transformation restricted to the supports of $|\psi ⟩$ on the factor spaces are proportional to unitaries. When that proportionality holds and the factor spaces have equal dimension, we find conditions for the deterministic transformation of a collection of several full Schmidt rank pure states $|{\psi }_j⟩$ to pure states $|{\varphi }_j⟩$.

Replaced with the published version. Any comments are welcome

References in corpus (7)

• Quantum Nonlocality without Entanglement
• Conditions for a class of entanglement transformations
• Local copying and local discrimination as a study for non-locality of a set
• Atemporal diagrams for quantum circuits
• Local copying of orthogonal entangled quantum states
• Local cloning of Bell states and distillable entanglement
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Cited by in corpus (11)

• Distinguishability of Quantum States by Separable Operations
• Separable Operations on Pure States
• Pure-state transformations and catalysis under operations that completely preserve positivity of partial transpose
• Local cloning of entangled states
• Censorship of Quantum Resources in Quantum Networks
• Computable entanglement conversion witness that is better than the negativity
• Operational symmetries of entangled states
• Extended necessary condition for local operations and classical communication: Tight bound for all measurements
• Entanglement concentration via measurement:- role of imaginarity
• The entangling power of non-entangling channels
• Separable Operations, Graph Codes and the Location of Quantum Information