Pure-state transformations and catalysis under operations that completely preserve positivity of partial transpose

Abstract

Motivated by the desire to better understand the class of quantum operations on bipartite systems that preserve positivity of partial transpose (PPT operations) and its relation to the class LOCC (local operations and classical communication), we present some results on deterministic bipartite pure state transformations by PPT operations. Restricting our attention to the case where we start with a rank K maximally entangled state, we give a necessary condition for transforming it into a given pure state, which we show is also sufficient when K is two and the final state has Schmidt rank three. We show that it is sufficient for all K and all final states provided a conjecture about a certain family of semidefinite programs is true. We also demonstrate that the phenomenon of catalysis can occur under PPT operations and that, unlike LOCC catalysis, a maximally entangled state can be a catalyst. Finally, we give a necessary and sufficient condition for the possibility of transforming a rank K maximally entangled state to an arbitrary pure state by PPT operations assisted by some maximally entangled catalyst.

12 pages, 2 figures. v2: Journal version; Typos fixed

References in corpus (9)

• Conditions for a class of entanglement transformations
• Entanglement-assisted local manipulation of pure quantum states
• The entanglement cost under operations preserving the positivity of partial transpose
• Irreversibility in asymptotic manipulations of entanglement
• Bound entanglement provides convertibility of pure entangled states
• Deterministic entanglement concentration
• Multi-particle entanglement manipulation under positive partial transpose preserving operations
• Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation
• Entanglement transformations using separable operations

Cited by in corpus (19)

• Quantum Resource Theories
• Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States
• Distinguishability of Quantum States by Positive Operator-Valued Measures with Positive Partial Transpose
• Cost of quantum entanglement simplified
• Non-asymptotic entanglement distillation
• Improved Semidefinite Programming Upper Bound on Distillable Entanglement
• Practical distributed quantum information processing with LOCCNet
• Dephasing-Covariant Operations Enable Asymptotic Reversibility of Quantum Resources
• One-shot entanglement distillation beyond local operations and classical communication
• Nonadditivity of Rains' bound for distillable entanglement
• $\alpha$-Logarithmic negativity
• Indistinguishability of bipartite states by positive-partial-transpose operations in the many-copy scenario
• Exact entanglement cost of quantum states and channels under PPT-preserving operations
• Catalytic and asymptotic equivalence for quantum entanglement
• Computable entanglement conversion witness that is better than the negativity
• The Zero-error Entanglement Cost is Highly Non-Additive
• Quantum Machine Learning for Distributed Quantum Protocols with Local Operations and Noisy Classical Communications
• Choi-Defined Resource Theories
• The entangling power of non-entangling channels