No-go theorem for entanglement distillation using catalysis

Abstract

The use of ancillary quantum systems known as catalysts is known to be able to enhance the capabilities of entanglement transformations under local operations and classical communication. However, the limits of these advantages have not been determined, and in particular it is not known if such assistance can overcome the known restrictions on asymptotic transformation rates -- notably the existence of bound entangled (undistillable) states. Here we establish a general limitation of entanglement catalysis: we show that catalytic transformations can never allow for the distillation of entanglement from a bound entangled state with positive partial transpose, even if the catalyst may become correlated with the system of interest, and even under permissive choices of free operations. This precludes the possibility that catalysis can make entanglement theory asymptotically reversible. Our methods are based on new asymptotic bounds for the distillable entanglement and entanglement cost assisted by correlated catalysts.

7+20 pages. v3: accepted version, title changed. Original title: "Catalysis cannot overcome bound entanglement"

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Cited by in corpus (9)

• No-Go Theorems for Universal Entanglement Purification
• Distillable entanglement under dually non-entangling operations
• Catalytic and asymptotic equivalence for quantum entanglement
• Complete Characterization of Entanglement Embezzlement
• Second Law of Entanglement Manipulation with Entanglement Battery
• Bipartite Bound Entanglement
• Multipartite entanglement theory with entanglement-nonincreasing operations
• The coherent measurement cost of coherence distillation
• Unveiling NPT bound problem: From Distillability Sets to Inequalities and Multivariable Insights