Catalytic and asymptotic equivalence for quantum entanglement

Abstract

Entanglement is a fundamental resource in quantum information processing, yet understanding its manipulation and transformation remains a challenge. Many tasks rely on highly entangled pure states, but obtaining such states is often challenging due to the presence of noise. Typically, entanglement manipulation procedures involving asymptotically many copies of a state are considered to overcome this problem. These procedures allow for distilling highly entangled pure states from noisy states, which enables a wide range of applications, such as quantum teleportation and quantum cryptography. When it comes to manipulating entangled quantum systems on a single copy level, using entangled states as catalysts can significantly broaden the range of achievable transformations. Similar to the concept of catalysis in chemistry, the entangled catalyst is returned unchanged at the end of the state manipulation procedure. Our results demonstrate that despite the apparent conceptual differences between the asymptotic and catalytic settings, they are actually strongly connected and fully equivalent for all distillable states. Our methods rely on the analysis of many-copy entanglement manipulation procedures which may establish correlations between different copies. As an important consequence, we demonstrate that using an entangled catalyst cannot enhance the asymptotic singlet distillation rate of a distillable quantum state. Our findings provide a comprehensive understanding of the capabilities and limitations of both catalytic and asymptotic state transformations of entangled states, and highlight the importance of correlations in these processes.

16 pages, 2 figures, close to published version

References in corpus (48)

• Quantum entanglement
• Mixed State Entanglement and Quantum Error Correction
• Quantum secret sharing
• Concentrating Partial Entanglement by Local Operations
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Entanglement detection
• How to share a quantum secret
• Quantum Resource Theories
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Distillation of secret key and entanglement from quantum states
• The second laws of quantum thermodynamics
• Quantum information can be negative
• "Squashed Entanglement" - An Additive Entanglement Measure
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Bound entanglement can be activated
• Entanglement-assisted local manipulation of pure quantum states
• An improved bound on distillable entanglement
• Continuity of quantum conditional information
• Evidence for Bound Entangled States with Negative Partial Transpose
• A rigorous treatment of distillable entanglement
• Entanglement Theory and the Second Law of Thermodynamics
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• Entanglement of assistance and multipartite state distillation
• Entanglement and permutational symmetry
• Nonadditivity of Bipartite Distillable Entanglement follows from Conjecture on Bound Entangled Werner States
• Sufficient conditions for three-particle entanglement and their tests in recent experiments
• Are the laws of entanglement theory thermodynamical?
• Correlating thermal machines and the second law at the nanoscale
• A few steps more towards NPT bound entanglement
• Von Neumann entropy from unitarity
• Catalytic quantum teleportation and beyond
• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• Distillability via protocols respecting the positivity of partial transpose
• Class of PPT bound entangled states associated to almost any set of pure entangled states
• Catalysis of entanglement and other quantum resources
• No second law of entanglement manipulation after all
• Multiple-copy entanglement transformation and entanglement catalysis
• Catalysis of entanglement manipulation for mixed states
• Fundamental Limits on Correlated Catalytic State Transformations
• Asymptotic state transformations of continuous variable resources
• Pure-state transformations and catalysis under operations that completely preserve positivity of partial transpose
• Rates of multi-partite entanglement transformations and applications in quantum networks
• Entanglement-assisted transformation is asymptotically equivalent to multiple-copy transformation
• Correlated entanglement distillation and the structure of the set of undistillable states
• Maximally entangled mixed states for a fixed spectrum do not always exist
• No-go theorem for entanglement distillation using catalysis
• Entanglement catalysis for quantum states and noisy channels

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• Second Law of Entanglement Manipulation with Entanglement Battery
• Communication with Quantum Catalysts
• Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
• Catalytic Activation of Bell Nonlocality
• Multipartite entanglement theory with entanglement-nonincreasing operations
• Advantage of flexible catalysis for entanglement and quantum thermodynamics