Statistics of Entanglement Transformation with Hierarchies among Catalysts

Abstract

The distribution of typical bipartite pure states is studied within the framework of state transformation via local operation and classical communication (LOCC). We report the statistics of comparable and incomparable states in different dimensions for single- and multi-copy regimes and establish a connection between state transformation and the difference between the entanglement contents of the initial and the target states. From the analysis of catalyst resources, required to further otherwise impossible LOCC transformations between pairs, we demonstrate a universal pattern in the average and minimum entanglement of the randomly generated catalysts. Furthermore, we introduce a concept of hierarchy between different kinds of catalysts and show how they can not only aid in the conversion of incomparable states but can also act as a less costly resource towards this goal. We confirm the existence of catalysts, referred to as strong catalysts, which can activate LOCC transformation between pairs at the single-copy level, when it is initially impossible even with multiple copies.

arXiv commentv2: Close to the published version

References in corpus (40)

• Quantum entanglement
• Concentrating Partial Entanglement by Local Operations
• Quantum Coherence as a Resource
• Random Numbers Certified by Bell's Theorem
• Measurement-based quantum computation
• Conditions for a class of entanglement transformations
• The second laws of quantum thermodynamics
• Quantum data processing and error correction
• Superadditivity of communication capacity using entangled inputs
• Catalytic Coherence
• Entanglement of pure states for a single copy
• The resource theory of informational nonequilibrium in thermodynamics
• Aspects of generic entanglement
• Entanglement-assisted local manipulation of pure quantum states
• Most quantum states are too entangled to be useful as computational resources
• Minimal conditions for local pure-state entanglement manipulation
• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• Generating random density matrices
• Approximate transformations and robust manipulation of bipartite pure state entanglement
• Are random pure states useful for quantum computation?
• Resource theory of imaginarity: Quantification and state conversion
• Limits to catalysis in quantum thermodynamics
• Catalytic coherence transformations
• Catalytic Transformations of Pure Entangled States
• Bounds on entanglement in qudit subsystems
• Entanglement Typicality
• Asymptotic entanglement transformation between W and GHZ states
• Entanglement of three-qubit random pure states
• All states are universal catalysts in quantum thermodynamics
• Necessary conditions on entanglement catalysts
• A classification of incomparable states
• Constructive Feedback of Non-Markovianity on Resources in Random Quantum States
• Uniform Decoherence Effect on Localizable Entanglement in Random Multi-qubit Pure States
• Rates of multi-partite entanglement transformations and applications in quantum networks
• $k$-uniform mixed states
• Performance of Dense Coding and Teleportation for Random States --Augmentation via Pre-processing
• Conditions for entanglement transformation between a class of multipartite pure states with generalized Schmidt decompositions
• Universality in Distribution of Monogamy Scores for Random Multiqubit Pure States
• Bounds On Entanglement Catalysts
• Restrictions on shareability of classical correlations for random multipartite quantum states