Entanglement cost in practical scenarios

Abstract

We quantify the one-shot entanglement cost of an arbitrary bipartite state, that is the minimum number of singlets needed by two distant parties to create a single copy of the state up to a finite accuracy, using local operations and classical communication only. This analysis, in contrast to the traditional one, pertains to scenarios of practical relevance, in which resources are finite and transformations can only be achieved approximately. Moreover, it unveils a fundamental relation between two well-known entanglement measures, namely, the Schmidt number and the entanglement of formation. Using this relation, we are able to recover the usual expression of the entanglement cost as a special case.

4+4 pages. See also arXiv:0704.1957; v2: minor typos corrected; v3: final version to appear on PRL

References in corpus (4)

• Coding Theorem and Strong Converse for Quantum Channels
• A Generalization of Quantum Stein's Lemma
• Distilling entanglement from arbitrary resources
• Epsilon-measures of entanglement

Cited by in corpus (46)

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• The structure of multidimensional entanglement in multipartite systems
• The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
• alpha-z-relative Renyi entropies
• Operational Resource Theory of Quantum Channels
• One-Shot Operational Quantum Resource Theory
• One-Shot Coherence Dilution
• A measure of majorisation emerging from single-shot statistical mechanics
• Entanglement Cost of Quantum Channels
• Distilling entanglement from arbitrary resources
• Cost of quantum entanglement simplified
• Entanglement cost and quantum channel simulation
• Min- and Max-Entropy in Infinite Dimensions
• A limit of the quantum Renyi divergence
• Universal and Operational Benchmarking of Quantum Memories
• High-Dimensional Entanglement in States with Positive Partial Transposition
• What is the probability of a thermodynamical transition?
• The Smooth Entropy Formalism for von Neumann Algebras
• Work fluctuations and entanglement in quantum batteries
• Unextendible entangled bases with fixed Schmidt number
• Device-independent Certification of One-shot Distillable Entanglement
• Quantum Correlation with Sandwiched Relative Entropies: Advantageous as Order Parameter in Quantum Phase Transitions
• Epsilon-smooth measure of coherence
• Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
• Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation
• A solution of the generalised quantum Stein's lemma
• Quantum coherence via conditional entropy
• Graph-associated entanglement cost of a multipartite state in exact and finite-block-length approximate constructions
• Parallel ergotropy: Maximum work extraction via parallel local unitary operations
• Interplay among entanglement, measurement incompatibility, and nonlocality
• An Extention of Entanglement Measures for Pure States
• Quantifying the unextendibility of entanglement
• Entropic relations for indistinguishable quantum particles
• Entanglement theory with limited computational resources
• Entanglement cost for infinite-dimensional physical systems
• Memory cost of quantum protocols
• The Zero-error Entanglement Cost is Highly Non-Additive
• A generalization of Schmidt number for multipartite states
• Computable entanglement cost under positive partial transpose operations
• Uncertainty relations between quantum Fisher information and entanglement monotones
• Local channels preserving maximal entanglement or Schmidt number
• Second Law of Entanglement Dynamics for the Non-Asymptotic Regime
• Single-shot entanglement manipulation of states and channels revisited
• Weight-based measure of quantum memory as a universal and operational benchmark
• One-Shot Distributed Source Simulation: As Quantum as it Can Get
• Measurement-device-independent Schmidt number certification of all entangled states