Resource theory of unextendibility and non-asymptotic quantum capacity

Abstract

In this paper, we introduce the resource theory of unextendibility as a relaxation of the resource theory of entanglement. The free states in this resource theory are the k-extendible states, associated with the inability to extend quantum entanglement in a given quantum state to multiple parties. The free channels are k-extendible channels, which preserve the class of k-extendible states. We define several quantifiers of unextendibility by means of generalized divergences and establish their properties. By utilizing this resource theory, we obtain non-asymptotic upper bounds on the rate at which quantum communication or entanglement preservation is possible over a finite number of uses of an arbitrary quantum channel assisted by k-extendible channels at no cost. These bounds are significantly tighter than previously known bounds for both the depolarizing and erasure channels. Finally, we revisit the pretty strong converse for the quantum capacity of antidegradable channels and establish an upper bound on the non-asymptotic quantum capacity of these channels.

27 pages, 7 figures, see companion paper at https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.070502

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• Quantifying the performance of approximate teleportation and quantum error correction via symmetric two-PPT-extendibility
• Cycle Index Polynomials and Generalized Quantum Separability Tests
• Quantifying the unextendibility of entanglement
• Schrödinger as a Quantum Programmer: Estimating Entanglement via Steering
• A Post-Quantum Associative Memory
• Choi-Defined Resource Theories
• Extendible quantum measurements and limitations on classical communication
• Entropic and operational characterizations of dynamic quantum resources
• Unextendible entanglement of quantum channels
• Extendibility limits quantum-secured communication and key distillation
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states