Entanglement of a bipartite channel

Abstract

The most general quantum object that can be shared between two distant parties is a bipartite channel, as it is the basic element to construct all quantum circuits. In general, bipartite channels can produce entangled states, and can be used to simulate quantum operations that are not local. While much effort over the last two decades has been devoted to the study of entanglement of bipartite states, very little is known about the entanglement of bipartite channels. In this work, we rigorously study the entanglement of bipartite channels as a resource theory of quantum processes. We present an infinite and complete family of measures of dynamical entanglement, which gives necessary and sufficient conditions for convertibility under local operations and classical communication. Then we focus on the dynamical resource theory where free operations are positive partial transpose (PPT) superchannels, but we do not assume that they are realized by PPT pre- and post-processing. This leads to a greater mathematical simplicity that allows us to express all resource protocols and the relevant resource measures in terms of semi-definite programs. Along the way, we generalize the negativity from states to channels, and introduce the max-logarithmic negativity, which has an operational interpretation as the exact asymptotic entanglement cost of a bipartite channel. Finally, we use the non-positive partial transpose (NPT) resource theory to derive a no-go result: it is impossible to distill entanglement out of bipartite PPT channels under any sets of free superchannels that can be used in entanglement theory. This allows us to generalize one of the long-standing open problems in quantum information - the NPT bound entanglement problem - from bipartite states to bipartite channels. It further leads us to the discovery of bound entangled POVMs.

22+2 pages, 11 figures, long version of arXiv:2009.12304, close to published version

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Cited by in corpus (30)

• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Universal Limitations on Quantum Key Distribution over a Network
• Application of the Resource Theory of Channels to Communication Scenarios
• On the Role of Coherence in Shor's Algorithm
• Cost of quantum entanglement simplified
• Dynamical Entanglement
• Fundamental limitations on distillation of quantum channel resources
• No-go theorems for quantum resource purification II: new approach and channel theory
• Experimental quantification of coherence of a tunable quantum detector
• One-Shot Manipulation of Dynamical Quantum Resources
• Resource Preservability
• Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps
• Quantifying dynamical coherence with dynamical entanglement
• Resource theory of causal connection
• Coherence of operations and interferometry
• The Communication Value of a Quantum Channel
• Noise effects on purity and quantum entanglement in terms of physical implementability
• Uniqueness and Optimality of Dynamical Extensions of Divergences
• A general theory of comparison of quantum channels (and beyond)
• Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
• Interplay of entanglement structures and stabilizer entropy in spin models
• Universal construction of decoders from encoding black boxes
• Entanglement resource theory of quantum channel
• Resource Marginal Problems
• Computable lower bounds on the entanglement cost of quantum channels
• On coherence of quantum operations by using Choi-Jamiołkowski isomorphism
• Projective robustness for quantum channels and measurements and their operational significance
• Quantifying the performance of bidirectional quantum teleportation
• Thermodynamic state convertibility is determined by qubit cooling and heating
• Second Law of Entanglement Dynamics for the Non-Asymptotic Regime