Entanglement resource theory of quantum channel

Abstract

Quantum channels can represent dynamic resources, which are indispensable elements in many physical scenarios. To describe certain facets of nonclassicality of the channels, it is necessary to quantify their properties. In the framework of resource theory of quantum channel, we show two general ways of constructing entanglement measure of channels. We also present several entanglement measures of channels based on the Choi relative entropy of channels, concurrence and $k$-ME concurrence and give some specific examples. These entanglement measures of channels can deepen the cognizing about channel and advance the research on the transformation between coherent resources and entangled resources. In addition, we prove that these measures satisfy the properties including nonnegativity, monotonicity, convexity and so on.

arXiv comment10 pages

References in corpus (41)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• A computable measure of entanglement
• Quantum sensing
• Entanglement of a Pair of Quantum Bits
• Quantifying Entanglement
• Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
• Entanglement Measures and Purification Procedures
• On the volume of the set of mixed entangled states
• Fundamental Limits of Repeaterless Quantum Communications
• General Benchmarks for Quantum Repeaters
• Quantum Resource Theories
• Measuring Quantum Coherence with Entanglement
• Universal state inversion and concurrence in arbitrary dimensions
• Quantum teleportation in high dimensions
• End-to-end capacities of a quantum communication network
• Concurrence of mixed bipartite quantum states in arbitrary dimensions
• The quantum capacity of channels with arbitrarily correlated noise
• Operational Resource Theory of Quantum Channels
• Optimal Controlled Teleportation
• Quantifying Operations with an Application to Coherence
• Approaches for approximate additivity of the Holevo information of quantum channels
• On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
• The asymptotic relative entropy of entanglement
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Measure of multipartite entanglement with computable lower bounds
• A resource theory of entanglement with a unique multipartite maximally entangled state
• How to quantify a dynamical quantum resource
• Genuinely Nonlocal Product Bases: Classification and Entanglement Assisted Discrimination
• Dynamical Entanglement
• Entanglement of a bipartite channel
• Detection of genuinely entangled and non-separable $n$-partite quantum states
• Quantifying the resource content of quantum channels: An operational approach
• Efficient $k$-separability criteria for mixed multipartite quantum states
• Fundamental limits on the capacities of bipartite quantum interactions
• Coherence of quantum channels
• Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
• Relative entropies of quantum channels with applications in resource theory
• Converting quantum coherence to genuine multipartite entanglement and nonlocality
• Optimal amount of entanglement to distinguish quantum states instantaneously

Cited by in corpus (7)

• Generation of quantum coherence for continuous variables between causally disconnected regions in dilaton spacetime
• Imaginarity of quantum channels: Refinement and Alternative
• Interplay of entanglement structures and stabilizer entropy in spin models
• DQC1 as an Open Quantum System
• Single-shot entanglement manipulation of states and channels revisited
• Mixed-permutation channel with its application to estimate quantum coherence
• The entangling power of non-entangling channels