One-Shot Static Entanglement Cost of Bipartite Quantum Channels
arXiv:2103.10014 · doi:10.1103/PhysRevA.103.062415
Abstract
We first investigate the one-shot static entanglement cost to simulate a bipartite quantum channel under the set of non-entangling channels. The lower bound on the static entanglement cost is given by the generalized robustness of the target channel as well as the robust-generating power of the channel, which implies that the cost necessary to generate a bipartite quantum channel might not be retrievable in general. Next, we conceive a set of quantum channels that extends the set of non-entangling channels. We find out that the one-shot static entanglement cost under the extended set of channels is given by the channel's standard log-robustness. This gives the one-shot dynamic entanglement cost under a set of free superchannels that do not generate dynamic entanglement resource; the extended set is shown to be equivalent to the set of free superchannels.
arXiv comment8 pages, 3 figures; a refined version with additional references
References in corpus (41)
- Quantum entanglement
- Separability Criterion for Density Matrices
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Quantum Resource Theories
- Quantum Nonlocality without Entanglement
- Quantum computations without definite causal structure
- Theoretical framework for quantum networks
- Optimal local implementation of non-local quantum gates
- Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
- Application of a resource theory for magic states to fault-tolerant quantum computing
- Quantum Circuits Architecture
- Transforming quantum operations: quantum supermaps
- An improved bound on distillable entanglement
- Separability and distillability of multiparticle quantum systems
- Entangling operations and their implementation using a small amount of entanglement
- Stabilizing Quantum Information
- General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
- Quantum dynamics as a physical resource
- How robust is a quantum gate in the presence of noise?
- All entangled states are useful for channel discrimination
- Resource Destroying Maps
- Comparison of Quantum Channels by Superchannels
- Quantifying the magic of quantum channels
- Operational Resource Theory of Quantum Channels
- Quantifying magic for multi-qubit operations
- Efficiently computable bounds for magic state distillation
- Convex geometry of quantum resource quantification
- How to quantify a dynamical quantum resource
- Using and reusing coherence to realize quantum processes
- Entanglement Cost of Quantum Channels
- Benchmarking one-shot distillation in general quantum resource theories
- Optimal resource cost for error mitigation
- Cost of quantum entanglement simplified
- Dynamical Resource Theory of Quantum Coherence
- Dynamical Entanglement
- Entropy of a quantum channel
- No-go theorems for quantum resource purification II: new approach and channel theory
- Nonlocal Entanglement Transformations Achievable by Separable Operations
- One-Shot Manipulation of Dynamical Quantum Resources
- One-shot entanglement distillation beyond local operations and classical communication
- One-shot manipulation of entanglement for quantum channels