Computable lower bounds on the entanglement cost of quantum channels
arXiv:2201.09257 · doi:10.1088/1751-8121/aca731
Abstract
A class of lower bounds for the entanglement cost of any quantum state was recently introduced in [arXiv:2111.02438] in the form of entanglement monotones known as the tempered robustness and tempered negativity. Here we extend their definitions to point-to-point quantum channels, establishing a lower bound for the asymptotic entanglement cost of any channel, whether finite or infinite dimensional. This leads, in particular, to a bound that is computable as a semidefinite program and that can outperform previously known lower bounds, including ones based on quantum relative entropy. In the course of our proof we establish a useful link between the robustness of entanglement of quantum states and quantum channels, which requires several technical developments such as showing the lower semicontinuity of the robustness of entanglement of a channel in the weak*-operator topology on bounded linear maps between spaces of trace class operators.
arXiv comment24 pages. Technical companion paper to [arXiv:2111.02438], now published as [Nat. Phys. 19, 184-189 (2023)]. In v2, which is close to the published version, we improved the presentation and corrected a few typos
References in corpus (62)
- Mixed State Entanglement and Quantum Error Correction
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Concentrating Partial Entanglement by Local Operations
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Quantifying Entanglement
- The logarithmic negativity: A full entanglement monotone that is not convex
- General Benchmarks for Quantum Repeaters
- Fundamental Limits of Repeaterless Quantum Communications
- Quantum Resource Theories
- The capacity of the noisy quantum channel
- Quantum correlations with no causal order
- Distance measures to compare real and ideal quantum processes
- General Entanglement Breaking Channels
- Robustness of entanglement
- Superadditivity of communication capacity using entangled inputs
- The Physics and Mathematics of the Second Law of Thermodynamics
- Quantum computations without definite causal structure
- Theoretical framework for quantum networks
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- "Squashed Entanglement" - An Additive Entanglement Measure
- The asymptotic entanglement cost of preparing a quantum state
- Transforming quantum operations: quantum supermaps
- Some Properties of the Computable Cross Norm Criterion for Separability
- Quantum Reverse Shannon Theorem
- A Resource Framework for Quantum Shannon Theory
- Faithful Squashed Entanglement
- Entanglement Theory and the Second Law of Thermodynamics
- Optimal discrimination of quantum operations
- The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
- On the capacities of bipartite Hamiltonians and unitary gates
- Operational Resource Theory of Quantum Channels
- The squashed entanglement of a quantum channel
- Tema Con Variazioni: Quantum Channel Capacity
- Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
- A reversible theory of entanglement and its relation to the second law
- How to quantify a dynamical quantum resource
- Monotonicity of the Quantum Relative Entropy Under Positive Maps
- Relative Entropy of Entanglement and Restricted Measurements
- On the power of PPT-preserving and non-signalling codes
- Relative Entropy Bounds on Quantum, Private and Repeater Capacities
- Entanglement Cost of Quantum Channels
- Quantum Entanglement and Conditional Information Transmission
- Cost of quantum entanglement simplified
- Energy-constrained diamond norms and their use in quantum information theory
- Binding entanglement channels
- Entanglement of a bipartite channel
- Fundamental limitations on distillation of quantum channel resources
- No second law of entanglement manipulation after all
- Entanglement cost and quantum channel simulation
- Universal and Operational Benchmarking of Quantum Memories
- Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities
- Semidefinite programming converse bounds for quantum communication
- Resource theories of quantum channels and the universal role of resource erasure
- Operational quantification of continuous-variable quantum resources
- Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
- Framework for resource quantification in infinite-dimensional general probabilistic theories
- Irreversibility of Asymptotic Entanglement Manipulation Under Quantum Operations Completely Preserving Positivity of Partial Transpose
- Amortization does not enhance the max-Rains information of a quantum channel
- Equivalence of Additivity Questions in Quantum Information Theory
- Squashed entanglement in infinite dimensions
- Functional analytic insights into irreversibility of quantum resources