Quantifying the unextendibility of entanglement
arXiv:1911.07433 · doi:10.1088/1367-2630/ad264e
Abstract
Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. In this paper, we present a framework for quantifying and investigating the unextendibility of general bipartite quantum states. First, we define the unextendible entanglement, a family of entanglement measures based on the concept of a state-dependent set of free states. The intuition behind these measures is that the more entangled a bipartite state is, the less entangled each of its individual systems is with a third party. Second, we demonstrate that the unextendible entanglement is an entanglement monotone under two-extendible quantum operations, including local operations and one-way classical communication as a special case. Normalization and faithfulness are two other desirable properties of unextendible entanglement, which we establish here. We further show that the unextendible entanglement provides efficiently computable benchmarks for the rate of exact entanglement or secret key distillation, as well as the overhead of probabilistic entanglement or secret key distillation.
arXiv commentv3: 43 pages, 2 figures, revised according to referees' comments
References in corpus (80)
- Quantum entanglement
- Mixed State Entanglement and Quantum Error Correction
- A computable measure of entanglement
- Distributed Entanglement
- Quantifying Entanglement
- Entanglement Measures and Purification Procedures
- Quantum Resource Theories
- General Monogamy Inequality for Bipartite Qubit Entanglement
- On quantum Renyi entropies: a new generalization and some properties
- Feasible Entanglement Purification for Quantum Communication
- Monogamy of entanglement and other correlations
- Creation of entangled states of distant atoms by interference
- Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- "Squashed Entanglement" - An Additive Entanglement Measure
- A complete family of separability criteria
- Entanglement of pure states for a single copy
- Codes for the Quantum Erasure Channel
- Distinguishing separable and entangled states
- The asymptotic entanglement cost of preparing a quantum state
- Secure key from bound entanglement
- An improved bound on distillable entanglement
- Asymptotic Error Rates in Quantum Hypothesis Testing
- Sandwiched Rényi Divergence Satisfies Data Processing Inequality
- Is Entanglement Monogamous?
- Monotonicity of a relative Rényi entropy
- Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
- Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
- Entanglement cost of mixed states
- General paradigm for distilling classical key from quantum states
- Optimizing practical entanglement distillation
- Different quantum f-divergences and the reversibility of quantum operations
- Local Hidden Variable Theories for Quantum States
- Semidefinite approximations of the matrix logarithm
- Should Entanglement Measures be Monogamous or Faithful?
- Multiplicativity of completely bounded -norms implies a strong converse for entanglement-assisted capacity
- Measurement based entanglement under conditions of extreme photon loss
- Principles of Quantum Communication Theory: A Modern Approach
- The Converse Part of The Theorem for Quantum Hoeffding Bound
- Strong converse rates for quantum communication
- Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
- Monogamy of entanglement without inequalities
- Efficient optimization of the quantum relative entropy
- Fidelity of recovery, geometric squashed entanglement, and measurement recoverability
- A simple proof of monogamy of entanglement
- Entanglement cost in practical scenarios
- Resource theory of asymmetric distinguishability
- Non-asymptotic entanglement distillation
- Useful states and entanglement distillation
- Improved Semidefinite Programming Upper Bound on Distillable Entanglement
- A limit of the quantum Renyi divergence
- What is the probability of a thermodynamical transition?
- The Fidelity of Recovery is Multiplicative
- Semidefinite programming converse bounds for quantum communication
- Optimized quantum f-divergences and data processing
- Deterministic entanglement concentration
- Practical distributed quantum information processing with LOCCNet
- Extendibility limits the performance of quantum processors
- Rényi squashed entanglement, discord, and relative entropy differences
- Error exponents for entanglement concentration
- Irreversibility of Asymptotic Entanglement Manipulation Under Quantum Operations Completely Preserving Positivity of Partial Transpose
- One-shot entanglement distillation beyond local operations and classical communication
- Quantum Channel Marginal Problem
- Nonadditivity of Rains' bound for distillable entanglement
- Compatible quantum correlations: on extension problems for Werner and isotropic states
- One-way quantum key distribution: Simple upper bound on the secret key rate
- Symmetric extension in two-way quantum key distribution
- Semidefinite programming hierarchies for constrained bilinear optimization
- Pretty good measures in quantum information theory
- Entanglement Theory and the Quantum Simulation of Many-Body Physics
- Resource theory of unextendibility and non-asymptotic quantum capacity
- Extendibility of bosonic Gaussian states
- Coherence manipulation with dephasing-covariant operations
- Numerical evidence for bound secrecy from two-way post-processing in quantum key distribution
- Simple test for quantum channel capacity
- A new quantum version of f-divergence
- Freely Scalable Quantum Technologies using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links
- Exact entanglement cost of quantum states and channels under PPT-preserving operations
- Efficiency of Deterministic Entanglement Transformation
- Approximate broadcasting of quantum correlations