Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt)
arXiv:1206.1307
Abstract
We demonstrate the convexity of the difference between the regularized entanglement of purification and the entropy, as a function of the state. This is proved by means of a new asymptotic protocol to prepare a state from pre-shared entanglement and by local operations only. We go on to employ this convexity property in an investigation of the additivity of the (single-copy) entanglement of purification: using numerical results for two-qubit Werner states we find strong evidence that the entanglement of purification is different from its regularization, hence that entanglement of purification is not additive.
arXiv comment5 pages, 2 eps figures
References in corpus (13)
- Quantum entanglement
- Concentrating Partial Entanglement by Local Operations
- On the quantum, classical and total amount of correlations in a quantum state
- Superadditivity of communication capacity using entangled inputs
- Entanglement Measures under Symmetry
- Quantum Communication With Zero-Capacity Channels
- The entanglement of purification
- Quantum Reverse Shannon Theorem
- Robustness of quantum Markov chains
- Uncertainty, Monogamy, and Locking of Quantum Correlations
- On the communication cost of entanglement transformations
- On quantum advantage in dense coding
- Optimal Visible Compression Rate For Mixed States Is Determined By Entanglement Of Purification
Cited by in corpus (7)
- Holographic Entanglement of Purification
- Quantum Reverse Shannon Theorem
- Entanglement of Purification in Free Scalar Field Theories
- Entanglement of Purification in Many Body Systems and Symmetry Breaking
- Correlation measures and distillable entanglement in AdS/CFT
- Optimized Measures of Bipartite Quantum Correlation
- Quantum Wiretap Channel Coding Assisted by Noisy Correlation