Concentrating tripartite quantum information

Abstract

We introduce the concentrated information of tripartite quantum states. For three parties Alice, Bob, and Charlie, it is defined as the maximal mutual information achievable between Alice and Charlie via local operations and classical communication performed by Charlie and Bob. We derive upper and lower bounds to the concentrated information, and obtain a closed expression for it on several classes of states including arbitrary pure tripartite states in the asymptotic setting. We show that distillable entanglement, entanglement of assistance, and quantum discord can all be expressed in terms of the concentrated information, thus revealing its role as a unifying informational primitive. We finally investigate quantum state merging of mixed states with and without additional entanglement. The gap between classical and quantum concentrated information is proven to be an operational figure of merit for mixed state merging in absence of additional entanglement. Contrary to pure state merging, our analysis shows that classical communication in both directions can provide advantage for merging of mixed states.

5+4 pages, 1 figure. Presentation significantly improved, new results added. Theorem 3 contains an application of recent results by Fawzi and Renner in arXiv:1410.0664. To be published in PRL

References in corpus (15)

• Distillation of secret key and entanglement from quantum states
• Area laws in quantum systems: mutual information and correlations
• On the quantum, classical and total amount of correlations in a quantum state
• Quantum information can be negative
• Interpreting quantum discord through quantum state merging
• Operational interpretations of quantum discord
• Quantum discord for general two--qubit states: Analytical progress
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Linking Quantum Discord to Entanglement in a Measurement
• All non-classical correlations can be activated into distillable entanglement
• Conservation law for distributed entanglement of formation and quantum discord
• Entanglement of assistance and multipartite state distillation
• Quantum Discord and its Role in Quantum Information Theory
• Quantum discord cannot be shared
• Binegativity and geometry of entangled states in two qubits

Cited by in corpus (8)

• Measures and applications of quantum correlations
• Unconditional security of entanglement-based continuous-variable quantum secret sharing
• Reducing the entropic uncertainty lower bound in the presence of quantum memory via local operation and classical communication
• Uniform Decoherence Effect on Localizable Entanglement in Random Multi-qubit Pure States
• Entanglement distribution and quantum discord
• Distinguishing Phases via Non-Markovian Dynamics of Entanglement in Topological Quantum Codes under Parallel Magnetic Field
• Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations
• Quantum state merging with bound entanglement