Distributed Compression and Multiparty Squashed Entanglement

Abstract

We study a protocol in which many parties use quantum communication to transfer a shared state to a receiver without communicating with each other. This protocol is a multiparty version of the fully quantum Slepian-Wolf protocol for two senders and arises through the repeated application of the two-sender protocol. We describe bounds on the achievable rate region for the distributed compression problem. The inner bound arises by expressing the achievable rate region for our protocol in terms of its vertices and extreme rays and, equivalently, in terms of facet inequalities. We also prove an outer bound on all possible rates for distributed compression based on the multiparty squashed entanglement, a measure of multiparty entanglement.

26 pages, 6 figures thanks to jPicEdt. In v2 we fixed some typos and made minor clarifications and updates

References in corpus (4)

• Distillation of secret key and entanglement from quantum states
• On the quantum, classical and total amount of correlations in a quantum state
• Quantum information can be negative
• On the distributed compression of quantum information

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• Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
• Tools for quantum network design
• A father protocol for quantum broadcast channels
• Quantum and Classical Correlations Inside the Entanglement Wedge
• Fundamental limitation on quantum broadcast networks
• Deconstruction and conditional erasure of quantum correlations
• Multipartite quantum correlations and local recoverability
• Unconstrained Capacities of Quantum Key Distribution and Entanglement Distillation for Pure-Loss Bosonic Broadcast Channels
• Energy-constrained two-way assisted private and quantum capacities of quantum channels
• Bounds on entanglement distillation and secret key agreement for quantum broadcast channels
• Unconstrained distillation capacities of a pure-loss bosonic broadcast channel
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states
• Continuity of characteristics of composite quantum systems
• Multipartite Intrinsic Non-Locality and Device-Independent Conference Key Agreement
• Efficient Dicke state generation in a network of lossy channels
• Entanglement monogamy via multivariate trace inequalities
• More on the upper bound of holographic n-partite information
• Uniform continuity bounds for characteristics of multipartite quantum systems
• Multipartite Optimized Correlation Measures and Holography
• Optimized Correlation Measures in Holography
• Quantum State Merging for Arbitrarily Small-Dimensional Systems
• On lower semicontinuity of the quantum conditional mutual information and its corollaries
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Squashed Entanglement from Generalized Rindler Wedge
• Genuine $k$-partite correlations and entanglement in the ground state of the Dicke model for interacting qubits
• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the multimode extreme bosonic Gaussian channels