Quantum message compression with applications

Abstract

We present a new scheme for the compression of one-way quantum messages, in the setting of coherent entanglement assisted quantum communication. For this, we present a new technical tool that we call the convex split lemma, which is inspired by the classical compression schemes that use rejection sampling procedure. As a consequence, we show new bounds on the quantum communication cost of single-shot entanglement-assisted one-way quantum state redistribution task and for the sub-tasks quantum state splitting and quantum state merging. Our upper and lower bounds are tight up to a constant and hence stronger than previously known best bounds for above tasks. Our protocols use explicit quantum operations on the sides of Alice and Bob, which are different from the decoupling by random unitaries approach used in previous works. As another application, we present a port-based teleportation scheme which works when the set of input states is restricted to a known ensemble, hence potentially saving the number of required ports. Furthermore, in case of no prior knowledge about the set of input states, our average success fidelity matches the known average success fidelity, providing a new port-based teleportation scheme with similar performance as appears in literature.

21 pages, 2 figures, version 4

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• Partially smoothed information measures
• Computable Rényi mutual information: Area laws and correlations
• Conditional quantum one-time pad
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• On the near-optimality of one-shot classical communication over quantum channels
• The variance of relative surprisal as single-shot quantifier
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
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• Channel Simulation: Finite Blocklengths and Broadcast Channels
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• Locality of Edge States and Entanglement Spectrum from Strong Subadditivity
• A unified approach to source and message compression
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• Quantum State Merging for Arbitrarily Small-Dimensional Systems
• Reliable Simulation of Quantum Channels: the Error Exponent
• Bounding the resources for thermalizing many-body localized systems
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• Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence
• One-Shot Triple-Resource Trade-Off in Quantum Channel Coding
• Noisy quantum state redistribution with promise and the Alpha-bit
• Optimality of meta-converse for channel simulation
• Communication with Quantum Catalysts
• On the compression of messages in the multi-party setting
• One-shot inner bounds for sending private classical information over a quantum MAC
• Expected communication cost of distributed quantum tasks
• Tight relations and equivalences between smooth relative entropies
• One-shot Multiple Access Channel Simulation
• A resource theory of asynchronous quantum information processing
• Fast suppression of classification error in variational quantum circuits