Noisy quantum state redistribution with promise and the Alpha-bit
arXiv:1803.03414 · doi:10.1109/TIT.2020.3021289
Abstract
We consider a variation of the well-studied quantum state redistribution task, in which the starting state is known only to the receiver Bob and not to the sender Alice. We refer to this as quantum state redistribution with a one-sided promise. In addition, we consider communication from Alice to Bob over a noisy channel , instead of the noiseless channel, as is usually considered in state redistribution. We take a natural approach towards the solution of this problem where we "embed" the promise as part of the state and then invoke known protocols for quantum state redistribution composed with known protocols for transfer of quantum information over noisy channels. Using our approach, we are able to reproduce the Alpha-bit capacities with or without entanglement assistance in Ref. [ArXiv:1706.09434], using known protocols for quantum state redistribution and quantum communication over noisy channels. Furthermore, we generalize the entanglement assisted classical Alpha-bit capacity, showing that any quantum state redistribution protocol can be used as a black box to simulate classical communication.
arXiv commentversion 2, 16 pages
References in corpus (34)
- Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
- Distance measures to compare real and ideal quantum processes
- Noncommuting mixed states cannot be broadcast
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- One-Shot Classical-Quantum Capacity and Hypothesis Testing
- A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
- Quantum state merging and negative information
- The mother of all protocols: Restructuring quantum information's family tree
- Quantum Reverse Shannon Theorem
- The quantum capacity of channels with arbitrarily correlated noise
- The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
- Second-order asymptotics for quantum hypothesis testing
- The exact cost of redistributing multipartite quantum states
- A family of quantum protocols
- Optimal quantum source coding with quantum information at the encoder and decoder
- Entanglement-assisted communication of classical and quantum information
- Finite blocklength converse bounds for quantum channels
- One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach
- Learning the Alpha-bits of Black Holes
- Quantum message compression with applications
- Single-shot Quantum State Merging
- The apex of the family tree of protocols: Optimal rates and resource inequalities
- One-shot entanglement-assisted quantum and classical communication
- Smooth Entropy Bounds on One-Shot Quantum State Redistribution
- Quantum state redistribution based on a generalized decoupling
- Channel Simulation and Coded Source Compression
- Approximate Quantum Error Correction Revisited: Introducing the Alpha-bit
- Weak Decoupling Duality and Quantum Identification
- An upper bound on the second order asymptotic expansion for the quantum communication cost of state redistribution
- Distributed Compression of Correlated Classical-Quantum Sources or: The Price of Ignorance
- A one-shot achievability result for quantum state redistribution
- A unified approach to source and message compression
- A hypothesis testing approach for communication over entanglement assisted compound quantum channel
- Direct Sum Theorem for Bounded Round Quantum Communication Complexity