Noisy quantum state redistribution with promise and the Alpha-bit

Institute of Electrical and Electronics Engineers (IEEE)
Publication Type:
Journal Article
IEEE Transactions on Information Theory, 2018, 66, (12), pp. 7772-7786
Issue Date:
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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 $\mathcal{N}$, instead of the noiseless channel, as is usually considered in state redistribution. We take a natural approach towards 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. We interpret the communication primitive Alpha-bit, recently introduced in Ref. [arXiv:1706.09434], as an instance of state transfer (a sub-task of state redistribution) with a one-sided promise 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 capacity of the Alpha-bit, showing that any quantum state redistribution protocol can be used as a black box to simulate classical communication.
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