Noisy quantum state redistribution with promise and the Alpha-bit
- Publisher:
- Institute of Electrical and Electronics Engineers (IEEE)
- Publication Type:
- Journal Article
- Citation:
- IEEE Transactions on Information Theory, 2018, 66, (12), pp. 7772-7786
- Issue Date:
- 2018
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| 09184888.pdf | 327.9 kB |
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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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