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2009

Single-shot Quantum State Merging

Berta, Mario

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We consider an unknown quantum state shared between two parties, Alice and Bob, and ask how much quantum communication is needed to transfer the full state to Bob.

This problem is known as state merging and was introduced in [Horodecki et al., Nature, 436, 673 (2005)].
It has been shown that for free classical communication the minimal number of quantum bits that need to be sent from Alice to Bob is given by the conditional von Neumann entropy.
However this result only holds asymptotically (in the sense that Alice and Bob share initially many identical copies of the state) and it was unclear how much quantum communication is necessary to merge a single copy.

Single-shot Quantum State Merging · Around

Built on

Positive functions on C*-algebras
W. Stinespring · 1955
Earlier work this paper cites.
Big Omicron and big Omega and big Theta
D. Knuth · 1976
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The transition probability in the state space of a *-algebra
A. Uhlmann · 1976
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Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
C. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. Wootters · 1993
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Fidelity for mixed quantum states
R. Jozsa · 1994
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Cryptographic distinguishability measures for quantum mechanical states
C. A. Fuchs and J. van de Graaf · 1999
Earlier work this paper cites.

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