期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 63, 期 2, 页码 1280-1298出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2016.2639523
关键词
Quantum Markov chain; random unitary operations
资金
- MEXT, Japan
- JSPS KAKENHI [23540463, 23240001, 26330006, 15H01677]
- ELC Project [24106009]
- Grants-in-Aid for Scientific Research [23240001, 26330006] Funding Source: KAKEN
We introduce and analyze a task that we call Markovianization, in which a tripartite quantum state is transformed to a quantum Markov chain by a randomizing operation on one of the three subsystems. We consider cases where the initial state is the tensor product of n copies of a tripartite state rho(ABC), and is transformed to a quantum Markov chain conditioned by B-n with a small error, using a random unitary operation on A(n). In an asymptotic limit of infinite copies and vanishingly small error, we analyze the Markovianizing cost, that is, the minimum cost of randomness per copy required for Markovianization. For tripartite pure states, we derive a single-letter formula for the Markovianizing costs. Counterintuitively, the Markovianizing cost is not a continuous function of states, and can be arbitrarily large even if the state is close to a quantum Markov chain. Our results have an application in analyzing the cost of resources for simulating a bipartite unitary gate by local operations and classical communication.
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