Quantum fidelity measures for mixed states

Yeong Cherng Liang, Yu Hao Yeh, Paulo E.M.F. Mendonça, Run Yan Teh, Margaret D. Reid, Peter D. Drummond

Research output: Contribution to journalReview articlepeer-review

35 Citations (Scopus)


Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more subtle for the more general case of mixed quantum states often found in practice. A large number of different proposals exist. In this review, we summarize the required properties of a quantum fidelity measure, and compare them, to determine which properties each of the different measures has. We show that there are large classes of measures that satisfy all the required properties of a fidelity measure, just as there are many norms of Hilbert space operators, and many measures of entropy. We compare these fidelities, with detailed proofs of their properties. We also summarize briefly the applications of these measures in teleportation, quantum memories and quantum computers, quantum communications, and quantum phase-space simulations.

Original languageEnglish
Article number076001
JournalReports on Progress in Physics
Issue number7
Publication statusPublished - 2019 Jun 24

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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