Construction of the least informative observable conserved by a given quantum instrument

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For a quantum measurement process described by a quantum instrument I and a system observable corresponding to a positive-operator valued measure (POVM) E, I is said to conserve the information of E if the joint successive measurement of I followed by E is equivalent to a single measurement of E. We show that for any quantum instrument I we can construct a POVM conserved by I. Intuitively, the construction gives the infinite joint successive measurement of I. We also show that the constructed POVM is the least informative observable among POVMs conserved by I, i.e., the constructed POVM can be realized by a classical post-processing of any POVM conserved by I. As typical examples of quantum instruments, we explicitly evaluate POVMs of infinite successive measurements for photon counting and quantum counter instruments.

Original languageEnglish
Article number092202
JournalJournal of Mathematical Physics
Issue number9
Publication statusPublished - Sep 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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