A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
State discrimination with postmeasurement information and incompatibility of quantum measurements
Tekijät: Carmeli C, Heinosaari T, Toigo A
Kustantaja: AMER PHYSICAL SOC
Julkaisuvuosi: 2018
Journal: Physical Review A
Tietokannassa oleva lehden nimi: PHYSICAL REVIEW A
Lehden akronyymi: PHYS REV A
Artikkelin numero: ARTN 012126
Vuosikerta: 98
Numero: 1
Sivujen määrä: 14
ISSN: 2469-9926
eISSN: 2469-9934
DOI: https://doi.org/10.1103/PhysRevA.98.012126
Tiivistelmä
We discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement setup after Alice has announced him the chosen ensemble, or he is forced to perform the measurement before Alice's announcement. In the latter case, he can only postprocess his measurement outcome when Alice's extra information becomes available. We compare the optimal guessing probabilities in the two scenarios, and we prove that they are the same if and only if there exist compatible (i.e., jointly measurable) optimal measurements for all of Alice's state ensembles. When this is the case, postprocessing any of the corresponding joint measurements is Bob's optimal strategy in the postmeasurement information scenario. Furthermore, we establish a connection between discrimination with postmeasurement information and the standard state discrimination. By means of this connection and exploiting the presence of symmetries, we are able to compute the various guessing probabilities in many concrete examples.
We discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement setup after Alice has announced him the chosen ensemble, or he is forced to perform the measurement before Alice's announcement. In the latter case, he can only postprocess his measurement outcome when Alice's extra information becomes available. We compare the optimal guessing probabilities in the two scenarios, and we prove that they are the same if and only if there exist compatible (i.e., jointly measurable) optimal measurements for all of Alice's state ensembles. When this is the case, postprocessing any of the corresponding joint measurements is Bob's optimal strategy in the postmeasurement information scenario. Furthermore, we establish a connection between discrimination with postmeasurement information and the standard state discrimination. By means of this connection and exploiting the presence of symmetries, we are able to compute the various guessing probabilities in many concrete examples.
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