On the optimal certification of von Neumann measurements
- URL: http://arxiv.org/abs/2009.06776v3
- Date: Fri, 11 Dec 2020 11:10:54 GMT
- Title: On the optimal certification of von Neumann measurements
- Authors: Paulina Lewandowska and Aleksandra Krawiec and Ryszard Kukulski and
{\L}ukasz Pawela and Zbigniew Pucha{\l}a
- Abstract summary: certification of quantum measurements can be viewed as the extension of quantum hypotheses testing.
We show the connection between the certification of quantum channels or von Neumann measurements and the notion of $q$-numerical range.
- Score: 55.41644538483948
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this report we study certification of quantum measurements, which can be
viewed as the extension of quantum hypotheses testing. This extension involves
also the study of the input state and the measurement procedure. Here, we will
be interested in two-point (binary) certification scheme in which the null and
alternative hypotheses are single element sets. Our goal is to minimize the
probability of the type II error given some fixed statistical significance. In
this report, we begin with studying the two-point certification of pure quantum
states and unitary channels to later use them to prove our main result, which
is the certification of von Neumann measurements in single-shot and parallel
scenarios. From our main result follow the conditions when two pure states,
unitary operations and von Neumann measurements cannot be distinguished
perfectly but still can be certified with a given statistical significance.
Moreover, we show the connection between the certification of quantum channels
or von Neumann measurements and the notion of $q$-numerical range.
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