308 research outputs found
Weak Measurements Beyond the Aharonov-Albert-Vaidman Formalism
We extend the idea of weak measurements to the general case, provide a
complete treatment and obtain results for both the regime when the pre-selected
and post-selected states (PPS) are almost orthogonal and the regime when they
are exactly orthogonal. We surprisingly find that for a fixed interaction
strength, there may exist a maximum signal amplification and a corresponding
optimum overlap of PPS to achieve it. For weak measurements in the orthogonal
regime, we find interesting quantities that play the same role that weak values
play in the non-orthogonal regime.Comment: 5 pages, 2 figure
Comparison of mixed quantum states
In this article, we study the problem of comparing mixed quantum states:
given unknown mixed quantum states, can one determine whether they are
identical or not with an unambiguous quantum measurement? We first study
universal comparison of mixed quantum states, and prove that this task is
generally impossible to accomplish. Then, we focus on unambiguous comparison of
mixed quantum states arbitrarily chosen from a set of mixed quantum
states. The condition for the existence of an unambiguous measurement operator
which can produce a conclusive result when the unknown states are actually the
same and the condition for the existence of an unambiguous measurement operator
when the unknown states are actually different are studied independently. We
derive a necessary and sufficient condition for the existence of the first
measurement operator, and a necessary condition and two sufficient conditions
for the second. Furthermore, we find that the sufficiency of the necessary
condition for the second measurement operator has simple and interesting
dependence on and . At the end, a unified condition is obtained for the
simultaneous existence of these two unambiguous measurement operators.Comment: 9 page
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