Title:	Measuring non-Hermitian operators via weak values
Authors:	Pati, Arun Kumar Singh, Uttam Sinha, Urbasi
Issue Date:	Nov-2015
Publisher:	American Physical Society
Citation:	Physical Review A, 2015, Vol.92, p052120
Abstract:	In quantum theory, a physical observable is represented by a Hermitian operator as it admits real eigenvalues. This stems from the fact that any measuring apparatus that is supposed to measure a physical observable will always yield a real number. However, the reality of an eigenvalue of some operator does not mean that it is necessarily Hermitian. There are examples of non-Hermitian operators that may admit real eigenvalues under some symmetry conditions. In general, given a non-Hermitian operator, its average value in a quantum state is a complex number and there are only very limited methods available to measure it. Following standard quantum mechanics, we provide an experimentally feasible protocol to measure the expectation value of any non-Hermitian operator via weak measurements. The average of a non-Hermitian operator in a pure state is a complex multiple of the weak value of the positive-semidefinite part of the non-Hermitian operator. We also prove an uncertainty relation for any two non-Hermitian operators and show that the fidelity of a quantum state under a quantum channel can be measured using the average of the corresponding Kraus operators. The importance of our method is shown in testing the stronger uncertainty relation, verifying the Ramanujan formula, and measuring the product of noncommuting projectors.
Description:	Open Access
URI:	http://hdl.handle.net/2289/6395
ISSN:	1050-2947 1094-1622 (online)
Alternative Location:	http://arxiv.org/abs/1406.3007 http://dx.doi.org/10.1103/PhysRevA.92.052120
Copyright:	2015 The American Physical Society
Appears in Collections:	Research Papers (LAMP)

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