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How measurement reversal could erroneously suggest the capability to discriminate the preparation basis of a quantum ensemble

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Singh,  Rajeev
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Goyal, S. K., Singh, R., & Ghosh, S. (2016). How measurement reversal could erroneously suggest the capability to discriminate the preparation basis of a quantum ensemble. Physical Review A, 93(1): 012114. doi:10.1103/PhysRevA.93.012114.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-B5B7-3
Abstract
Mixed states of a quantum system, represented by density operators, can be decomposed as a statistical mixture of pure states in a number of
ways where each decomposition can be viewed as a different preparation
recipe. However the fact that the density matrix contains full
information about the ensemble makes it impossible to estimate the
preparation basis for the quantum system. Here we present a measurement
scheme to (seemingly) improve the performance of unsharp measurements.
We argue that in some situations this scheme is capable of providing
statistics from a single copy of the quantum system, thus making it
possible to perform state tomography from a single copy. One of the
by-products of the scheme is a way to distinguish between different
preparation methods used to prepare the state of the quantum system.
However, our numerical simulations disagree with our intuitive
predictions. We show that a counterintuitive property of a biased
classical random walk is responsible for the proposed mechanism not
working.