Quantum Optics Seminar by János A. Bergou – Niels Bohr Institute - University of Copenhagen

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Niels Bohr Institute > Calendar > Activities 2013 > Quantum Optics Seminar...

Quantum Optics Seminar by János A. Bergou

Abstract:

Sequential quantum measurements

János A. Bergou*, Edgar Feldman**, and Mark Hillery* 

*Department of Physics and Astronomy, CUNY Hunter College, 695 Park Avenue, New York, NY 10065, USA

**Department of Mathematics, CUNY Graduate Center, 365 Fifth Avenue, New York, NY 10016, USA

It is generally assumed that in the process of performing a measurement on a quantum system the state of the system collapses to one of the eigenstates of the physical quantity that is being measured, although recent works are challenging this concept [1].  Here, using the formalism of generalized quantum measurements we show that this so-called collapse postulate is not absolute; there are ways to get around it [2].  In fact, the post-measurement state of the system can be designed with a great deal of flexibility.  If one chooses an appropriate figure of merit to characterize further processing of the system after the measurement has been performed, one can even optimize the post-measurement states to maximize the corresponding figure of merit.  We will illustrate the ideas on two examples.  In the first example multiple observers determine the initial state of a qubit, employing the strategy of unambiguous state discrimination, by performing subsequent observations on the same qubit without revealing the measurement results to each other.  In the second example multiple observers determine the initial state of a qubit, but this time employing the strategy of minimum error discrimination, again by performing subsequent observations on the same qubit without revealing the measurement results to each other.  State discrimination with minimum error is the prime example for a standard (projective) quantum measurement, so it is even more surprising that the post-measurement states can be designed with some flexibility.  In both scenarios we optimize the post-measurement states to maximize the joint probability of success, i.e., the probability that each observer in the sequence will learn the initial state of the qubit. 

References

[1] P. Rapčan, J. Calsamiglia, R. Muñoz-Tapia, E. Bagan, and V. Bužek, Phys. Rev. A 84, 032326 (2012).

[2] J. A. Bergou, E. Feldman, and M. Hillery, Extracting information from a qubit by multiple observers: Toward a theory of sequential state discrimination, arXiv:1305.4290 (2013).