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Fragile entanglement statistics

Brody, Dorje C, Hughston, Lane P and Meier, David M (2015) Fragile entanglement statistics Journal of Physics A: Mathematical and Theoretical, 48 (42).


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If X and Y are independent, Y and Z are independent, and so are X and Z, one might be tempted to conclude that X, Y, and Z are independent. But it has long been known in classical probability theory that, intuitive as it may seem, this is not true in general. In quantum mechanics one can ask whether analogous statistics can emerge for configurations of particles in certain types of entangled states. The explicit construction of such states, along with the specification of suitable sets of observables that have the purported statistical properties, is not entirely straightforward. We show that an example of such a configuration arises in the case of an N-particle GHZ state, and we are able to identify a family of observables with the property that the associated measurement outcomes are independent for any choice of $2,3,\ldots ,N-1$ of the particles, even though the measurement outcomes for all N particles are not independent. Although such states are highly entangled, the entanglement turns out to be 'fragile', i.e. the associated density matrix has the property that if one traces out the freedom associated with even a single particle, the resulting reduced density matrix is separable.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Brody, Dorje
Hughston, Lane P
Meier, David M
Date : 21 September 2015
DOI : 10.1088/1751-8113/48/42/425301
Copyright Disclaimer : © 2015 IOP Publishing Ltd
Uncontrolled Keywords : Entanglement; Statistical dependence; GHZ state
Depositing User : Claudio Svaluto
Date Deposited : 18 Sep 2018 13:33
Last Modified : 18 Sep 2018 13:33

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