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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Using entanglement in photonic qubit measurements

Geoff J. Pryde, Jeremy L. O’Brien, Andrew G. White, Timothy C. Ralph, Stephen D. Bartlett, Howard M. Wiseman

Published Aug 18, 2005• 0 citations
Publisher

Abstract

Two-qubit entangling gates allow the realization of new types of generalized quantum measurement. We discuss, and use photonic systems to demonstrate, two instances of this: two-qubit entangling measurements realizing superior discrimination of locally prepared two-qubit quantum states relative to what is achievable with local measurements and classical communication; and nondestructive weak measurements with postselection, leading to quantum weak values.

DOI
10.1117/12.616166

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Two-qubit entangling gates allow the realization of new types of generalized quantum measurement. We discuss, and use photonic systems to demonstrate, two instances of this: two-qubit entangling measurements realizing superior discrimination of locally prepared two-qubit quantum states relative to what is achievable with local measurements and classical communication; and nondestructive weak measurements with postselection, leading to quantum weak values.
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We propose a new protocol for the weak measurement of any observable with remote pre and postselections. We show that if two parties share a pure entangled state, then by using local operations and classical communication they can preselect and postselect at distant locations leading to the weak value of an observable as a shift in the pointer of the apparatus at one location in the process of the weak measurement. This can be achieved with either sharing of a pure maximally or non-maximally entangled state. We generalize the protocol for realizing the weak value of any observable with remote pre and postselection of mixed states. Finally, we show how the weak value is modified in the remote pre and postselection setting if Alice and Bob share a mixed entangled state.
Quantum weak values arise when the mean outcome of a weak measurement made on certain preselected and postselected quantum systems goes beyond the eigenvalue range for a quantum observable. Here, we propose how to determine quantum weak values for superpositions of states with a macroscopically or mesoscopically distinct mode number, that might be realized as two-mode Bose-Einstein condensate or photonic NOON states. Specifically, we give a model for a weak measurement of the Schwinger spin of a two-mode NOON state, for arbitrary NNN. The weak measurement arises from a nondestructive measurement of the two-mode occupation number difference, which for atomic NOON states might be realized via phase contrast imaging and the ac Stark effect using an optical meter prepared in a coherent state. The meter-system coupling results in an entangled cat-state. By subsequently evolving the system under the action of a nonlinear Josephson Hamiltonian, we show how postselection leads to quantum weak values, for arbitrary NNN. Since the weak measurement can be shown to be minimally invasive, the weak values provide a useful strategy for a Leggett-Garg test of NNN-scopic realism.