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arXiv:quant-ph/9808007 · Physical Review A

Entanglement of projection and a new class of quantum erasers

Robert Garisto, Lucién Hardy

Published Aug 1, 1999• 27 citations
arXivHTMLPDF

Abstract

We define a new measurement of entanglement, the entanglement of projection, and find that it is natural to write the entanglements of formation and assistance in terms of it. Our measure allows us to describe a new class of quantum erasers which restore entanglement rather than just interference. Such erasers can be implemented with simple quantum computer components. We propose realistic optical versions of these erasers.

DOI
10.1103/physreva.60.827

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We define a new measurement of entanglement, the entanglement of projection, and find that it is natural to write the entanglements of formation and assistance in terms of it. Our measure allows us to describe a new class of quantum erasers which restore entanglement rather than just interference. Such erasers can be implemented with simple quantum computer components. We propose realistic optical versions of these erasers.
Interaction with a measuring apparatus can cause otherwise interfering paths of a particle to become distinguishable. Under some conditions, however, it is possible to ``erase'' the distinguishability, thereby restoring interference. The concept of a quantum eraser is useful for understanding the role of entanglement in interference. Several attempts to investigate the phenomenon have been made using the correlated photons from spontaneous parametric down-conversion. However, none of the experiments previously performed in connection with quantum erasure has provided an optimal demonstration. We propose three improved down-conversion schemes, each of which satisfies all the criteria for a true quantum eraser. As the proposed schemes are all modifications or combinations of previously completed experiments, they are deemed to be feasible.
We have implemented an optical quantum eraser with the aim of studying this phenomenon in the context of state discrimination. An interfering single photon is entangled with another one serving as a which-path marker. As a consequence, the visibility of the interference as well as the which-path information are constrained by the overlap (measured by the inner product) between the which-path marker states, which in a more general situation are non-orthogonal. In order to perform which-path or quantum eraser measurements while analysing non-orthogonal states, we resort to a probabilistic method for the unambiguous modification of the inner product between the two states of the which-path marker in a discrimination-like process.
The newfound importance of ``entanglement as a resource'' in quantum computation and quantum communication compels us to quantify it in as many distinct ways as possible. Here we explore a new measure of entanglement for mixed quantum states of bipartite systems, which we name the Entanglement of Assistance. We show it to be the maximum average entanglement of all pure-state ensembles consistent with the given density matrix. In this sense, the Entanglement of Assistance is a quantity directly dual to the more standard Entanglement of Formation. With the help of lower and upper bounds, we calculate the Entanglement of Assistance for a few cases and use these results to show that it possesses the surprising property of superadditivity. We believe that this may shed some light on the question of additivity for the Entanglement of Formation.