General linear-optical quantum state generation scheme: Applications to maximally path-entangled states

N. M. VanMeter, P. Lougovski, D. B. Uskov, K. Kieling, J. Eisert, and Jonathan P. Dowling
Phys. Rev. A 76, 063808 – Published 12 December 2007

Abstract

We introduce schemes for linear-optical quantum state generation. A quantum state generator is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and postselection using photon counters. We show that this device can be concisely described in terms of polynomial equations and unitary constraints. We illustrate the power of this language by applying the Gröbner-basis technique along with the notion of vacuum extensions to solve the problem of how to construct a quantum state generator analytically for any desired state, and use methods of convex optimization to identify bounds to success probabilities. In particular, we disprove a conjecture concerning the preparation of the maximally path-entangled n,0+0,n (NOON) state by providing a counterexample using these methods, and we derive a new upper bound on the resources required for NOON-state generation.

  • Figure
  • Received 2 January 2007

DOI:https://doi.org/10.1103/PhysRevA.76.063808

©2007 American Physical Society

Authors & Affiliations

N. M. VanMeter1, P. Lougovski1, D. B. Uskov1,2, K. Kieling3,4, J. Eisert3,4, and Jonathan P. Dowling1

  • 1Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803, USA
  • 2Department of Physics, Tulane University, 2001 Percival Stern Hall, New Orleans, Louisiana 70118, USA
  • 3Institute for Mathematical Sciences, Imperial College London, London SW7 2PE, United Kingdom
  • 4QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom

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Issue

Vol. 76, Iss. 6 — December 2007

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