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arXiv:quant-ph/0106041 · Journal of Modern Optics

The role of auxiliary photons in state discrimination with linear optical devices

Angelo C. M. Carollo, G. Massimo Palma

Published Jun 1, 2002• 6 citations
arXivHTMLPDF

Abstract

The role of auxiliary photons in the problem of identifying a state secretly chosen from a given set of L-photon states is analysed. It is shown that auxiliary photons do not increase the ability to discriminate such states by means of a global measurement using only optical linear elements, conditional transformation and auxiliary photons.

DOI
10.1080/09500340110098370

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The role of auxiliary photons in the problem of identifying a state secretly chosen from a given set of L-photon states is analysed. It is shown that auxiliary photons do not increase the ability to discriminate such states by means of a global measurement using only optical linear elements, conditional transformation and auxiliary photons.
The question of the discrimination of the Bell states of two qudits (i.e., d-dimensional quantum systems) by means of passive linear optical elements and conditional measurements is discussed. A qudit is supposed to be represented by d optical modes containing exactly one photon altogether. From recent results of Calsamiglia it follows that there is no way how to distinguish the Bell states of two qudits for d>2 - not even with the probability of success lower than one - without any auxiliary photons in ancillary modes. Following the results of Carollo and Palma it is proved that it is impossible to distinguish even only one such a Bell state with certainty (i.e., with the probability of success equal to one), irrespective of how many auxiliary photons are involved. However, it is shown that auxiliary photons can help to discriminate the Bell states of qudits with the high probability of success: A Bell-state analyzer based on the idea of linear optics quantum computation that can achieve the probability of success arbitrarily close to one is described. It requires many auxiliary photons that must be first "combined" into entangled states.
In a recent paper, Bennett et al. [Phys. Rev. A 59, 1070 (1999)] have shown the existence of a basis of product states of a bipartite system with manifest nonlocal properties. In particular these states cannot be completely discriminated by means of bilocal measurements. In this paper we propose an optical realization of these states and we will show that they cannot be completely discriminate by means of a global measurement using only optical linear elements, conditional transformation, and auxiliary photons.
In this paper, we present a linear optical scheme for optimal unambiguous discrimination among nonorthogonal quantum states in terms of the multiple-rail and polarization representation of a single photon. In our scheme, discriminated quantum states are expressed by using the spatial degree of freedom of a single photon while the polarization degree of freedom of the single photon is used to act as an auxiliary qubit. The optical components used in our scheme are only passive linear optical elements such as polarizing beam splitters, wave plates, polarizers, single photon detectors, and single photon source.
The possibility of implementing a given photonic projective measurement with linear optics and photon detectors is discussed. This problem can be viewed as a single-shot discrimination of orthogonal pure quantum states. It is particularly shown that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. This means that one can construct any binary projective measurement with these means, but without any nonclassical ancillary state. The statement holds in the asymptotic limit of a large number of these physical resources. To extend this result, we also address the problem of discriminating a simple set of three orthogonal states.