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Conference on Lasers and Electro-Optics

Error-free discrimination between two non-orthogonal states

Roger B. M. Clarke, Erling Riis, S. M. Barnett, John Jeffers, Anthony Chefles

Published Aug 29, 2005• 0 citations

Abstract

Summary form only given. It is not possible to discriminate infallibly between non-orthogonal states. Attempts to do so will inevitably result in incorrect or inconclusive results, or both. One limiting case is the Helstrom measurement, which always gives a result, but not necessarily the correct one. The other is the Ivanovic-Dieks-Peres case, which sometimes gives an inconclusive result, but when it provides a discrimination between the states it is always correct. Here we present an experimental demonstration of measurement of this second type. The results were in excellent agreement with the theoretical predictions and demonstrated significant advantages over previous experimental techniques. We used a free-space interferometer constructed from four polarising beam splitters to perform this task. Two nonorthogonal linear polarisations of heavily attenuated pulses of mode-locked laser light formed the states to be discriminated.

DOI: 10.1109/iqec.2000.908070

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Summary form only given. It is not possible to discriminate infallibly between non-orthogonal states. Attempts to do so will inevitably result in incorrect or inconclusive results, or both. One limiting case is the Helstrom measurement, which always gives a result, but not necessarily the correct one. The other is the Ivanovic-Dieks-Peres case, which sometimes gives an inconclusive result, but when it provides a discrimination between the states it is always correct. Here we present an experimental demonstration of measurement of this second type. The results were in excellent agreement with the theoretical predictions and demonstrated significant advantages over previous experimental techniques. We used a free-space interferometer constructed from four polarising beam splitters to perform this task. Two nonorthogonal linear polarisations of heavily attenuated pulses of mode-locked laser light formed the states to be discriminated.

We present a full demonstration of unambiguous state discrimination between nonorthogonal quantum states. Using a free-space interferometer we have realized the optimum quantum measurement scheme for two nonorthogonal states of light, known as the Ivanovic-Dieks-Peres (IDP) measurement. We have gained access to all three possible outcomes of this measurement. All aspects of this generalized measurement scheme, including its superiority over a standard von Neumann measurement, have been demonstrated within 1.5% of the IDP predictions.

Any measurement strategy designed to discriminate between nonorthogonal quantum states will have a finite probability of yielding erroneous or inconclusive results. The lower bounds on these probabilities for conclusive and error-free strategies are given by the Helstrom and Ivanovic–Feres limits respectively. We consider intermediate measurements which interpolate between these extremes and derive a general lower bound on the combination of errors and inconclusive results. We also describe a family of measurement strategies which attains this limit.

We present the results of generalized measurements of optical polarization designed to provide one of three or four distinct outcomes. This has allowed us to discriminate between non-orthogonal polarization states with an error probability that is close to the minimum allowed by quantum theory. The sets of states we have prepared and measured are (i) two non-orthogonal states of linear polarisation, (ii) the trine, consisting of three states of linear polarization separated by 60º and, (iii) the tetrad, consisting of four polarization states (two linear and two elliptical) arranged in a tetrahedron on the Poincaré sphere. This has enabled us to realize the generalized measurements required for (i) optimal unambiguous discrimination between two non-orthogonal polarization states, (ii) discrimination between the three trine states and four tetrad states with minimum probability of error and, (iii) maximizing the mutual information associated with our trine and tetrad measurements and showing that it exceeds the value assocated with the best possible von Neumann measurement. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Strategies to optimally discriminate between quantum states are critical in quantum technologies. We present an experimental demonstration of minimum-error discrimination between entangled states, encoded in the polarization of pairs of photons. Although the optimal measurement involves projection onto entangled states, we use a result of J. Walgate et al. [Phys. Rev. Lett. 85, 4972 (2000)] to design an optical implementation employing only local polarization measurements and feed-forward, which performs at the Helstrom bound. Our scheme can achieve perfect discrimination of orthogonal states and minimum-error discrimination of nonorthogonal states. Our experimental results show a definite advantage over schemes not using feed-forward.

An important task for quantum-information processing is optimal discrimination between two nonorthogonal quantum states, which until now has been realized only optically. Here, we present and compare experimental realizations of optimal quantum measurements for distinguishing between two nonorthogonal quantum states encoded in a single (14)N nuclear spin at a nitrogen-vacancy defect in diamond. Implemented measurement schemes are the minimum-error measurement (known as Helstrom measurement), unambiguous state discrimination using a standard projective measurement, and optimal unambiguous state discrimination [known as Ivanovic-Dieks-Peres (IDP) measurement], which utilizes a three-dimensional Hilbert space. This allows us to benchmark the IDP measurement against the standard projective measurements. Measurement efficiencies are found to be above 80% for all schemes and reach a value of 90% for the IDP measurement.