We present an experimental realization of discrimination between non-orthogonal polarization states at the Helstrom bound for minimum probability of error. The experiment was performed with highly attenuated laser light with a mean number of about 0·1 photons per pulse.
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.
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.
We present the first experimental demonstration of the maximum confidence measurement strategy for quantum state discrimination. Applying this strategy to an arbitrary set of states assigns to each input state a measurement outcome which, when realized, gives the highest possible confidence that the state was indeed present. The theoretically optimal measurement for discriminating between three equiprobable symmetric qubit states is implemented in a polarization-based free-space interferometer. The maximum confidence in the measurement result is 2/3. This is the first explicit demonstration that an improvement in the confidence over the optimal minimum error measurement is possible for linearly dependent states.
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.