It is a fundamental consequence of the superposition principle for quantum states that there must exist nonorthogonal states, that is, states that, although different, have a nonzero overlap. This finite overlap means that there is no way of determining with certainty in which of two such states a given physical system has been prepared. We review the various strategies that have been devised to discriminate optimally between nonorthogonal states and some of the optical experiments that have been performed to realize these

We present an approach to building interferometric telescopes using ideas of quantum information. Current optical interferometers have limited baseline lengths, and thus limited resolution, because of noise and loss of signal due to the transmission of photons between the telescopes. The technology of quantum repeaters has the potential to eliminate this limit, allowing in principle interferometers with arbitrarily long baselines.

We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result. For linearly dependent sets an analogous measurement is one which allows us to be as confident as possible that when a given state is identified on the basis of the measurement result, it is indeed the correct state.

Complex vectorial light fields, non-separable in their polarization and spatial degree of freedom, are of relevance in a wide variety of fields encompassing microscopy, metrology, communication and topological studies. Controversially, they have been suggested as analogues to quantum entanglement, raising fundamental questions on the relation between non-separability in classical systems, and entanglement in quantum systems. Here we propose and demonstrate basis-independent tomography of arbitrary vectorial light fields by relating their concurrence to spatially resolved Stokes projections. We generate vector fields with controllable non-separability using a novel compact interferometer that incorporates a digital micro-mirror device (DMD), thus offering a holistic toolbox for the generation and quantitative analysis of arbitrary vectorial light fields.

Many important techniques for investigating the properties of extragalactic radio sources, such as spectral-index and rotation-measure mapping, involve the comparison of images at two or more frequencies. In the case of radio interferometric data, this can be done by comparing the CLEAN maps obtained at the different frequencies. However, intrinsic differences in images due to the frequency dependence of the radio emission can be distorted by additional differences that arise due to source variability (if the data to be compared are obtained at different times), image misalignment, and the frequency dependence of the sensitivity to weak emission and the angular resolution provided by the observations (the resolution of an interferometer depends on the lengths of its baselines in units of the observing wavelength). These effects must be corrected for as best as possible before multifrequency data comparison techniques can be applied. We consider the origins for the aforementioned factors, outline the standard techniques used to overcome these difficulties, and describe in detail a technique developed by us, based on the cross-correlation technique widely used in other fields, to correct for misalignments between maps at different frequencies

We provide a simple proof for the necessity of conditions for discriminating with minimum error between a known set of quantum states.

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.

We discuss the prospect of PT -symmetric Hamiltonians finding applications in quantum information science, and conclude that such evolution is unlikely to provide any benefit over existing techniques. Although it has been known for some time that PT -symmetric quantum theory, when viewed as a unitary theory, is exactly equivalent to standard quantum mechanics, proposals continue to be put forward for schemes in which PT -symmetric quantum theory can outperform standard quantum theory. The most recent of these is the suggestion to use PT -symmetric Hamiltonians to perform an exponentially fast database search, a task known to be impossible with a quantum computer. Further, such a scheme has been shown to apparently produce effects in conflict with fundamental information-theoretic principles, such as the impossibility of superluminal information transfer, and the invariance of entanglement under local operations. In this paper we propose three inequivalent experimental implementations of PT -symmetric Hamiltonians, with careful attention to the resources required to realize each such evolution. Such an operational approach allows us to resolve these apparent conflicts, and evaluate fully schemes proposed in the literature for faster time evolution and state discrimination.