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.

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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.

We discuss the prospect of $\mathcal{PT}$-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 $\mathcal{PT}$-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 $\mathcal{PT}$-symmetric quantum theory can outperform standard quantum theory. The most recent of these is the suggestion to use $\mathcal{PT}$-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 $\mathcal{PT}$-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.