PT-symmetric Hamiltonians and their application in quantum information

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Croke, Sarah (2015)

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