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arXiv:quant-ph/0202076 · Journal of Geometry and Physics

The pure state space of quantum mechanics as Hermitian symmetric space

R. Cirelli, Matteo Gatti, A. Manià

Published Jan 21, 2003• 16 citations
arXivHTMLPDF
DOI
10.1016/s0393-0440(01)00031-6

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If the system is known to be in one of two non-orthogonal quantum states, ∣ψ1⟩|ψ_1\rangle∣ψ1​⟩ or ∣ψ2⟩|ψ_2\rangle∣ψ2​⟩, PT\mathcal{PT}PT-symmetric quantum mechanics can discriminate them, \textit{in principle}, by a single measurement. We extend this approach by combining PT\mathcal{PT}PT-symmetric and Hermitian measurements and show that it's possible to distinguish an arbitrary number of pure quantum states by an appropriate choice of the parameters of PT\mathcal{PT}PT-symmetric Hamiltonian.
If the system is known to be in one of two non-orthogonal quantum states, ∣ψ1⟩|\psi_1\rangle∣ψ1​⟩ or ∣ψ2⟩|\psi_2\rangle∣ψ2​⟩, PT\mathcal{PT}PT-symmetric quantum mechanics can discriminate them, \textit{in principle}, by a single measurement. We extend this approach by combining PT\mathcal{PT}PT-symmetric and Hermitian measurements and show that it's possible to distinguish an arbitrary number of pure quantum states by an appropriate choice of the parameters of PT\mathcal{PT}PT-symmetric Hamiltonian.