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تسجيل مستخدم جديدPT-symmetric quantum state discrimination
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Suppose that a system is known to be in one of two quantum states, $|psi_1 > $ or $|psi_2 >$. If these states are not orthogonal, then in conventional quantum mechanics it is impossible with one measurement to determine with certainty which state the system is in. However, because a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states, it is always possible to choose this inner product so that the two states $|psi_1 > $ and $|psi_2 > $ are orthogonal. Thus, quantum state discrimination can, in principle, be achieved with a single measurement.
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More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, $mathcal{PT}$. It was sho
wn that if $mathcal{PT}$ is unbroken, energies were, in fact, positive, and unitarity was satisifed. Since quantum mechanics is quantum field theory in 1 dimension, time, it was natural to extend this idea to higher-dimensional field theory, and in fact an apparently viable version of $mathcal{PT}$-invariant quantum electrodynamics was proposed. However, it has proved difficult to establish that the unitarity of the scattering matrix, for example, the Kallen spectral representation for the photon propagator, can be maintained in this theory. This has led to questions of whether, in fact, even quantum mechanical systems are consistent with probability conservation when Greens functions are examined, since the latter have to possess physical requirements of analyticity. The status of $mathcal{PT}$QED will be reviewed in this report, as well as the general issue of unitarity.
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We theoretically demonstrate soliton steering in $mathcal{PT}$-symmetric coupled nonlinear dimers. We show that if the length of the $mathcal{PT}$-symmetric system is set to $2pi$ contrary to the conventional one which operates satisfactorily well on
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Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem associated wit
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