On a Stroboscopic Approach to Quantum Tomography of Qudits Governed by Gaussian Semigroups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On a Stroboscopic Approach to Quantum Tomography of Qudits Governed by Gaussian Semigroups

Authors:	Jamio?kowski Andrzej

Affiliation:	Andrzej Jamiokowski

Abstract:	In this paper, we discuss the minimal number of observables Q ₁, ..., Q , where expectation values at some time instants t ₁, ..., t _r determine the trajectory of a d-level quantum system (qudit) governed by the Gaussian semigroup $\Phi (t)\rho = \frac{1}{{\sqrt {2\pi t} }}\int\limits_{ - \infty }^\infty {d{\text{ }}s{\text{ }}e^{ - s^2 /(2t)} e^{ - iHs} \rho e^{iHs} }$ . We assume that the macroscopic information about the system in question is given by the mean values E _j(Q _i) = tr(Q _i(t _j)) of n selfadjoint operators Q ₁, ..., Q _n at some time instants t ₁ < t ₂ < ... < t _r, where n < d ²– 1 and r deg (, $\mathbb{L}$ ). Here (, $\mathbb{L}$ ) stands for the minimal polynomial of the generator $\mathbb{L}\rho = - \frac{1}{2}\left {H,\left {H,\rho } \right]} \right]$ of the Gaussian flow (t).

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