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Semigroup of positive maps for qudit states and entanglement in tomographic probability representation

Vladimir I. Man’ko, Giuseppe Marmo, Alberto Simoni +1 more

arXiv:0807.0329Physics Letters ASep 7, 200825 citations

Characterization of Gaussian Quantum Markov Semigroups

Damiano Poletti

Springer proceedings in mathematics & statisticsJan 1, 20224 citations

Quantum state tomography of spatial-mode qudits

Nathan K. Langford, R. B. Dalton, M. Harvey +4 more

Dec 1, 20030 citations

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

Andrzej Jamiołkowski

In this paper, we discuss the minimal number η of observables Q1,…, Qη, where expectation values at some time instants t1,…,tr determine the trajectory of a d-level quantum system (“qudit”) governed by the Gaussian semigroup [Formula: see text] We assume that the macroscopic information about the system in question is given by the mean values [Formula: see text] of n selfadjoint operators Q1,…, Qn at some time instants t1< t2 < … <tr, where n < d2 − 1 and r ≤ deg μ(λ, 𝕃). Here μ(λ, 𝕃) stands for the minimal polynomial of the generator [Formula: see text] of the Gaussian flow Φ(t).In this paper, we discuss the minimal number η of observables Q1,…, Qη, where expectation values at some time instants t1,…,tr determine the trajectory of a d-level quantum system (“qudit”) governed by the Gaussian semigroup [Formula: see text] We assume that the macroscopic information about the system in question is given by the mean values [Formula: see text] of n selfadjoint operators Q1,…, Qn at some time instants t1< t2 < … <tr, where n < d2 − 1 and r ≤ deg μ(λ, 𝕃). Here μ(λ, 𝕃) stands for the minimal polynomial of the generator [Formula: see text] of the Gaussian flow Φ(t).

arXiv:quant-ph/0408171Open Systems & Information DynamicsMar 1, 200413 citations

A STROBOSCOPIC APPROACH TO QUANTUM TOMOGRAPHY

Andrzej Jamiołkowski

Mar 1, 20061 citation

Gaussian Dynamical Quantum State Tomography

Hjalmar Rall

Standard quantum state tomography assumes sufficient control of a system to measure an informationally complete set of observables. Dynamical quantum state tomography (DQST) presents an alternative: given a system with known dynamics and a single fixed observable, it almost always suffices to control only the time at which each i.i.d. copy of the system is measured. This work presents an analogous scheme for tomography of multi-mode Bosonic Gaussian states undergoing Gaussian evolution, using a fixed single-mode homodyne measurement and only assuming control of the time of measurement. I prove that the scheme enables tomography for all discrete homogenous Gaussian evolutions and Gaussian quantum dynamical semigroups except for a null set which includes unitary evolution. When the state is known to be pure, a smaller number of measurement times is shown to be sufficient.Standard quantum state tomography assumes sufficient control of a system to measure an informationally complete set of observables. Dynamical quantum state tomography (DQST) presents an alternative: given a system with known dynamics and a single fixed observable, it almost always suffices to control only the time at which each i.i.d. copy of the system is measured. This work presents an analogous scheme for tomography of multi-mode Bosonic Gaussian states undergoing Gaussian evolution, using a fixed single-mode homodyne measurement and only assuming control of the time of measurement. I prove that the scheme enables tomography for all discrete homogenous Gaussian evolutions and Gaussian quantum dynamical semigroups except for a null set which includes unitary evolution. When the state is known to be pure, a smaller number of measurement times is shown to be sufficient.

quant-pharXiv:2602.18044Feb 23, 20260 citations

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

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

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