Distance measures are used to quantify the extent to which information is preserved or altered by quantum processes, and thus are indispensable tools in quantum information and quantum computing. In this paper we propose a new distance measure for mixed quantum states, which we call the dynamic distance measure, and we show that it is a proper distance measure. The dynamic distance measure is defined in terms of a measurable quantity, which makes it suitable for applications. In a final section we compare the dynamic distance measure with the well-known Bures distance measure.Distance measures are used to quantify the extent to which information is preserved or altered by quantum processes, and thus are indispensable tools in quantum information and quantum computing. In this paper we propose a new distance measure for mixed quantum states, which we call the dynamic distance measure, and we show that it is a proper distance measure. The dynamic distance measure is defined in terms of a measurable quantity, which makes it suitable for applications. In a final section we compare the dynamic distance measure with the well-known Bures distance measure.

arXiv:1306.2526EntropySep 6, 201312 citations

Quantum dynamics driven by continuous laser fields under measurements: Towards measurement-assisted quantum dynamics control

Michihiko Sugawara

We study quantum system dynamics driven by continuous laser fields under the measurement process. In order to take into account the system transition due to the measurement, we define the superoperator which eliminates the coherence relevant to the measured quantum states. We clarify that the dynamics of the measured states is frozen in the frequent measurement limit, while the space spanned by unmeasured states is isolated from the original system. We also derive the effective Liouvillian which governs incoherent population dynamics under the condition, in which measurements are frequently applied. We apply the formulation to two-level and Lambda-type three-level systems and clarify how the quantum measurements hinder the coherent population dynamics driven by the continuous laser fields in practical examples. Analysis on the laser field amplitude dependency of the final distribution in the t-->infinity limit suggests the possibility of the measurement-assisted quantum control.We study quantum system dynamics driven by continuous laser fields under the measurement process. In order to take into account the system transition due to the measurement, we define the superoperator which eliminates the coherence relevant to the measured quantum states. We clarify that the dynamics of the measured states is frozen in the frequent measurement limit, while the space spanned by unmeasured states is isolated from the original system. We also derive the effective Liouvillian which governs incoherent population dynamics under the condition, in which measurements are frequently applied. We apply the formulation to two-level and Lambda-type three-level systems and clarify how the quantum measurements hinder the coherent population dynamics driven by the continuous laser fields in practical examples. Analysis on the laser field amplitude dependency of the final distribution in the t-->infinity limit suggests the possibility of the measurement-assisted quantum control.

The Journal of Chemical PhysicsNov 22, 200518 citations

Dynamics of ideal quantum measurement of a spin 1 with a Curie-Weiss magnet

Theodorus Maria Nieuwenhuizen

Quantum measurement is a dynamical process of an apparatus coupled to a test system. Ideal measurement of the $z$ -component of a spin- $\frac{1}{2}$ ( $s_z=\pm\frac{1}{2}$ ) has been modeled by the Curie-Weiss model for quantum measurement. Recently, the model was generalized to higher spin and the thermodynamics was solved. Here the dynamics is considered. To this end, the dynamics for spin- $\frac{1}{2}$ case are cast in general notation. The dynamics of the measurement of the $z$ -component of a spin-1 ( $s_z=0,\pm 1$ ) are solved in detail and evaluated numerically. Energy costs of the measurement, which are macroscopic, are evaluated. Generalization to higher spin is straightforward.Quantum measurement is a dynamical process of an apparatus coupled to a test system. Ideal measurement of the $z$-component of a spin-$\frac{1}{2}$ ($s_z=\pm\frac{1}{2}$) has been modeled by the Curie-Weiss model for quantum measurement. Recently, the model was generalized to higher spin and the thermodynamics was solved. Here the dynamics is considered. To this end, the dynamics for spin-$\frac{1}{2}$ case are cast in general notation. The dynamics of the measurement of the $z$-component of a spin-1 ($s_z=0,\pm 1$) are solved in detail and evaluated numerically. Energy costs of the measurement, which are macroscopic, are evaluated. Generalization to higher spin is straightforward.

quant-pharXiv:2603.07153Frontiers in Quantum Science and TechnologyMar 10, 20260 citations

Characterizing Quantum Measurement

ScienceMar 7, 20130 citations

Understanding quantum measurement from the solution of dynamical models

ARMEN E. ALLAHVERDYAN, Roger Balian, Theo M. Nieuwenhuizen

arXiv:1107.2138Physics ReportsNov 14, 2012239 citations

Quantum measurement is a dynamical process of an apparatus coupled to a test system. Ideal measurement of the

z

-component of a spin-

\frac{1}{2}

(

s_z=\pm\frac{1}{2}

) has been modeled by the Curie-Weiss model for quantum measurement. Recently, the model was generalized to higher spin and the thermodynamics was solved. Here the dynamics is considered. To this end, the dynamics for spin-

\frac{1}{2}

case are cast in general notation. The dynamics of the measurement of the

z

-component of a spin-1 (

s_z=0,\pm 1

) are solved in detail and evaluated numerically. Energy costs of the measurement, which are macroscopic, are evaluated. Generalization to higher spin is straightforward.