TY - JOUR

T1 - Quantum state transformation by optimal projective measurements

AU - Wang, Yaoxiong

AU - Wu, Rebing

AU - Chen, Xin

AU - Ge, Yunjian

AU - Shi, Junhui

AU - Rabitz, Herschel Albert

AU - Shuang, Feng

PY - 2011/1/1

Y1 - 2011/1/1

N2 - This paper explores the optimal control of quantum state transformations in finite-dimensional quantum systems by a sequence of non-selective projective measurements. In our schemes, the projectors of each measurement are represented by a unitary matrix. Through variational analysis of the objective function over the unitary group, the necessary condition for a measurement sequence to be a critical point of the underlying state transformation objective is found to be a highly symmetric form as a chain of equalities. Since these equality relations are generally difficult to solve analytically, we focus on the fundamental case employing a single measurement, in which analytical solutions for maximizing the state transformation probability are found between pure states, or between mixed and pure states, or between orthogonal mixed states under two typical type of measurements. These results suggest a new way of designing optimal quantum dynamics control strategies by quantum measurements.

AB - This paper explores the optimal control of quantum state transformations in finite-dimensional quantum systems by a sequence of non-selective projective measurements. In our schemes, the projectors of each measurement are represented by a unitary matrix. Through variational analysis of the objective function over the unitary group, the necessary condition for a measurement sequence to be a critical point of the underlying state transformation objective is found to be a highly symmetric form as a chain of equalities. Since these equality relations are generally difficult to solve analytically, we focus on the fundamental case employing a single measurement, in which analytical solutions for maximizing the state transformation probability are found between pure states, or between mixed and pure states, or between orthogonal mixed states under two typical type of measurements. These results suggest a new way of designing optimal quantum dynamics control strategies by quantum measurements.

KW - Optimal control

KW - Projective measurement

KW - Quantum control

KW - Quantum measurement

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U2 - 10.1007/s10910-010-9755-6

DO - 10.1007/s10910-010-9755-6

M3 - Article

AN - SCOPUS:78751704346

VL - 49

SP - 507

EP - 519

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 2

ER -