Dynamical and kinematic bounds for quantum metrology in open systems

Mankei Tsang

S. Alipour, Mohammad Mehboudi, A. T. Rezakhani

Estimation of parameters is a pivotal task throughout science and technology. The quantum Cramér-Rao bound provides a fundamental limit of precision allowed to be achieved under quantum theory. For closed quantum systems, it has been shown how the estimation precision depends on the underlying dynamics. Here, we propose a general formulation for metrology scenarios in open quantum systems, aiming to relate the precision more directly to properties of the underlying dynamics. This feature may be employed to enhance an estimation precision, e.g., by quantum control techniques. Specifically, we derive a Cramér-Rao bound for a fairly large class of open system dynamics, which is governed by a (time-dependent) dynamical semigroup map. We illustrate the utility of this scenario through three examples.

Adolfo del Campo, I. L. Egusquiza, Martin Bodo Plenio +1 more

Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics, and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive, and trace preserving evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the role of the Hamiltonian being played by the adjoint of the generator of the dynamical semigroup. The utility of the new bound is exemplified in different scenarios, ranging from the estimation of the passage time to the determination of precision limits for quantum metrology in the presence of dephasing noise.

Seyed Mohammad Hosseiny, Jamileh Seyed‐Yazdi, Milad Norouzi +1 more

J.V. Leahy, S. G. Schirmer

Girardeau et al. (1998) derived kinematical bounds on the optimization of observables for mixed-state quantum systems and showed that they are dynamically realizable if the system is completely controllable. In this paper the problem of finding dynamically realizable bounds for systems that are not completely controllable is addressed. We derive such bounds for systems whose dynamics can be decomposed into subspace dynamics. We also study systems that are not decomposable yet fail to be completely controllable. For these systems, the question of dynamical realizability of the kinematical bounds depends on the accessibility of the target states for which the expectation value of the observable assumes its kinematical maximum.

Andrew N. Jordan, Shengshi Pang, Jing Yang