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arXiv:quant-ph/0603040 · Physical Review A

Parametrization of the feedback Hamiltonian realizing a pure steady state

Naoki Yamamoto

Published Aug 30, 2005• 49 citations
arXivHTMLPDF

Abstract

Feedback control is expected to considerably protect quantum states against decoherence caused by interaction between the system and environment. Especially, Markovian feedback scheme developed by Wiseman can modify the properties of decoherence and eventually recover the purity of the steady state of the corresponding master equation. This paper provides a condition for which the modified master equation has a pure steady state. By applying this condition to a two-qubit system, we obtain a complete parametrization of the feedback Hamiltonian such that the steady state becomes a maximally entangled state.

DOI
10.1103/physreva.72.024104

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Feedback control is expected to considerably protect quantum states against decoherence caused by interaction between the system and environment. Especially, Markovian feedback scheme developed by Wiseman can modify the properties of decoherence and eventually recover the purity of the steady state of the corresponding master equation. This paper provides a condition for which the modified master equation has a pure steady state. By applying this condition to a two-qubit system, we obtain a complete parametrization of the feedback Hamiltonian such that the steady state becomes a maximally entangled state.
We consider the system consisting of two qubits collectively damped,with the output being unit-efficiency measured and subsequently fed back to control the system state.Our primary goal in this paper is (ⅰ) to solve the feedback-modified master equation,(ⅱ) to demonstrate the ability of feedback control based on the solutions,and (ⅲ) to pick out different steady states by choosing different driving strengths and feedback strengths to counteract the effects of both damping and the measurement back-action on the system.We further investigate some properties of the equilibrium steady state,its distribution probability and entanglement vs.the driving and feedback amplitudes.We find that in our feedback model feedback plays a negative role in producing entanglement.
We consider the system consisting of two qubits collectively damped, with the output being unit-efficiency measured and subsequently fed back to control the system state. Our primary goal in this paper is (i) to solve the feedback-modified master equation, (ii) to demonstrate the ability of feedback control based on the solutions, and (iii) to pick out different steady states by choosing different driving strengths and feedback strengths to counteract the effects of both damping and the measurement back-action on the system. We further investigate some properties of the equilibrium steady state, its distribution probability and entanglement vs. the driving and feedback amplitudes. We find that in our feedback model feedback plays a negative role in producing entanglement.
A Markovian open quantum system which relaxes to a unique steady state ${\ensuremath{\rho}}_{\mathrm{ss}}$ of finite rank can be decomposed into a finite physically realizable ensemble (PRE) of pure states. That is, as shown by R. I. Karasik and H. M. Wiseman [Phys. Rev. Lett. 106, 020406 (2011)], in principle there is a way to monitor the environment so that in the long-time limit the conditional state jumps between a finite number of possible pure states. In this paper we show how to apply this idea to the dynamics of a double quantum dot arising from the feedback control of quantum transport, as previously considered by C. P\"oltl, C. Emary, and T. Brandes [Phys. Rev. B 84, 085302 (2011)]. Specifically, we consider the limit where the system can be described as a qubit, and show that while the control scheme can always realize a two-state PRE, in the incoherent-tunneling regime there are infinitely many PREs compatible with the dynamics that cannot be so realized. For the two-state PREs that are realized, we calculate the counting statistics and see a clear distinction between the coherent and incoherent regimes.
We propose an all-electronic technique to manipulate and control interacting quantum systems by unitary single-jump feedback conditioned on the outcome of a capacitively coupled electrometer and, in particular, a single-electron transistor. We provide a general scheme for stabilizing pure states in the quantum system and use an effective Hamiltonian method for the quantum master equation to elaborate on the nature of stabilizable states and the conditions under which state purification can be achieved. The state engineering within the quantum feedback scheme is shown to be linked with the solution of an inverse eigenvalue problem. Two applications of the feedback scheme are presented in detail: (i) stabilization of delocalized pure states in a single charge qubit and (ii) entanglement stabilization in two coupled charge qubits. In the latter example, we demonstrate the stabilization of a maximally entangled Bell state for certain detector positions and local feedback operations.
We consider the system consisting of two qubits collectively damped,with the output being unit-efficiencymeasured and subsequently fed back to control the system state.Our primary goal in this paper is (ⅰ) to solve thefeedback-modified master equation,(ⅱ) to demonstrate the ability of feedback control based on the solutions,and (ⅲ) topick out different steady states by choosing different driving strengths and feedback strengths to counteract the effects ofboth damping and the measurement back-action on the system.We further investigate some properties of the equilibriumsteady state,its distribution probability and entanglement vs.the driving and feedback amplitudes.We find that in ourfeedback model feedback plays a negative role in producing entanglement.
We determine a general upper bound for the steady-state entanglement achievable by continuous feedback for a system of any number of bosonic degrees of freedom. We apply such a bound to the specific case of parametric interactions--the most common practical way to generate entanglement in quantum optics--and single out optimal feedback strategies that achieve the maximal entanglement. We also consider the case of feedback schemes entirely restricted to local operations and compare their performance to the optimal, generally nonlocal, schemes.