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SICE Annual Conference (SICE)

Generation of quantum entangled state via continuous feedback control

Tomonari Abe, Koji Tsumura

Published Aug 1, 2008• 11 citations
Publisher

Abstract

In this paper, we consider a stabilization problem of a two-qubit system under continuous measurement. Our objective is to stabilize two types of quantum entangled state which play an important role in quantum information technology. In this paper, we show that the global stabilization at a specific quantum entangled state by continuous inputs is possible. An effectiveness of the control input is verified by numerical simulation.

DOI
10.1109/sice.2008.4655235

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In this paper, we consider a stabilization problem of a two-qubit system under continuous measurement. Our objective is to stabilize two types of quantum entangled state which play an important role in quantum information technology. In this paper, we show that the global stabilization at a specific quantum entangled state by continuous inputs is possible. An effectiveness of the control input is verified by numerical simulation.
A pair of spins is the most simple quantum system that can possess entanglement, a non-classical property playing an essential role in quantum information technologies. In this paper, feedback control problems of the two-spin system conditioned on a continuous measurement are considered. In order to make some useful formulas in stochastic control theory directly applicable, we first derive a two-dimensional description of the system. We then prove that a feedback controller stabilizes an entangled state of the two spins almost globally with probability one. Furthermore, it is shown that another entangled state, which corresponds to a non-equilibrium point of the dynamics, is stabilized via feedback in the sense that the expectation of the distance from the target can be made arbitrarily small.
Bell states play a central role in the field of quantum information. For two‐qubit systems, this study proposes a new non‐smooth control strategy within the theoretical framework of quantum continuous measurement, and achieves global feedback stabilisation in any target Bell state. For a target Bell state, the authors select one measured observable and two control channels, where the control law associated with one channel is kept constant. They design a non‐smooth control law for the other control channel, and prove the stability of the whole closed‐loop system. Some simulation experiments show that the control strategy in this paper has a good control effect.
In this paper, a stabilization problem of quantum spin systems in general dimension under continuous measurement is considered and it is shown that the global stabilization at an eigenstate by continuous inputs is possible. Quantum states of spin systems under continuous measurement by mutual interference with laser beams can be continuously estimated by quantum filtering and with its information, the intension of magnetic field, which is applied to atoms, can be controlled. Because of the structural symmetry of the nonlinear dynamics, this stabilization problem by continuous feedback has been considered to be hard and recently a switching rule was introduced which attains the global stability. Our proposing control rule is the sum of two terms: a term which attracts the quantum states to a target and the other term which draw apart from the other equilibrium points. The proof is done by the strict analysis on the sample paths of solutions of a stochastic differential equation. We also show numerical examples to demonstrate the efficiency of the proposing control rule.
In this chapter, we introduce our recent results on feedback control of quantum spin systems. The quantum systems are composed of atoms held in a cavity under continuous measurement by photons and a magnetic field that is applied to atoms for controlling the quantum states. The quantum states can be estimated by quan- tum filtering through the continuous measurement, and the intension of magnetic field is controlled depending on the estimations. We show that our proposing control input attains the global stability on the assigned eigenstates.
Bell states are the maximally entangled states in two-qubit quantum systems, and play a significant role in quantum computation and quantum communication. Feedback control of stochastic quantum systems usually suffers from time-delay problems caused by the computation time for filter states and the control input. This paper addresses the preparation of Bell states in two-qubit systems with a constant delay time. A Lyapunov method is used to design a switching control law and a constant is introduced to compensate for the computation time of the estimated states and the feedback control input, thereby stabilizing the target Bell state globally. Numerical results show the effectiveness of the proposed control law.
In this paper, we consider a two-qubit system undergoing continuous-time measurements. In presence of multiple channels, we provide sufficient conditions on the continuous feedback control law ensuring almost sure exponential convergence to a predetermined Bell state. This is obtained by applying stochastic tools, Lyapunov methods and geometric control tools. With one channel, we establish asymptotic convergence towards a predetermined Bell state. In both cases, we provide explicit expressions of feedback control laws satisfying the above-mentioned conditions. Finally, we demonstrate the effectiveness of our methodology through numerical simulations.