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Proceedings of the ... American Control Conference/Proceedings of the American Control Conference

Realtime generation of the bell states by linear-nonlocal measurements and bang-bang control

Thanh Long Vu, Jaspreet Singh Dhupia

Published Jun 1, 2013• 1 citation
Publisher

Abstract

We present a realtime feedback control scheme to deterministically produce the maximally entangled Bell states of two partially separated atoms. The recently introduced concept of SWM- (simultaneous weak measurements)-induced quantum state reduction is generalized to the case of anti-commutative observables. This generalization enables the probabilistic preparation of the Bell states via the SWMs of one linear observable and one nonlocal observable. The deterministic generation of the desired Bell state is then carried out by combining SWM-induced quantum state reduction with feedback control. The realtime implementation of the proposed control scheme is guaranteed by using the time delay control approach in which the computation time of filter-based control is compensated for by the delay time in control input.

DOI
10.1109/acc.2013.6580219

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Quantum control concerns driving quantum systems to the desired properties or states. This objective is hindered by the non-deterministic nature of quantum systems and the symmetric topology of the quantum state space. This paper introduces a coupling Lyapunov functions approach to counter for the stochastic nature of quantum measurements and break the symmetric topology of resulting filter state space. As an example, we then apply it to synthesize non-smooth control almost surely globally stabilizing the desired Bell state-the maximally entangled two-qubit state with various applications. It turns out that this approach enables the short time convergence of the system state, which is essential in the control of entanglement. More interestingly, its combination with the generalized concept of SWM (simultaneous weak measurement)-induced quantum state reduction allows us to deterministically generate the maximally entangled Bell state with little non-local effects. We use numerical illustration to validate the proposed scheme.
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.
Current methods of preparing maximally entangled states in the laboratory need an extremely accurate control of interaction times, requiring sophisticated experimental techniques. Here, we show that such precise control is not necessary when one utilizes short or weak interactions followed by measurements. We present a scheme for the probabilistic generation of Bell states in a pair of cavities, after each has interacted briefly with an atom. The advantage of the scheme, as compared to present schemes, is its low sensitivity to the exact values of experimental parameters such as atomic velocity and coupling strength, in fact, for a large range of parameters, the fidelity of the Bell states generated remains close to unity.
Continuous measurement and feedback hold tremendous potential for producing non-Gaussian quantum states that are useful for quantum communication and computation. We present a new feedback scheme to deterministically produce quantum non-Gaussian states from linear optical elements and feedback. In our scheme, measurement outcomes are used in two different ways. One implements a multiplicative feedback control which produces nonlinear effects in the system. The other stabilizes the system to produce a desired state deterministically. A design example of the multi-loop feedback structure is demonstrated for the deterministic generation of Schrodinger-cat states as the practical use of quantum feedback control.