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Physical Review A

Real-time deterministic generation of maximally entangled two-qubit and three-qubit states via bang-bang control

Thanh Long Vu, Shuzhi Sam Ge, Chang Chieh Hang

Published Jan 30, 2012• 24 citations
Publisher

Abstract

We exploit the notion of SWM- (simultaneous-weak-measurements)-induced quantum state reduction, enabling the use of measurement backaction to produce the desired quantum states. The probabilistic generation of maximally entangled Bell states and the $|\mathrm{GHZ}\ensuremath{\rangle}$ (Greenberger-Horne-Zeilinger) state are then performed as a consequence of this notion. By combining SWM-induced quantum state reduction with feedback control, we are able to deterministically generate any desired Bell state as well as the $|\mathrm{GHZ}\ensuremath{\rangle}$ state, without the knowledge of the initial state. The control-computation time is compensated for by the delay time in the time-delay bang-bang control, through which the real-time implementation of the control scheme is guaranteed. The effectiveness of the proposed scheme is illustrated numerically.

DOI
10.1103/physreva.85.012332

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We exploit the notion of SWM- (simultaneous-weak-measurements)-induced quantum state reduction, enabling the use of measurement backaction to produce the desired quantum states. The probabilistic generation of maximally entangled Bell states and the ∣GHZ\ensuremath⟩|\mathrm{GHZ}\ensuremath{\rangle}∣GHZ\ensuremath⟩ (Greenberger-Horne-Zeilinger) state are then performed as a consequence of this notion. By combining SWM-induced quantum state reduction with feedback control, we are able to deterministically generate any desired Bell state as well as the ∣GHZ\ensuremath⟩|\mathrm{GHZ}\ensuremath{\rangle}∣GHZ\ensuremath⟩ state, without the knowledge of the initial state. The control-computation time is compensated for by the delay time in the time-delay bang-bang control, through which the real-time implementation of the control scheme is guaranteed. The effectiveness of the proposed scheme is illustrated numerically.
We exploit our recently introduced concept of SWM- (simultaneous weak measurements)-induced quantum state reduction, enabling the use of multiple measurements to produce the desired quantum states. The probabilistic generation of the maximally entangled Bell states is then performed as a consequence of this concept. By combining SWM-induced quantum state reduction with feedback control, we are able to deterministically generate any desired Bell state, without the knowledge of initial state. The control-computation time is compensated for by the delay time in the time delay bang-bang control, through which the real-time implementation of the control scheme is guaranteed. The effectiveness of the proposed scheme is illustrated numerically.
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.
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.
We report the deterministic creation of maximally entangled three-qubit states-specifically the Greenberger-Horne-Zeilinger (GHZ) state and the W state-with a trapped-ion quantum computer. We read out one of the qubits selectively and show how GHZ and W states are affected by this local measurement. Additionally, we demonstrate conditional operations controlled by the results from reading out one qubit. Tripartite entanglement is deterministically transformed into bipartite entanglement by local operations only. These operations are the measurement of one qubit of a GHZ state in a rotated basis and, conditioned on this measurement result, the application of single-qubit rotations.
We consider the task of deterministically entangling two remote qubits using joint measurement and feedback, but no directly entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average-sense locally optimal feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols that can deterministically create maximal entanglement: a semiclassical feedback protocol for low-efficiency measurements and a quantum feedback protocol for high-efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can be modeled by a Wiseman-Milburn feedback master equation, which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics and we exploit this feature to derive a superior hybrid protocol for arbitrary nonunit measurement efficiency that switches between quantum and semiclassical protocols. Finally, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.