Generating on-demand maximally entangled states is one of the cornerstones for quantum information processing. Parity measurements can serve to create Bell states and have been implemented via an electronic Mach-Zehnder interferometer among others. However, the entanglement generation is necessarily harmed by measurement-induced dephasing processes in one of the two parity subspaces. In this work, we propose two different schemes of continuous feedback for a parity measurement. They enable us to avoid both the measurement-induced dephasing process and the experimentally unavoidable dephasing, e.g., due to fluctuations of the gate voltages controlling the initialization of the qubits. We show that we can generate maximally entangled steady states in both parity subspaces. Importantly, the measurement scheme we propose is valid for implementation of parity measurements with feedback loops in various solid-state environments.
Generating on-demand maximally entangled states is one of the cornerstones for quantum information processing. Parity measurements can serve to create Bell states and have been implemented via an electronic Mach-Zehnder interferometer among others. However, the entanglement generation is necessarily harmed by measurement-induced dephasing processes in one of the two parity subspaces. In this work, we propose two different schemes of continuous feedback for a parity measurement. They enable us to avoid both the measurement-induced dephasing process and the experimentally unavoidable dephasing, e.g., due to fluctuations of the gate voltages controlling the initialization of the qubits. We show that we can generate maximally entangled steady states in both parity subspaces. Importantly, the measurement scheme we propose is valid for implementation of parity measurements with feedback loops in various solid-state environments.
We propose and analyze a protocol for stabilizing a maximally entangled state of two noninteracting qubits using active state-dependent feedback from a continuous two-qubit half-parity measurement in coordination with a concurrent, noncommuting dynamical decoupling drive. We demonstrate that such a drive can be simultaneous with the measurement and feedback, while also playing a key part in the feedback protocol itself. We show that robust stabilization with near-unit fidelity can be achieved even in the presence of realistic nonidealities, such as time delay in the feedback loop, imperfect state-tracking, inefficient measurements, dephasing from 1/f-distributed qubit-frequency noise, and relaxation. We mitigate feedback-delay error by introducing a forward-state-estimation strategy in the feedback controller that tracks the effects of control signals already in transit. More generally, the steady state is globally attractive without the need for ancillas, regardless of the error state, in contrast to most known feedback and error-correction schemes.
Recent work has shown that use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. Here we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and prove that it is globally optimal for several figures of merit, including maximal concurrence or fidelity, and minimal time to reach a specified concurrence or fidelity. For the full-parity measurement, we derive a protocol for rapid entanglement generation related to that of (C. Hill, J. Ralph, Phys. Rev. A 77, 014305 (2008)), and then map the dynamics of the concurrence of the state to the Bloch vector length of an effective qubit. This mapping allows us to prove several optimality results for feedback protocols with full-parity measurements. We further show that our full-parity protocol transfers entanglement optimally from one qubit to the other amongst all measurement-based schemes. The methods developed here will be useful for deriving feedback protocols and determining their optimality properties in many other quantum systems subject to measurement and unitary operations.
Abstract Recent work has shown that the use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. Here we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and prove that it is globally optimal for several figures of merit, including maximal concurrence or fidelity and minimal time to reach a specified concurrence or fidelity. For the full-parity measurement, we derive a protocol for rapid entanglement generation related to that of (Hill, Ralph, Phys. Rev. A 77 , 014305), and then map the dynamics of the concurrence of the state to the Bloch vector length of an effective qubit. This mapping allows us to prove several optimality results for feedback protocols with full-parity measurements. We further show that our full-parity protocol transfers entanglement optimally from one qubit to the other amongst all measurement-based schemes. The methods developed here will be useful for deriving feedback protocols and determining their optimality properties in many other quantum systems subject to measurement and unitary operations.
We analyze a two-qubit parity measurement based on dispersive readout in circuit quantum electrodynamics. The back action on the qubits has two qualitatively different contributions. One is an unavoidable dephasing in one of the parity subspaces, arising during the transient time of switching on the measurement. The other part is a stochastic rotation of the phase in the same subspace, which persists during the whole measurement. The latter can be determined from the full measurement record using the method of state estimation. Our main result is that the outcome of this phase determination process is independent of the initial state in the state estimation procedure. The procedure can thus be used in a measurement situation where the initial state is unknown. We discuss how this feedback method can be used to achieve a high-fidelity parity measurement for moderate values of the cavity-qubit coupling strength. Finally, we discuss the robustness of the feedback procedure toward errors in the measurement record.
Entanglement generation and preservation is a key task in quantum information processing, and a variety of protocols exist to entangle remote qubits via measurement of their spontaneous emission. We here propose feedback methods, based on monitoring the fluorescence of two qubits and using only local $\ensuremath{\pi}$ pulses for control, to increase the yield and/or lifetime of entangled two-qubit states. Specifically, we describe a protocol based on photodetection of spontaneous emission (i.e., using quantum jump trajectories) which allows for entanglement preservation via measurement undoing, creating a limit cycle around Bell states. We then demonstrate that a similar modification can be made to a recent feedback scheme based on homodyne measurement (i.e., using diffusive quantum trajectories) [L. S. Martin and K. B. Whaley, arXiv:1912.00067] in order to increase the lifetime of the entanglement it creates. Our schemes are most effective for high measurement efficiencies, and the impact of less-than-ideal measurement efficiency is quantified. Our method provides a pathway towards generating and protecting entangled states, complementing others in the literature with similar aims, such that two-qubit entanglement may be used in various applications on demand.
The problem of on-demand generation of entanglement between single-atom qubits via a common photonic channel is examined within the framework of optical interferometry. As expected, for a Mach-Zehnder interferometer with coherent laser beam as input, a high-finesse optical cavity is required to overcome sensitivity to spontaneous emission. We show, however, that with a twin-Fock input, useful entanglement can in principle be created without cavity enhancement. Both approaches require single-photon resolving detectors, and best results would be obtained by combining both cavity feedback and twin-Fock inputs. Such an approach may allow a fidelity of 0.99 using a two-photon input and currently available mirror and detector technology. In addition, we study interferometers based on NOON states, i.e., maximally entangled N-particle states, and show that they perform similarly to the twin-Fock states, yet without the need for high-precision photodetectors. The present interferometrical approach can serve as a universal, scalable circuit element for quantum information processing, from which fast quantum gates, deterministic teleportation, entanglement swapping, etc., can be realized with the aid of single-qubit operations.