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Ukrainian Journal of Physics

Multiple Joint Weak Measurements as a Way to Suppress the Decoherence

O. M. Konovalenko, Z. А. Maizelis

Published Aug 11, 2025• 1 citation
Publisher

Abstract

We apply the multiple, equally spaced in time, weak measurements, to the two-qubit entangled system to decrease the rate of its decoherence, i.e., to prevent the decrease of the off-diagonal elements. The scheme is similar to the Quantum Zeno Effect, but differs by the frequency of the measurements. While the conventional Quantum Zeno Effect assumes rapid measurements which mitigates the Hamiltonian dynamics, the proposed method makes use of entanglement between the qubits to decrease the decoherence rate. We will show that it allows us to partially suppress the decoherence in the case of Lindblad evolution.

DOI
10.15407/ujpe70.8.516

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We apply the multiple, equally spaced in time, weak measurements, to the two-qubit entangled system to decrease the rate of its decoherence, i.e., to prevent the decrease of the off-diagonal elements. The scheme is similar to the Quantum Zeno Effect, but differs by the frequency of the measurements. While the conventional Quantum Zeno Effect assumes rapid measurements which mitigates the Hamiltonian dynamics, the proposed method makes use of entanglement between the qubits to decrease the decoherence rate. We will show that it allows us to partially suppress the decoherence in the case of Lindblad evolution.
We propose a method to suppress decoherence in entangled systems by applying the series of joint measurements. While the standard Quantum Zeno Effect approach can only compensate for the slow enough Hamiltonian dynamics of the quantum system, the characteristic frequencies of the thermal bath contacting system may be greater than the maximal achievable frequencies of measurements. In this case, they cannot cancel out non-Hamiltonian evolution leading to the decoherence. We propose to use entanglement between the qubits of a quantum register to mitigate the negative effects of the interaction with the thermal bath, even with the lower frequencies of measurement. We show that even though this protocol does not lead to a complete freezing of the initial state, it still allows effective preservation of the entanglement in the system.
We examine the appearance of Zeno and anti-Zeno effects (Misra and Sudarshan 1977 J. Math. Phys. 18 756; Kofman and Kurizki 2000 Nature 405 546; Kofman and Kurizki 1996 Phys. Rev. A 54 3750; Facchi et al 2001 Phys. Rev. Lett. 86 2699) in the entanglement dynamics of two qubits off-resonantly coupled to the same lossy cavity when the unitary evolution of the system is interrupted by repeated projective measurements. We describe in detail these quantum effects by comparing the measurement-induced coarse-grained dynamics to the entanglement evolution in the absence of measurements in several scenarios (Francica et al 2009 Phys. Rev. A 79 032310). In particular, we examine the strong and weak coupling regimes, the role of the relative coupling strengths between the two qubits and the reservoir and the effect of the detuning from the main cavity frequency. We show that the anti-Zeno effect can occur in the entanglement dynamics when the qubit frequencies are detuned from the main reservoir frequency. Furthermore, we find that Zeno and anti-Zeno effects can even appear sequentially many times as a function of the interval between the measurements. Finally, we show that, in the off-resonant regime, we can preserve the entanglement using the quantum Zeno effect more efficiently than in the resonant limit (Maniscalco et al 2008 Phys. Rev. Lett. 100 090503), even if, in this case, no sub-radiant state exists.
We have studied quantum coherent oscillations of two qubits under continuous measurement by a symmetrically coupled mesoscopic detector. The analysis is based on a Bayesian formalism that is applicable to individual quantum systems. Measurement continuously collapses the two-qubit system to one of the subspaces of the Bell basis. For a detector with linear response this corresponds to measurement of the total spin of the qubits. In the other extreme of purely quadratic response the operator ${\ensuremath{\sigma}}_{y}^{1}{\ensuremath{\sigma}}_{y}^{2}+{\ensuremath{\sigma}}_{z}^{1}{\ensuremath{\sigma}}_{z}^{2}$ is measured. In both cases, collapse naturally leads to spontaneous entanglement which can be identified by measurement of the power spectrum and/or the average current of the detector. Asymmetry between the two qubits results in evolution between the different measurement subspaces. However, when the qubits are even weakly coupled to the detector, a kind of quantum Zeno effect cancels the gradual evolution and replaces it with rare, abrupt switching events. We obtain the asymptotic switching rates for these events and confirm them with numerical simulations. We show how such switching affects the observable power spectrum on different time scales.
The quantum Zeno effect is a distinctive phenomenon in quantum mechanics, describing the nontrivial effect of frequent projective measurements on hindering the evolution of a quantum system. However, when subjected to environmental noise, the quantum system may dissipate, and the quantum Zeno effect no longer works. This research starts from the physical mechanism for the decay of the quantum Zeno effect in the presence of noise and investigates the effect of coherent quantum controls on mitigating the decrease of the survival probability that the system stays in the initial state induced by the noise. We derive the decay rate of the survival probability with and without coherent quantum controls in general, and show that when the frequency of the projective measurements is large but finite, proper coherent controls by sufficiently strong Hamiltonians can be designed to decrease the decay rate of the survival probability. A two-level quantum system suffering from typical unitary and nonunitary noise is then considered to demonstrate the effect of the proposed coherent quantum control scheme in protecting the quantum Zeno effect against the noise. The decay rate of the survival probability is obtained in the presence of noise, and the control Hamiltonian is further optimized analytically to minimize the decay rate by a variational approach. The evolution paths of the quantum system with the optimal coherent controls are illustrated numerically for different scenarios to explicitly show how the coherent control scheme works in lowering the decay of survival probability.
We examine the quantum Zeno effect on the dynamics of quantum discord in two initially entangled qubits which are subjected to frequent measurements via decoherent coupling with independent reservoirs. The links between characteristic parameters such as system bias, measurement time duration, strength of initial entanglement between the two qubit systems and the dynamics of quantum discord are examined in the case of two initial state configurations. For weak or unsharp measurements, the quantum discord, which is an intrinsically distinct entity from concurrence, serves as a reliable indicator of the crossover point in Zeno to anti-Zeno transitions. However at highly precise quantum measurements, the monitoring device interferes significantly with the evolution dynamics of the monitored system, and the quantum discord yields indeterminate values in a reference frame where the observer is not an active constituent of the subsystems.
At first glance it is surprising that there are papers describing experiments fitting to the quantum Zeno effect and on the other hand there are very similar experiments which seem to contradict to the quantum Zeno effect.Now the quantum Zeno effect should be related to a suppression of the time evolution in case of an "almost continuous measurement".What does that mean?In this paper we discuss two possibilities to give a precise notion of such a suppression.That completes the considerations of the quantum Zeno scheme in our previous paper (K.-H.Fichtner and K. Inoue, 2013).