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Physics of Complex Systems

Beyond the standard quantum Zeno effect

Andrey A. Borisov, Anton A. Borisov, T. F. Kamalov

Published Jan 1, 2026• 0 citations
Publisher

Abstract

In this paper, we introduce a functional for the decoherence rate of a quantum system. The quantum system is modeled as a qubit that can be in the state |1〉, |0〉, or in a superposition. In addition to external dephasing and the Zeno attenuation rate acting on the quantum system, resource losses of the measuring channel are taken into account. It is shown that for the parameters corresponding to the limit of ideally frequent measurements in the quantum Zeno effect, the stability of the qubit state is not increased. The existence of optimal values of the measurement time interval and the measurement imperfection parameter is established; at these values, the decoherence rate of the qubit state reaches a minimum. Calculations show that in the case under consideration, the qubit coherence time increases by a factor of 11.5, which ensures an increase in the stability of the qubit state.

DOI
10.33910/2687-153x-2026-7-3-123-130

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In this paper, we introduce a functional for the decoherence rate of a quantum system. The quantum system is modeled as a qubit that can be in the state |1〉, |0〉, or in a superposition. In addition to external dephasing and the Zeno attenuation rate acting on the quantum system, resource losses of the measuring channel are taken into account. It is shown that for the parameters corresponding to the limit of ideally frequent measurements in the quantum Zeno effect, the stability of the qubit state is not increased. The existence of optimal values of the measurement time interval and the measurement imperfection parameter is established; at these values, the decoherence rate of the qubit state reaches a minimum. Calculations show that in the case under consideration, the qubit coherence time increases by a factor of 11.5, which ensures an increase in the stability of the qubit state.
The quantum Zeno effect lies in the suppression of the quantum system’s evolution due to frequent successive measurements, which leads to the inhibition of transitions between quantum states. The paper presumes that a qubit can be found in an excited state |1) or in the non-excited state |0). The work aims to investigate how the quantum Zeno effect can be applied to the stable excited state of a qubit to prevent its spontaneous transition to the state |0). An As atom is exploited as the physical realization of a qubit, and it is suggested to register its quantum state using the scanning probe microscopy methods. The work demonstrates the condition necessary for the occurrence of the quantum Zeno effect in the system under study. Calculation results show that the diameter of the excited-state As atom orbit is 1.5 times larger than the diameter of an unexcited atom orbit. This ratio serves as an experimental criterion for identifying the state of a qubit.
Projective measurements are an essential element of quantum mechanics. In most cases, they cause an irreversible change of the quantum system on which they act. However, measurements can also be used to stabilize quantum states from decay processes, which is known as the quantum Zeno effect (QZE). Here, we demonstrate this effect for the case of a superposition state of a nuclear spin qubit, using an ancilla to perform the measurement. As a result, the quantum state of the qubit is protected against dephasing without relying on an ensemble nature of NMR experiments. We also propose a scheme to protect an arbitrary state by using QZE.
We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation (Nature {\bf 405}, 546 (2000)). The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly {\it enhanced} by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with {\it arbitrary} temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.
Abstract We investigate how the classical correlations between successive actions of a colored dephasing channel affect the decoherence of a two-qubit system. Our calculation shows that the l 1 norm of coherence, the relative entropy of coherence, and the robustness of coherence can be noticeably enhanced by increasing the strength of classical correlations in the whole time interval during which the two qubits pass through the channel, while the coherence weight is enhanced only when exceeds a critical value. Moreover, in the infinite-time limit, all the coherence measures reach their steady values which are determined only by .
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.
We use a non-Markovian approach to study the decoherence dynamics of a qubit in either a low- or high-frequency bath modeling the qubit environment. This is done for two separate cases: either with measurements or without them. This approach is based on a unitary transformation and does not require the rotating-wave approximation. In the case without measurement, we show that, for low-frequency noise, the bath shifts the qubit energy toward higher energies (blue shift), while the ordinary high-frequency cutoff Ohmic bath shifts the qubit energy toward lower energies (red shift). In order to preserve the coherence of the qubit, we also investigate the dynamics of the qubit subject to measurements (quantum Zeno regime) in two cases: low- and high-frequency baths. For very frequent projective measurements, the low-frequency bath gives rise to the quantum anti-Zeno effect on the qubit. The quantum Zeno effect only occurs in the high-frequency-cutoff Ohmic bath, after counterrotating terms are considered. In the condition that the decay rate due to the two kinds of baths are equal under the Wigner-Weisskopf approximation, we find that without the approximation, for a high-frequency environment, the decay rate should be faster (without measurements) or slower (with frequent measurements, in the Zeno regime), compared to the low-frequency bath case. The experimental implementation of our results here could distinguish the type of bath (either a low- or high-frequency one) and protect the coherence of the qubit by modulating the dominant frequency of its environment.