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arXiv:2606.04681

Protecting Quantum States via the Super-Zeno Effect and Anticoherence

C. Chryssomalakos, A. G. Flores-Delgado, E. Guzmán-González, L. Hanotel

quant-phSubmitted Jun 3, 2026• Announced Jun 4, 2026• 0 citations
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Abstract

We consider a spin system coupled to a noisy environment via an interaction Hamiltonian $H$ which is a polynomial of degree $n$ in the spin operators $S_i$ ($n$-magnetic Hamiltonian), and show that the use of the quantum super-Zeno effect in conjunction with a spin-anticoherent subspace, is highly effective in protecting the spin from the noise. When $n=1$, as in the case of unwanted rotations induced by stray magnetic fields, our scheme provides a quantum gyroscope, a concept that generalizes naturally to higher $n$ values (a quantum $n$-gyroscope). The gist of the proposed protocol is to use the quantum super-Zeno effect to confine a state to the subspace, and then exploit anticoherence to freeze its evolution within it.

Comments
5 pages + 7 pages supplemental material,5 figures

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We consider a spin system coupled to a noisy environment via an interaction Hamiltonian HHH which is a polynomial of degree nnn in the spin operators SiS_iSi​ (nnn-magnetic Hamiltonian), and show that the use of the quantum super-Zeno effect in conjunction with a spin-anticoherent subspace, is highly effective in protecting the spin from the noise. When n=1n=1n=1, as in the case of unwanted rotations induced by stray magnetic fields, our scheme provides a quantum gyroscope, a concept that generalizes naturally to higher nnn values (a quantum nnn-gyroscope). The gist of the proposed protocol is to use the quantum super-Zeno effect to confine a state to the subspace, and then exploit anticoherence to freeze its evolution within it.
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.
The time evolution of some quantum states can be slowed down or even stopped under frequent measurements. This is the usual quantum Zeno effect. Here, we report an operator quantum Zeno effect, in which the evolution of some physical observables is slowed down through measurements even though the quantum state changes randomly with time. Based on the operator quantum Zeno effect, we show how we can protect quantum information from decoherence with two-qubit measurements, realizable with noisy two-qubit interactions.
Quantum control is a fundamental tool for quantum technologies, and quantum Zeno (QZE) and anti-Zeno (AZE) effects, respectively denoting the slowdown and speedup of quantum system evolution by frequent interruptions/operations, represent quantum control paradigms. Indeed, they allow either protecting (QZE) or steering (AZE) the state of a quantum system via the interplay between frequent operations (system control) and the coupling of the system to its environment. Here we present two experiments demonstrating the possibility to exploit QZE and AZE to extract information on noise processes occurring in a quantum channel. In the first experiment, we realize the first noise diagnostics scheme based on repeated quantum measurements, showing how a single photon undergoing a noise process (in our case, random polarization fluctuations) can quantify non-Markovian temporal correlations within such a noise. In the second experiment, we show how a QZE-protection mechanism applied to a quantum state can become a noise sensing technique, allowing to estimate the statistical distribution of decoherence effects occurring on a photonic qubit during its propagation in a noisy quantum channel.
Gyroscope for rotation sensing plays a key role in inertial navigation systems. Developing more precise gyroscopes than the conventional ones bounded by the classical shot-noise limit by using quantum resources has attracted much attention. However, existing quantum gyroscope schemes suffer severe deterioration under the influence of decoherence, which is called the no-go theorem of noisy metrology. Here, by using two quantized optical fields as the quantum probe, we propose a quantum gyroscope scheme breaking through the constraint of the no-go theorem. Our exact analysis of the non-Markovian noise reveals that both the evolution time as a resource in enhancing the sensitivity and the achieved super-Heisenberg limit in the noiseless case are asymptotically recoverable when each optical field forms a bound state with its environment. The result provides a guideline for realizing high-precision rotation sensing in realistic noisy environments.
We experimentally demonstrate the freezing of evolution of quantum states in one- and two-dimensional subspaces of two qubits, on an NMR quantum information processor. State evolution was frozen and leakage of the state from its subspace to an orthogonal subspace was successfully prevented using super-Zeno sequences [Phys. Rev. Lett. 96, 100405 (2006)], comprising a set of radio frequency (rf) pulses punctuated by pre-selected time intervals. We demonstrate the efficacy of the scheme by preserving different types of states, including separable and maximally entangled states in one- and two-dimensional subspaces of two qubits. The change in the experimental density matrices was tracked by carrying out full state tomography at several time points. We use the fidelity measure for the one-dimensional case and the leakage (fraction) into the orthogonal subspace for the two-dimensional case, as qualitative indicators to estimate the resemblance of the density matrix at a later time to the initially prepared density matrix. For the case of entangled states, we additionally compute an entanglement parameter to indicate the presence of entanglement in the state at different times. We experimentally demonstrate that the super-Zeno scheme is able to successfully confine state evolution to the one- or two-dimensional subspace being protected.
In order to reduce errors, error correction codes need to be implemented fast. They can correct the errors corresponding to the first few orders in the Taylor expansion of the time evolution operator corresponding to the Hamiltonian of the interaction with the environment. If implemented fast enough, the zeroth order error predominates and the dominant effect is of error prevention by measurement (Zeno effect) rather than correction. In this ``Zeno regime,'' codes with less redundancy are sufficient for protection. We describe such a simple scheme, which uses two ``noiseless'' qubits to protect a large number, nnn, of information qubits from noise from the environment. The ``noisless qubits'' can be realized by treating them as logical qubits to be encoded by one of the previously introduced encoding schemes.