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In practical quantum processors, residual coupling to uncontrolled environmental degrees of freedom unavoidably induces decoherence, washing out phase relations and progressively destroying entanglement, which are key resources for quantum sensing and computation [1,2]. We report the results of further development of the approach proposed in [3], which suppresses decoherence in an entangled two-qubit register by applying multiple joint weak measurements that are equally spaced in time. The scheme is conceptually related to the quantum Zeno effect [4], but it departs from the usual requirement of extremely frequent projective measurements that aim to freeze the entire evolution. Instead, the protocol operates at moderate measurement cadence and exploits the presence of entanglement: the cumulative back-action of many weak joint measurements steers the state toward a Bell-type subspace while keeping measurement-induced disturbance controllable.
In the proposed algorithm, joint weak measurements are performed on the subspace spanned by the Bell states. Between measurement steps, the density matrix evolves according to Lindblad equation, capturing relaxation, dephasing, and temperature-driven effects [2]. Each weak measurement (parameterized by a strength $q$) provides controlled, nonselective bias toward the targeted entangled subspace without fully collapsing the state. Repeating this operation $N$ times over a fixed time window reshapes the open-system trajectory so that coherence-bearing off-diagonal elements decay more slowly than in free evolution. We quantify coherence by the off-diagonal terms of the density matrix (in the chosen basis) as $\ell_1$-norm [5], and we quantify entanglement using concurrence [6]. A key analytical result is that, for an optimal measurement choice, the short-time entanglement decay becomes dominated primarily by dephasing, while relaxation and temperature-dependent contributions strongly suppressed. Numerical simulations confirm that this slowdown persists over finite times.
To compare regimes, we introduce efficiency ratios based on initial decay slopes, the time to reach a fixed concurrence threshold, and the analogous slope ratio for $\ell_1$-norm. These indicators behave consistently and reveal a useful optimum at a moderate number of measurements for the studied parameters, while significantly degrading when the measurement strength $q$ is reduced below its optimal value. The protocol is especially relevant when the exact state to be preserved is not known, but information about the entanglement structure is available, for instance, in quantum algorithms where a subset of qubits remains idle between gate operations.
References:
1. M. M. Wolf, J. Eisert, T. S. Cubitt, J. I. Cirac (2008) - Assessing Non-Markovian Quantum Dynamics, Phys. Rev. Lett. 101, 150402. DOI: 10.1103/PhysRevLett.101.150402.
2. H.-P. Breuer, E.-M. Laine, J. Piilo, B. Vacchini (2016) - Colloquium: Non-Markovian dynamics in open quantum systems, Rev. Mod. Phys. 88, 021002. DOI: 10.1103/RevModPhys.88.021002.
3. O. M. Konovalenko, Z. A. Maizelis (2025) - Multiple Joint Weak Measurements as a Way to Suppress the Decoherence, Ukrainian Journal of Physics 70(8), 516–523. DOI: 10.15407/ujpe70.8.516.
4. B. Misra, E. C. G. Sudarshan (1977) - The Zeno’s paradox in quantum theory, J. Math. Phys. 18, 756–763. DOI: 10.1063/1.523304.
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6. W. K. Wootters (1998) - Entanglement of Formation of an Arbitrary State of Two Qubits, Phys. Rev. Lett. 80, 2245–2248. DOI: 10.1103/PhysRevLett.80.2245.