In this work an exactly solvable model of $N$ two-level systems interacting with a single bosonic dephasing reservoir is considered to unravel the role played by collective non-Markovian dephasing. We show that phase estimation with entangled states for this model can exceed the standard quantum limit and demonstrate Heisenberg scaling with the number of atoms for an arbitrary temperature. For a certain class of reservoir densities of states decoherence can be suppressed in the limit of a large number of atoms and the Heisenberg limit can be restored for arbitrary interrogation times. We identify the second class of densities when the Heisenberg scaling can be restored for any finite interrogation time. We also find the third class of densities when the standard quantum limit can be exceeded only on the initial stage of dynamics in the Zeno regime.
In this work an exactly solvable model of N two-level systems interacting with a single bosonic dephasing reservoir is considered to unravel the role played by collective non-Markovian dephasing. We show that phase estimation with entangled states for this model can exceed the standard quantum limit and demonstrate Heisenberg scaling with the number of atoms for an arbitrary temperature. For a certain class of reservoir densities of states decoherence can be suppressed in the limit of a large number of atoms and the Heisenberg limit can be restored for arbitrary interrogation times. We identify the second class of densities when the Heisenberg scaling can be restored for any finite interrogation time. We also find the third class of densities when the standard quantum limit can be exceeded only on the initial stage of dynamics in the Zeno regime.
A quantum system can be prepared in an entangled state that is very sensitive to changes introduced to its dynamics and thus potentially can be utilized as a precise sensor of dynamics parameters. N entangled two-level atoms evolving unitarily can be used for frequency estimation with Heisenberg-limited precision which scales as ${N}^{\ensuremath{-}2}$, whereas uncorrelated states give only a standard-limited precision which scales as ${N}^{\ensuremath{-}1}$. As entangled states are also sensitive to disturbances introduced by interactions with external environments, quantum enhancement of the precision may be significantly limited for open quantum systems. This is the case when an interaction with an environment leads to local Markovian dephasing and the precision scales as ${N}^{\ensuremath{-}1}$ for all atom preparations. For local non-Markovian dephasing, however, Matsuzaki et al. [Phys. Rev. A 84, 012103 (2011)] and Chin et al. [Phys. Rev. Lett. 109, 233601 (2012)] showed that the atoms prepared in the maximally entangled state achieve Zeno scaling $\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}{N}^{\ensuremath{-}3/2}$ in precision and argued that this limit should hold for any entangled state. Here we prove that Zeno scaling is indeed the best possible scaling for all local non-Markovian dephasing models which feature initial Zeno dynamics. Moreover, Zeno scaling can hold only for experiments in the Zeno-dynamics regime, otherwise scaling of the precision is standard.
We analyze precision bounds for a local phase estimation in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under strictly Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite bandwidth dephasing environment, we demonstrate that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states using otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and therefore the obtained scaling with the number of particles, which surpasses the standard quantum limit but does not achieve Heisenberg resolution, possesses general validity that goes beyond specific models. This is in marked contrast with the situation encountered under general Markovian noise, where an arbitrarily small amount of noise is enough to restore the scaling dictated by the standard quantum limit.
The goal of quantum metrology is the precise estimation of parameters using quantum properties such as entanglement. This estimation usually consists of three steps: state preparation, time evolution during which information of the parameters is encoded in the state, and readout of the state. Decoherence during the time evolution typically degrades the performance of quantum metrology and is considered to be one of the major obstacles to realizing entanglement-enhanced sensing. We show, however, that under suitable conditions, this decoherence can be exploited to improve the sensitivity. Assume that we have two axes, and our aim is to estimate the relative angle between them. Our results reveal that the use of Markovian collective dephasing to estimate the relative angle between the two directions affords Heisenberg-limited sensitivity. Moreover, our protocol based on Markovian collective dephasing is robust against environmental noise: it is possible to achieve the Heisenberg limit by applying the collective dephasing even under the effect of independent dephasing. Our counterintuitive proposal with the decoherence leads to alternative applications in quantum metrology.
We consider the buildup and decay of two-spin entanglement through phase interactions in a finite environment of surrounding spins, as realized in quantum computing platforms based on arrays of atoms, molecules, or nitrogen vacancy centers. The non-Markovian dephasing caused by the spin environment through Ising-type phase interactions can be solved exactly and compared to an effective Markovian treatment based on collision models. In a first case study on a dynamic lattice of randomly hopping spins, we find that non-Markovianity boosts the dephasing rate caused by nearest-neighbor interactions with the surroundings, degrading the maximum achievable entanglement. However, we also demonstrate that additional three-body interactions can mitigate this degradation, and that randomly timed reset operations performed on the two-spin system can help sustain a finite average amount of steady-state entanglement. In a second case study based on a model nuclear magnetic resonance system, we elucidate the role of bath correlations at finite temperature on non-Markovian dephasing. They speed up the dephasing at low temperatures while slowing it down at high temperatures, compared to an uncorrelated bath, which is related to the number of thermally accessible spin configurations with and without interactions.
Open-system descriptions are typically introduced by coupling a quantum system to an external environment. Here we show that a closed interacting many-body system can itself generate a controlled non-Markovian quantum channel acting on a reduced nonlinear qubit through finite-size corrections to a nonlinear mean-field limit. We demonstrate this using the Kitagawa-Ueda one-axis twisting model, H=χJz2, a paradigmatic model of collective spin dynamics, spin squeezing, and two-component Bose-Einstein condensates. Although the large-N regime of this model has been extensively studied, the conventional fixed-χ scaling does not yield a nontrivial dynamical large-N limit. In this paper, we investigate a complementary large-N formulation obtained from the double limit N→∞ and χ→O(g/N), where g is a coupling constant. We derive the leading finite-N corrections to this limit and show that they correspond to an emergent non-Markovian dephasing process, producing a Gaussian decay of the Bloch-vector coherence with characteristic timescale tφ≥N/(2g). Exact finite-N calculations demonstrate that this effective open-system description becomes quantitatively accurate for systems containing on the order of one hundred qubits. The resulting framework provides a microscopic realization of non-Markovian dephasing generated intrinsically by a closed many-body system and enables efficient simulation of collective quantum dynamics beyond unitary mean-field theory. These results link the long-studied phenomenon of phase diffusion in atomic ensembles and Bose-Einstein condensates to the growing effort to characterize non-Markovian, beyond-Lindblad noise in quantum computing hardware, providing a rare case in which such a noise channel is derived from microscopic dynamics rather than fit phenomenologically.
Abstract We study the estimation precision attainable by entanglement-enhanced Ramsey interferometry in the presence of spatiotemporally correlated non-classical noise. Our analysis relies on an exact expression of the reduced density matrix of the qubit probes under general zero-mean Gaussian stationary dephasing, which is established through cumulant-expansion techniques and may be of independent interest in the context of non-Markovian open dynamics. By continuing and expanding our previous work (Beaudoin et al 2018 Phys. Rev. A 98 020102(R)), we analyze the effects of a non-collective coupling regime between the qubit probes and their environment, focusing on two limiting scenarios where the couplings may take only two or a continuum of possible values. In the paradigmatic case of spin–boson dephasing noise from a thermal environment, we find that it is in principle possible to suppress, on average, the effect of spatial correlations by randomizing the location of the probes, as long as enough configurations are sampled where noise correlations are negative. As a result, superclassical precision scaling is asymptotically restored for initial entangled states, including experimentally accessible one-axis spin-squeezed states.