non-Markovian Dephasing Research Articles

Frozen discord for three qubits in a non-Markovian dephasing channel

The analytic form of quantum discord by Radhakrishnan et al. (2020) is derived for three qubits under a non-Markovian dephasing channel, where tripartite entanglement is explicitly calculated for reference. The necessary and sufficient conditions for the frozen discord are presented. It is shown that tripartite discord can exhibit multiple intervals of freezing under such conditions, while the entanglement displays multiply sudden deaths and revivals.

Attainable and usable coherence in X states over Markovian and non-Markovian channels

The relations between the resource theoretic measures of quantum coherence are rigorously investigated for various Markovian and non-Markovian channels for the two-qubit $X$ states with specific attention to the maximum and minimum attainable coherence and usefulness of these states in performing quantum teleportation in noisy environment. The investigation has revealed that under both dephasing and dissipative type noises the maximally entangled mixed states and Werner states lose their form and usefulness. However, maximally non-local mixed states (MNMSs) lose their identity in dissipative noise only. Thus, MNMSs are established to be useful in teleporting a qubit with fidelity greater than the classical limit in the presence of dephasing noise. MNMSs also remain useful for device independent quantum key distribution in this case as they still violate Bell's inequality. In the presence of noise, coherence measured by relative entropy of coherence is found to fall faster than the same measured using $l_1$ norm of coherence. Further, information back-flow from the environment to the system is observed over non-Markovian channels which leads to revival in coherence. Additionally, sequential interaction of two qubits with the same environment is found to result in correlated noise on both qubits, and coherence is observed to be frozen in this case under dephasing channel. Under the effect of Markovian and non-Markovian dephasing channels studied here, we observed that MNMSs have maximum relative coherence, i.e., they have the maximum amount of $l_1$ norm of coherence among the states with the same amount of relative entropy of coherence. However, this feature is not visible in any $X$ state evolving over dissipative channels.

Non-Markovian dephasing of disordered quasi-one-dimensional fermion systems

As a potential window on transitions out of the ergodic, many-body-delocalized phase, we study the dephasing of weakly disordered, quasi-one-dimensional fermion systems due to a diffusive, non-Markovian noise bath. Such a bath is self-generated by the fermions, via inelastic scattering mediated by short-ranged interactions. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling. However, the expansion breaks down at long times, and is not stabilized by including a mean-field decay rate, signaling a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interactions perturbatively and the Coulomb interaction exactly. The latter provides a physical infrared regularization that stabilizes perturbation theory at long times, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. At first order in the diffusive bath coupling, we find an enhancement of the dephasing rate, but at second order we find a rephasing contribution. Our results differ qualitatively from those obtained via self-consistent calculations and are relevant in two different contexts. First, in the search for precursors to many-body localization in the ergodic phase. Second, our results provide a mechanism for the enhancement of dephasing at low temperatures in spin SU(2)-symmetric quantum wires, beyond the Altshuler-Aronov-Khmelnitsky result. The enhancement is possible due to the amplification of the triplet-channel interaction strength, and provides an additional mechanism that could contribute to the experimentally observed low-temperature saturation of the dephasing time.

Enhancing quantum transport efficiency by tuning non-Markovian dephasing

We consider the problem of energy transport in a chain of coupled dissipative quantum systems in the presence of non-Markovian dephasing. We use a model of non-Markovianity which is experimentally realizable in the context of controlled quantum systems. We show that non-Markovian dephasing can significantly enhance quantum transport, and we characterize this phenomenon in terms of internal coupling strengths of the chain for some chain lengths. Finally, we show that the phenomenon of dephasing-assisted quantum transport is also enhanced in the non-Markovian scenario when compared to the Markovian case. Our work brings together engineered environments, which are a reality in quantum technologies, and energy transport, which is typically discussed in terms of complex molecular systems. We then expect that it may motivate experimental work and further theoretical investigations on resources which can enhance transport efficiency in a controllable way. This can help in the design of quantum devices with lower dissipation rates, an important concern in any practical application.

Coherence-based measure of quantumness in (non-) Markovian channels

We make a detailed analysis of quantumness for various quantum noise channels, both Markovian and non-Markovian. The noise channels considered include dephasing channels like random telegraph noise, non-Markovian dephasing and phase damping, as well as the non-dephasing channels such as generalized amplitude damping and Unruh channels. We make use of a recently introduced witness for quantumness based on the square $l_1$ norm of coherence. It is found that the increase in the degree of non-Markovianity increases the quantumness of the channel.

Non-Markovian pure dephasing in a dielectric excited by a few-cycle laser pulse

We develop the theory of pure dephasing in a solid exposed to an ultrashort laser pulse beyond the commonly used Markov approximation. This approach takes into account the finite cutoff energy of the bath and can be applied to both many-particle and phonon environments. With numerical simulations performed with the time-dependent Hartree-Fock equations, we investigate how the excitation probability and high-harmonic generation are described by different models of decoherence. It is shown that the time-dependent rates allow for temporally high dephasing to successfully reproduce the main features of high-harmonics spectrum and avoid an overestimation of the charge carrier population after the pulse, which is a common problem of the Markov approximation.

Facets of quantum information under non-Markovian evolution

We consider two non-Markovian models: Random Telegraph Noise (RTN) and non-Markovian dephasing (NMD). The memory in these models is studied from the perspective of quantum Fisher information flow. This is found to be consistent with the other well known witnesses of non-Markovianity. The two noise channels are characterized quantum information theoretically by studying their gate and channel fidelities. Further, the quantum coherence and its balance with mixedness is studied. This helps to put in perspective the role that the two noise channels can play in various facets of quantum information processing and quantum communication.

Restoring the Heisenberg limit via collective non-Markovian dephasing

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 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.

Non-Markovian dephasing and depolarizing channels

We introduce a method to construct non-Markovian variants of completely positive (CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity with the breakdown in CP-divisibility of the map, i.e., appearance of a not-completely-positive (NCP) intermediate map. In particular, we consider the case of non-Markovian dephasing in detail. The eigenvalues of the Choi matrix of the intermediate map crossover at a point which corresponds to a singularity in the canonical decoherence rate of the corresponding master equation, and thus to a momentary non-invertibility of the map. Thereafter, the rate becomes negative, indicating non-Markovianity. We quantify the non-Markovianity by two methods, one based on CP-divisibility (Hall et al., PRA 89, 042120, 2014), which doesn't require optimization but requires normalization to handle the singularity, and another method, based on distinguishability (Breuer et al. PRL 103, 210401, 2009), which requires optimization but is insensitive to the singularity.

Machine Learning for Predictive Estimation of Qubit Dynamics Subject to Dephasing

Decoherence remains a major challenge in quantum computing hardware and a variety of physical-layer controls provide opportunities to mitigate the impact of this phenomenon through feedback and feedforward control. In this work, we compare a variety of machine learning algorithms derived from diverse fields for the task of state estimation (retrodiction) and forward prediction of future qubit state evolution for a single qubit subject to classical, non-Markovian dephasing. Our approaches involve the construction of a dynamical model capturing qubit dynamics via autoregressive or Fourier-type protocols using only a historical record of projective measurements. A detailed comparison of achievable prediction horizons, model robustness, and measurement-noise-filtering capabilities for Kalman Filters (KF) and Gaussian Process Regression (GPR) algorithms is provided. We demonstrate superior performance from the autoregressive KF relative to Fourier-based KF approaches and focus on the role of filter optimization in achieving suitable performance. Finally, we examine several realizations of GPR using different kernels and discover that these approaches are generally not suitable for forward prediction. We highlight the underlying failure mechanism in this application and identify ways in which the output of the algorithm may be misidentified numerical artefacts.

Trapped-ion quantum simulation of excitation transport: Disordered, noisy, and long-range connected quantum networks

The transport of excitations governs fundamental properties of matter. Particularly rich physics emerges in the interplay between disorder and environmental noise, even in small systems such as photosynthetic biomolecules. Counterintuitively, noise can enhance coherent quantum transport, which has been proposed as a mechanism behind the high transport efficiencies observed in photosynthetic complexes. This effect has been called "environmental-assisted quantum transport" (ENAQT). Here, we propose a quantum simulation of the excitation transport in an open quantum network, taking advantage of the high controllability of current trapped-ion experiments. Our scheme allows for the controlled study of various different aspects of the excitation transfer, ranging from the influence of static disorder and interaction range, over the effect of Markovian and non-Markovian dephasing, to the impact of a continuous insertion of excitations. Our proposal discusses experimental error sources and realistic parameters, showing that it can be implemented in state-of-the-art ion-chain experiments.

Enhancement of frequency estimation by spatially correlated environments

In metrological tasks, employing entanglement can quantitatively improve the precision of parameter estimation. However, susceptibility of the entanglement to decoherence fades this capability in the realistic metrology and limits ultimate quantum improvement. One of the most destructive decoherence-type noise is uncorrelated Markovian noise which commutes with the parameter-encoding Hamiltonian and is modeled as a semigroup dynamics, for which the quantum improvement is constrained to a constant factor. It has been shown (Chin et al., 2012) that when the noisy time evolution is governed by a local and non-semigroup dynamics (e.g., induced by an uncorrelated non-Markovian dephasing), emerging the Zeno regime at short times can result in the Zeno scaling in the precision. Here, by considering the impact of the correlated noise in metrology, we show that spatially correlated environments which lead to a nonlocal and non-semigroup dynamics can improve the precision of a noisy frequency measurement beyond the Zeno scaling. In particular, it is demonstrated that one can find decoherence-free subspaces and subsequently achieve the Heisenberg precision scaling for an approximated dynamics induced by spatially correlated environments.

Quantum metrology in coarsened measurement reference

We investigate the role of coarsened measurement reference in quantum metrology. Coarsened measurement reference comes from the coarsened reference time and basis. When the measurement based on one common reference basis, the disadvantage can be removed by symmetry. Due to the coarsened reference basis, entangled states can not perform better than product states for large number of probe particles. Given a finite uncertainty of the coarsened reference basis, the optimal number of probe particle is obtained in estimating phase. Finally, we prove that the maximally entangled state always achieves better precision under the case of non-Markovian dephasing than that under the case of Markovian dephasing. The product state is more resistant to interference of the coarsened reference time than the entangled state.

Zeno limit in frequency estimation with non-Markovian environments

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.

Dynamics of genuine multipartite entanglement under local non-Markovian dephasing

We study dynamics of genuine entanglement for quantum states of three and four qubits under non-Markovian dephasing. Using a computable entanglement monotone for multipartite systems, we find that GHZ state is quite resilient state whereas the W state is the most fragile. We compare dynamics of chosen quantum states with dynamics of random pure states and weighted graph states.

Long-time correlation in non-Markovian dephasing of an exciton-phonon system in InAs quantum dots.

We have observed a time-correlated frequency fluctuation in non-Markovian dephasing of excitons in InAs quantum dots using a six-wave mixing technique. In this measurement, the arrival times of the excitation pulses were controlled to eliminate the influence of Markovian dephasing and to measure the pure non-Markovian behavior. The experimental result shows that the time correlation of the frequency fluctuation due to exciton-phonon interactions was maintained in the quantum dots for over 10ps. This long-time correlation is caused by the modification of the phonon coupling distribution.

Conditions for the Freezing Phenomena of Geometric Measure of Quantum Discord for Arbitrary Two-Qubit X-states under Non-dissipative Dephasing Noises

We study the dynamics of geometric measure of quantum discord (GMQD) under the influences of two local phase damping noises. Consider the two qubits initially in arbitrary X-states, we find the necessary and sufficient conditions for which GMQD is unaffected for a finite period. It is further shown that such results also hold for the non-Markovian dephasing process.

Interaction-induced correlations and non-Markovianity of quantum dynamics

We investigate the conditions under which the trace distance between two different states of a given open system increases in time due to the interaction with an environment, therefore signalling non-Markovianity. We find that the finite-time difference in trace distance is bounded by two sharply defined quantities that are strictly linked to the occurrence of system-environment correlations created throughout their interaction and affecting the subsequent evolution of the system. This allows to shed light on the origin of non-Markovian behaviours in quantum dynamics. We best illustrate our findings by tackling two physically relevant examples: a non-Markovian dephasing mechanism that has been the focus of a recent experimental endeavour and the open-system dynamics experienced by a spin connected to a finite-size quantum spin chain.

DYNAMICS OF QUANTUM CORRELATIONS IN TWO-QUBIT SYSTEMS WITHIN NON-MARKOVIAN ENVIRONMENTS

Knowledge of the dynamical behavior of correlations with no classical counterpart, like entanglement, nonlocal correlations and quantum discord, in open quantum systems is of primary interest because of the possibility to exploit these correlations for quantum information tasks. Here we review some of the most recent results on the dynamics of correlations in bipartite systems embedded in non-Markovian environments that, with their memory effects, influence in a relevant way the system dynamics and appear to be more fundamental than the Markovian ones for practical purposes. Firstly, we review the phenomenon of entanglement revivals in a two-qubit system for both independent environments and a common environment. We then consider the dynamics of quantum discord in non-Markovian dephasing channel and briefly discuss the occurrence of revivals of quantum correlations in classical environments.

Necessary and sufficient conditions for the freezing phenomena of quantum discord under phase damping

We investigate the freezing phenomenon of quantum discord occurring in phase damping noise processes. By relating the expression of the time variation of the discord to the convex function of relative entropy, we obtain the necessary and sufficient conditions of the phenomenon for standard Bell-diagonal states. These conditions are applicable also to the phenomenon occurring in a non-Markovian dephasing process. Moreover, we show that the same condition and phenomenon coincide in a new sort of Bell-diagonal states beyond the standard form.