arXiv subjects

Hossein Rangani Jahromi

Publications and source records attributed to Hossein Rangani Jahromi.

12 recordsLinked to original sources

arXiv2026

Contractivity of the Hilbert--Schmidt Speed and Unitality--Divisibility-Based Witnesses in Finite-Dimensional Quantum Dynamics

We investigate the Hilbert--Schmidt speed as a witness of non-Markovianity in finite-dimensional quantum dynamics. For a differentiable one-parameter family of quantum states, the Hilbert--Schmidt speed is defined, up to a conventional factor, as the Hilbert--Schmidt norm of the corresponding Hermitian traceless tangent operator. We show that, for unital dynamics in arbitrary finite dimension, P-divisibility implies the monotonic decrease of the Hilbert--Schmidt speed. Hence, any increase in this quantity signals the breakdown of P-divisibility, and therefore also excludes CP-divisibility. For qubit systems, we establish a stronger result: every P-divisible evolution decreases the Hilbert--Schmidt speed, independently of unitality. Thus, in dimension two, HSS growth is a valid witness of non-Markovian behaviour for arbitrary positive divisible dynamics. This conclusion is dimension dependent. In dimensions $d\geq3$, non-unitality can generate HSS growth even under CP-divisible dynamics. We demonstrate this by constructing an explicit non-unital CP-divisible qutrit semigroup for which the Hilbert--Schmidt speed strictly increases. Finally, for unital GKSL dynamics, we derive a generator-level dissipation identity explaining the monotonic decay of the Hilbert--Schmidt speed. These results specify the regimes in which HSS growth can be interpreted as evidence of the failure of divisibility and clarify its limitation for higher-dimensional non-unital evolutions.

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arXiv2026

Trace-to-Hilbert-Schmidt Speed Ratio in Quantum Dynamics: Universal Bounds and Effective Rank

We address the ratio between the trace speed and the Hilbert-Schmidt speed for differentiable finite-dimensional quantum states, $\mathcal R=\|\partial_ϕρ\|_1/\|\partial_ϕρ\|_2$. Since the tangent $\partial_ϕρ$ is Hermitian and traceless, $\mathcal R$ obeys stronger bounds than those for generic operators. For any nonzero tangent of rank $r$, we prove the sharp bounds $\sqrt{2}\le\mathcal R\le\sqrt{r}$ for even $r$ and $\sqrt{2}\le\mathcal R\le\sqrt{r-1/r}$ for odd $r$, characterizing all equality cases. Nonstationary pure-state and qubit families saturate the lower bound $\mathcal R=\sqrt2$. For odd Hilbert-space dimension $d$, we further prove the sharp global maximum $\mathcal R\le\sqrt{d-1/d}$. Interpreting $\mathcal R^2$ as the participation ratio of the singular-value distribution yields an effective-rank picture, $r_{\mathrm{eff}}=\mathcal R^2$. We decompose the effective rank into classical eigenvalue and quantum eigenvector contributions and obtain the bound $r_{\mathrm{eff}}\le r_C+r_Q$, with equality when either component vanishes. Linking the effective rank to the quantum Fisher information $F$ gives $r_{\mathrm{eff}}\ge 8\,\mathrm{TS}^2/F$, showing that a large effective rank is required when this lower bound substantially exceeds the universal minimum value $2$. Finally, a hierarchy of quantum speed limits shows how the effective rank controls the tightness of bounds expressed through the Hilbert-Schmidt speed.

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arXiv2025

Witnessing global memory effects of multiqubit correlated noisy channels by Hilbert-Schmidt speed

In correlated noisy channels, the global memory effects on the dynamics of a quantum system depend on both non-Markovianity of the single noisy channel (intrinsic memory) and classical correlations between multiple uses of the channel itself (correlation-based memory). We show that the Hilbert-Schmidt speed (HSS), a measure of non-Markovianity, serves as a reliable figure of merit for evaluating the role of this correlation-based memory on the global memory effects, for both unital and non-unital channels. The intensity of the correlation-based memory is ruled by a classical correlation strength between consecutive applications of the channel. We demonstrate that, for unital noisy channels, increasing the number of qubits of the system significantly weakens the sensitivity of the HSS to this classical correlation strength. Such a pattern indicates that the state evolution of large quantum systems may be less prone to be affected by classical correlations between noisy channels. Moreover, assuming the qubits are affected by independent or classically correlated local non-Markovian unital channels, we observe that, as the number of qubits increases, the collective behavior of the multiqubit system inhibits the non-Markovian features of the overall system dynamics.

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arXiv2022

Monitoring variations of refractive index via Hilbert-Schmidt speed and applying this phenomenon to improve quantum metrology

Effective nonlinear optical interactions are essential for many applications in modern photonics. In this paper, we investigate the role of the nonlinear response of a material to improve quantum metrology. In particular, the collective optical behavior of an atomic ensemble is applied to enhance frequency estimation through one of the atoms. Moreover, we introduce Hilbert-Schmidt speed, an easily computable theoretical tool, to monitor the variations of linear as well as nonlinear refractive indices and evaluate the strength of the nonlinear response of optical materials. Furthermore, we illustrate that quantum Fisher information and Hilbert-Schmidt speed can efficiently detect negative permittivity and refractive index, which is of great importance from a practical point of view.

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arXiv2022

Relativistic quantum thermometry through a moving sensor

Using a two-level moving probe, we address the temperature estimation of a static thermal bath modeled by a massless scalar field prepared in a thermal state. Different couplings of the probe to the field are discussed under various scenarios. We find that the thermometry is completely unaffected by the Lamb shift of the energy levels. We take into account the roles of probe velocity, its initial preparation, and environmental control parameters for achieving optimal temperature estimation. We show that a practical technique can be utilized to implement such a quantum thermometry. Finally, exploiting the thermal sensor moving at high velocity to probe temperature within a multiparameter-estimation strategy, we demonstrate perfect supremacy of the joint estimation over the individual one.

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arXiv2022

Memory effects in high-dimensional systems faithfully identified by Hilbert-Schmidt speed-based witness

A witness of non-Markovianity based on the Hilbert-Schmidt speed (HSS), a special type of quantum statistical speed, has been recently introduced for low-dimensional quantum systems. Such a non-Markovianity witness is particularly useful, being easily computable since no diagonalization of the system density matrix is required. We investigate the sensitivity of this HSS-based witness to detect non-Markovianity in various high-dimensional and multipartite open quantum systems. We find that the time behaviors of the HSS-based witness are always in agreement with those of quantum negativity or quantum correlation measure. These results show that the HSS-based witness is a faithful identifier of the memory effects appearing in the quantum evolution of a high-dimensional system.

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arXiv2021

Remote sensing and faithful quantum teleportation through non-localized qubits

One of the most important applications of quantum physics is quantum teleportation, the possibility to transfer quantum states over arbitrary distances. In this paper, we address the idea of remote sensing in a teleportation scenario with topological qubits more robust against noise. We also investigate the enhancement of quantum teleportation through non-local characteristics of the topological qubits. In particular, we show that how this nonlocal property, helps us to achieve near-perfect quantum teleportation even with mixed quantum states. Considering the limitations imposed by decoherence and the subsequent mixedness of the resource state, we find that our results may solve important challenges in realizing faithful teleportation over long distances.

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arXiv2021

Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{PT}\!-$symmetric systems

Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry and anti-$\mathcal{PT}$ symmetry give rise to exceptional points (EPs) with intriguing properties related to, e.g., chiral transport and enhanced sensitivity, due to the coalescence of eigenvectors. In this paper, we propose a powerful and easily computable tool, based on the Hilbert-Schmidt speed (HSS), which does not require the diagonalization of the evolved density matrix, to detect exactly the EPs and hence the critical behavior of the (anti-)$\mathcal{PT}\!-$symmetric systems, especially high-dimensional ones. Our theoretical predictions, made without the need for modification of the Hilbert space, which is performed by diagonalizing one of the observables, are completely consistent with results extracted from recent experiments studying the criticality in (anti-)$\mathcal{PT}\!-$symmetric systems. Nevertheless, not modifying the Hilbert space of the non-Hermitian system, we find that the trace distance, a measure of distinguishability of two arbitrary quantum states, whose dynamics is known as a faithful witness of non-Markovianity in Hermitian systems, may be non-contractive under the non-Hermitian evolution of the system. Therefore, it lacks one of the most important characteristics which must be met by any standard witness of non-Markovianity.

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arXiv2021

Estimating energy levels of a three-level atom in single and multi-parameter metrological schemes

Determining the energy levels of a quantum system is a significant task, for instance, to analyze reaction rates in drug discovery and catalysis or characterize the compatibility of materials. In this paper we exploit quantum metrology, the research field focusing on the estimation of unknown parameters exploiting quantum resources, to address this problem for a three-level system interacting with laser fields. The performance of simultaneous estimation of the levels compared to independent one is also investigated in various scenarios. Moreover, we introduce, the Hilbert-Schmidt speed (HSS), a special type of quantum statistical speed, as a powerful figure of merit for enhancing estimation of energy spectrum. This measure is easily computable, because it does not require diagonalization of the system state, verifying its efficiency in high-dimensional systems.

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arXiv2020

Hilbert-Schmidt speed as an efficient tool in quantum metrology

We investigate how the Hilbert-Schmidt speed (HSS), a special type of quantum statistical speed, can be exploited as a powerful and easily computable tool for quantum phase estimation in a $n$-qubit system. We find that, when both the HSS and quantum Fisher information (QFI) are computed with respect to the phase parameter encoded into the initial state of the $n$-qubit register, the zeros of the HSS dynamics are essentially the same as those of the QFI dynamics. Moreover, the positivity (negativity) of the time-derivative of the HSS exactly coincides with the positivity (negativity) of the time-derivative of the QFI. Our results also provide strong evidence for contractivity of the HSS under completely positive and trace preserving maps in high-dimensional systems, as predicted in previous studies.

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arXiv2020

Multiparameter estimation, lower bound on quantum Fisher information and non-Markovianity witnesses of noisy two-qubit systems

By using the quantum Fisher information (QFI), we address the process of \textit{single}-parameter estimation in the presence of bosonic as well as fermionic environments and protection of information against the noise. In particular, the quantum interferometric power (IP) of the evolved state of the system is uncovered as an important lower bound for the QFIs of initially encoded parameters. Moreover, we unveil new witnesses of non-Markovianity, that can be used to detect efficiently the memory effects and backflow of information from the environment to the system. On the other hand, we also investigate the \textit{multiparameter} estimation of initial parameters encoded into the quantum state of a two qubit system and obtain analytical formula of the corresponding QFI matrix. In particular, the corresponding quantum Cramer-Rao bounds in both single and multiparameter estimations are analysed. In addition, we illustrate that the quantum \textit{coherence} and \textit{purity} of the evolved state of the probes are two key elements in realizing optimum multiparameter estimation.

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arXiv2020

Witnessing non-Markovian effects of quantum processes through Hilbert-Schmidt speed

Non-Markovian effects can speed up the dynamics of quantum systems while the limits of the evolution time can be derived by quantifiers of quantum statistical speed. We introduce a witness for characterizing the non-Markovianity of quantum evolutions through the Hilbert-Schmidt speed (HSS), which is a special type of quantum statistical speed. This witness has the advantage of not requiring diagonalization of evolved density matrix. Its sensitivity is investigated by considering several paradigmatic instances of open quantum systems, such as one qubit subject to phase-covariant noise and Pauli channel, two independent qubits locally interacting with leaky cavities, V-type and $Λ$-type three-level atom (qutrit) in a dissipative cavity. We show that the proposed HSS-based non-Markovianity witness detects memory effects in agreement with the well-established trace distance-based witness, being sensitive to system-environment information backflows.

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