arXiv subjects

Shrikant Utagi

Publications and source records attributed to Shrikant Utagi.

11 recordsLinked to original sources

arXiv2025

Detecting and quantifying non-Markovianity via quantum direct cause

We study the efficacy of the two recently introduced witnesses of non-Markovianity, namely that based on temporal correlations in pseudo-density matrix and temporal steering correlations in detecting information backflow. We show, through specific counterexamples taken from existing literature, that they can witness a process to be non-Markovian where trace distance and entropic distinguishability measures may fail. We further show that, since the pseudo-density matrix is directly related to the Choi matrix of a channel via the partial transpose, it can be generalized to quantify the total quantum memory in any indivisible process. Moreover, we make an interesting observation that temporal steerable correlations-based measure may not capture eternal non-Markovianity hence may not be proportional to Choi-matrix-based methods, while pseudo-density matrix-based measures introduced in this work faithfully capture eternal non-Markovianity. Our work highlights important distinction between weak and strong forms of quantum direct cause in quantum mechanics when applied to open system dynamics.

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arXiv2025

Quantum walks under superposition of causal order

We set the criteria under which superposition of causal order can be incorporated in to quantum walks. In particular, we show that only periodic quantum walks or those with at least one disorder exhibit Superposition of causal order under the action of `quantum switch'. We exemplify our results with a simple example of two-period discrete-time quantum walks. In particular, we observe that periodic quantum walks exhibit causal asymmetry pertaining to the dynamics of the reduced coin state: the dynamics are more non-Markovian for one temporal order than the other. We also note that the non-Markovianity of the reduced coin state due to indefiniteness in causal order tends to match the dynamics of a particular temporal order of the coin state. We substantiate our results with numerical simulations.

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arXiv2024

Noise-adapted Quantum Error Correction for Non-Markovian Noise

We consider the problem of quantum error correction (QEC) for non-Markovian noise. Using the well known Petz recovery map, we first show that conditions for approximate QEC can be easily generalized for the case of non-Markovian noise, in the strong coupling regime where the noise map becomes non-completely-positive at intermediate times. While certain approximate QEC schemes are ineffective against quantum non-Markovian noise, in the sense that the fidelity vanishes in finite time, the Petz map adapted to non-Markovian noise uniquely safeguards the code space even at the maximum noise limit. Focusing on the case of non-Markovian amplitude damping noise, we further show that the non-Markovian Petz map also outperforms the standard, stabilizer-based QEC code. Since implementing such a non-Markovian map poses practical challenges, we also construct a Markovian Petz map that achieves similar performance, with only a slight compromise on the fidelity.

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arXiv2024

Protocols for counterfactual and twin-field quantum digital signature

Quantum digital signature (QDS) is the quantum version of its classical counterpart, and can offer security against attacks of repudiation, signature forging and external eavesdropping, on the basis of quantum mechanical no-go principles. Here we propose a QDS scheme based on quantum counterfactuality, which leverages the concept of interaction-free measurement. Employing the idea behind twin-field cryptography, we show how this two-way protocol can be turned into an equivalent non-counterfactual, one-way protocol, that is both more practical and also theoretically helpful in assessing the experimental feasibility of the first protocol. The proposed QDS protocol can be experimentally implemented with current quantum technology.

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arXiv2023

On the eternal non-Markovianity of non-unital quantum channels

The eternally non-Markovian Pauli channel is an example of a unital channel characterized by a negative decay rate for all time $t>0$. Here we consider the problem of constructing an analogous non-unital channel, and show in particular that a $d$-dimensional generalized amplitude damping (GAD) channel cannot be eternally non-Markovian when the non-Markovianity originates solely from the non-unital part of the channel. We study specific ramifications of this result for qubit GAD. Specifically, we construct a quasi-eternally non-Markovian qubit GAD channel, characterized by a time $t^\ast > 0$, such that the channel is non-Markovian only and for all time $t > t^\ast$. We further point out that our negative result for the qudit GAD channel, namely the impossibility of the eternal non-Markovian property, does not hold for a general qubit or higher-dimensional non-unital channel.

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arXiv2022

On the non-Markovianity of quantum semi-Markov processes

The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of memory based on the deviation from semigroup evolution, that provides a unified description of divisible and indivisible channels. This is shown to bring out the property of QSM processes to exhibit memory effects even in the CP-divisible regime, in agreement with an earlier result. An operational meaning to the non-Markovian nature of semi-Markov processes is also provided.

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arXiv2021

A class of quasi-eternal non-Markovian Pauli channels and their measure

We study a class of qubit non-Markovian general Pauli dynamical maps with multiple singularities in the generator. We discuss a few easy examples involving trigonometric or other non-monotonic time dependence of the map, and discuss in detail the structure of channels which don't have any trigonometric functional dependence. We demystify the concept of a singularity here, showing that it corresponds to a point where the dynamics can be regular but the map is momentarily non-invertible, and this gives a basic guideline to construct such non-invertible non-Markovian channels. Most members of the channels in the considered family are quasi-eternally non-Markovian (QENM), which is a broader class of non-Markovian channels than the eternal non-Markovian channels. In specific, the measure of quasi-eternal non-Markovian (QENM) channels in the considered class is shown to be $\frac{2}{3}$ in the isotropic case, and about 0.96 in the anisotropic case.

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arXiv2021

Singularities, mixing and non-Markovianity of Pauli dynamical maps

Quantum non-Markovianity of channels can be produced by mixing Markovian channels, as observed recently by various authors. We consider an analogous question of whether singularities of the channel can be produced by mixing non-singular channels, i.e., ones that lack them. Here we answer the question in the negative in the context of qubit Pauli channels. On the other hand, mixing channels with a singularity can lead to the elimination of singularities in the resultant channel. We distinguish between two types of singular channels, which lead under mixing to broadly quite different properties of the singularity in the resultant channel. The connection to non-Markovianity (in the sense of completely positive indivisibility) is pointed out. These results impose nontrivial restrictions on the experimental realization of non-invertible quantum channels by a process of channel mixing.

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arXiv2020

Quantum causal correlations and non-Markovianity of quantum evolution

A non-Markovianity measure for quantum channels is introduced based on causality measure - a monotone of causal (temporal) correlations - arising out of the pseudo-density matrix (PDM) formalism which treats quantum correlations in space and time on an equal footing. Using the well known damped Jaynes-Cummings model of a two-level system interacting with a bosonic reservoir at zero temperature as an example, it is shown that breakdown of monotonicity of the causality measure is associated with the revival of temporal (causal) correlations hence with the negativity of the decay rate. Also, a note on the comparison with other well known non-Markovianity measures is given.

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arXiv2020

Ping-pong quantum key distribution with trusted noise: non-Markovian advantage

The ping-pong protocol adapted for quantum key distribution is studied in the trusted quantum noise scenario, wherein the legitimate parties can add noise locally. For a well-studied attack model, we show how non-unital quantum non-Markovianity of the added noise can improve the key rate. We also point out that this noise-induced advantage cannot be obtained by Alice and Bob by adding local classical noise to their post-measurement data.

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arXiv2020

Temporal self-similarity of quantum dynamical maps as a concept of memorylessness

The problem of defining quantum non-Markovianity has proven elusive, with various in-equivalent criteria put forth to address it. The concept of CP-indivisibility and the hierarchy of stronger divisibility criteria going up to P-indivisibility, capture a fundamental aspect of memory in quantum non-Markovianity. In practice, however, there can be a memory-like influence associated with divisible channels in the form of weakening, if not reversing, the effects of decoherence. Arguably, such a facet of memory relates to CP-indivisibility as quantum discord relates to entanglement. We concretize this weaker notion of non-Markovianity by identifying it with deviation from ``temporal self-similarity'', the property of a system dynamics whereby the propagator between two intermediate states is independent of the initial time $t_0$. We illustrate this idea through examples, and propose a geometric quantification of temporal self-similarity, and show how our approach complements the divisibility-based criterion of quantum non-Markovianity.

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