arXiv subjects

Subhashish Banerjee

Publications and source records attributed to Subhashish Banerjee.

At least 91 records · Page 5Linked to original sources

arXiv2021

Revisiting the quantum open system dynamics of central spin model

In this article we revisit the theory of open quantum systems from the perspective of fermionic baths. Specifically, we concentrate on the dynamics of a central spin half particle interacting with a spin bath. We have calculated the exact reduced dynamics of the central spin and constructed the Kraus operators in relation to that. Further, the exact Lindblad type cannonical master equation corresponding to the reduced dynamics is constructed. We have also briefly touch upon the aspect of non-Markovianity from the backdrop of the reduced dynamics of the central spin.

quant-ph↗

arXiv2021

Experimental Snapshot Verification of non-Markovianity with Unknown System-Probe Coupling

We apply the recently proposed quantum probing protocols with an unknown system-probe coupling to probe the convex coefficients in mixtures of commuting states. By using two reference states instead of one as originally suggested, we are able to probe both lower and upper bounds for the convex coefficient. We perform extensive analysis for the roles of the parameters characterizing the double peaked Gaussian frequency spectrum in the Markovian-to-non-Markovian transition of the polarization dynamics of a single photon. We apply the probing of the convex coefficient to the transition-inducing frequency parameter and show that the non-Markovianity of the polarization dynamics can be confirmed with a single snapshot measurement of the polarization qubit performed at unknown time and even with unknown coupling. We also show how the protocol can identify Markovian and non-Markovian time intervals in the dynamics. The results are validated with single photon experiments.

quant-ph↗

arXiv2021

$\mathcal{PT}$ symmetric evolution, coherence and violation of Leggett-Garg inequalities

We report an unusual buildup of the quantum coherence in a qubit subjected to non-Hermitian evolution generated by a Parity-Time ($\mathcal{PT}$) symmetric Hamiltonian, which is reinterpreted as a Hermitian system in a higher dimensional space using Naimark dilation. The coherence is found to be maximum about the exceptional points (EPs), i.e., the points of coalescence of the eigenvalues as well as the eigenvectors. The nontrivial physics about EPs has been observed in various systems, particularly in photonic systems. As a consequence of enhancement in coherence, the various formulations of Leggett-Garg inequality tests show maximal violation about the EPs.

quant-ph↗

arXiv2021

Characterizing qubit channels in the context of quantum teleportation

We consider a scenario where a party, say, Alice prepares a pure two-qubit (either maximally entangled or non-maximally entangled) state and sends one half of this state to another distant party, say, Bob through a qubit (either unital or non-unital) channel. Finally, the shared state is used as a teleportation channel. In this scenario, we focus on characterizing the set of qubit channels with respect to the final state's efficacy as a resource of quantum teleportation (QT) in terms of maximal average fidelity and fidelity deviation (fluctuation in fidelity values over the input states). Importantly, we point out the existence of a subset of qubit channels for which the final state becomes useful for universal QT (having maximal average fidelity strictly greater than the classical bound and having zero fidelity deviation) when the initially prepared state is either useful for universal QT (i.e., for a maximally entangled state) or not useful for universal QT (i.e., for a subset of non-maximally entangled pure states). Interestingly, in the latter case, we show that non-unital channels (dissipative interactions) are more effective than unital channels (non-dissipative interactions) in producing useful states for universal QT from non-maximally entangled pure states.

quant-ph↗

arXiv2021

Projective measurements under qubit quantum channels

The action of qubit channels on projective measurements on a qubit state is used to establish an equivalence between channels and properties of generalized measurements characterized by bias and sharpness parameters. This can be interpreted as shifting the description of measurement dynamics from the Schrodinger to the Heisenberg picture. In particular, unital quantum channels are shown to induce unbiased measurements. The Markovian channels are found to be equivalent to measurements for which sharpness is a monotonically decreasing function of time. These results are illustrated by considering various noise channels. Further, the effect of bias and sharpness parameters on the energy cost of a measurement and its interplay with non-Markovianity of dynamics is also discussed

quant-ph↗

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.

quant-ph↗

arXiv2021

Characteristics of interaction between Gravitons and Photons

The direct detection of gravitational waves from binary mergers has been hailed as the discovery of the century. In the light of recent evidence on the existence of gravitational waves, it is now possible to know about the properties of matter under extreme conditions in compact astrophysical objects and different dynamical spacetimes. The foremost theme of the present article is to bring out the various features of the interaction between photons and gravitons that can be used in astrophysical observations. The effective action of interacting photons containing light-matter coupling and self-interaction term is constructed by eliminating the graviton degrees of freedom coupled to both matter and photons. It is shown that the equation of state of matter can be probed from the dynamics of light in this theory. The vacuum birefringence is also shown to be a generic property in this theory that arises from the non-linear nature of the self-interaction between gauge fields. Further, the non-local nature of quantum effective action with modified dispersion relation is also discussed in great detail. The above results also open an alternate way to infer the properties of gravitational waves without their direct measurement using the features of photon-graviton interaction.

gr-qc↗

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.

quant-ph↗

arXiv2021

Quantumness of channels

The reliability of quantum channels for transmitting information is of profound importance from the perspective of quantum information. This naturally leads to the question as how well a quantum state is preserved when subjected to a quantum channel. We propose a measure of quantumness of channels based on non-commutativity of quantum states that is intuitive and easy to compute. We apply the proposed measure to some well known noise channels, both Markovian as well as non-Markovian and find that the results are in good agreement with those from a recently introduced $l_1$-norm coherence based measure.

quant-ph↗

arXiv2020

Effect of memory on the violation of Leggett-Garg inequality

The Leggett-Garg inequalities impose restrictions on the values taken by some combinations of the two-time correlation functions of observables in order to be explainable by a noninvasive-realist classical model. While in the unitary dynamics, it is straightforward to compute these correlation functions, open system effects bring in subtleties. Specifically, for non-Markovian dynamics, which involves setting up of system-bath correlations, the Leggett-Garg measurements disrupt these correlations, making a full system-bath Hamiltonian approach natural. However, here we point out that the problem can also be dealt with from a reduced dynamics perspective. The key point is that the noise superoperator acting on the system must be suitably updated after measurement interventions. Also considered is the effect of Markovian versus non-Markovian behavior as well as classically non-Markovian processes on the violation of Leggett-Garg inequalities.

quant-ph↗

arXiv2020

Distinguishing environment-induced non-Markovianity from subsystem dynamics

Quantum non-Markovianity modifies the environmental decoherence of a system. This situation is enriched in complex systems owing to interactions among subsystems. We consider the problem of distinguishing the multiple sources of non-Markovianity using a simple power spectrum technique, applied to a qubit interacting with another qubit via a Jaynes-Cummings type Hamiltonian and simultaneously subjected to some well known noise channels, such as, the random telegraph noise and non-Markovian amplitude damping, which exhibit both Markovian as well as non-Markovian dynamics under different parameter ranges.

quant-ph↗

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.

quant-ph↗

arXiv2020

Exploring the extent of validity of quantum work fluctuation theorems in the presence of weak measurements

Quantum work fluctuation theorems are known to hold when the work is defined as the difference between the outcomes of projective measurements carried out on the Hamiltonian of the system at the initial and the final time instants of the experimental realization of the process. A recent study showed that the theorem breaks down if the measurement is of a more general nature, i.e. if a positive operator valued measurement is used, and the deviation vanishes only in the limit where the operators become projective in nature. We study a simple two-state system subjected to a unitary evolution under a Hamiltonian that is linearly dependent on time, and verify the validity of the above statement. We further define a weak value of work and show that the deviation from the exact work fluctuation theorems are much less in this formalism.

cond-mat.stat-mech↗

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.

quant-ph↗

arXiv2020

Phase Squeezing of Quantum Hypergraph States

Corresponding to a hypergraph $G$ with $d$ vertices, a quantum hypergraph state is defined by $|G\rangle = \frac{1}{\sqrt{2^d}}\sum_{n = 0}^{2^d - 1} (-1)^{f(n)} |n \rangle$, where $f$ is a $d$-variable Boolean function depending on the hypergraph $G$, and $|n \rangle$ denotes a binary vector of length $2^d$ with $1$ at $n$-th position for $n = 0, 1, \dots (2^d - 1)$. The non-classical properties of these states are studied. We consider annihilation and creation operator on the Hilbert space of dimension $2^d$ acting on the number states $\{|n \rangle: n = 0, 1, \dots (2^d - 1)\}$. The Hermitian number and phase operators, in finite dimensions, are constructed. The number-phase uncertainty for these states leads to the idea of phase squeezing. We establish that these states are squeezed in the phase quadrature only and satisfy the Agarwal-Tara criterion for non-classicality, which only depends on the number of vertices of the hypergraphs. We also point out that coherence is observed in the phase quadrature.

quant-ph↗

arXiv2020

Experimental Quantum Probing Measurements With No Knowledge on the System-Probe Interaction

In any natural science, measurements are the essential link between theory and observable reality. Is it possible to obtain accurate and relevant information via measurement whose action on the probed system is unknown? In other words, can one be convinced to know something about the nature without knowing in detail how the information was obtained? In this paper, we show that the answer is surprisingly, yes. We construct and experimentally implement a quantum optical probing measurement where measurements on the probes, the photons' polarization states, are used to extract information on the systems, the frequency spectra of the same photons. Unlike the pre-existing probing protocols, our measurement does not require any knowledge of the interaction between the probe and the system.

quant-ph↗

arXiv2020

Probing inequivalent forms of Legget-Garg inequality in subatomic systems

We study various formulations of Leggett-Garg inequality (LGI), specifically, the Wigner and Clauser-Horne forms of LGI, in the context of subatomic systems, in particular, three flavor neutrino as well as meson systems. The optimal forms of various LGIs for either neutrinos or mesons are seen to depend on measurement settings. For the neutrinos, some of these inequalities can be written completely in terms of experimentally measurable probabilities. Hence, the Wigner and Clauser-Horne forms of LGI are found to be more suitable as compared to the standard LGI from the experimental point of view for the neutrino system. Further, these inequalities exhibit maximum quantum violation around the energies roughly corresponding to the maximum neutrino flux. The Leggett-Garg type inequality is seen to be more suited for the meson dynamics. The meson system being inherently a decaying system, allows one to see the effect of decoherence on the extent of violation of various inequalities. Decoherence is observed to reduce the degree of violation, and hence the nonclassical nature of the system.

hep-ph↗

arXiv2020

Non-Markovian channel from the reduced dynamics of coin in quantum walk

The quantum channels with memory, known as non-Markovian channels, are of crucial importance for a realistic description of a variety of physical systems, and pave ways for new methods of decoherence control by manipulating the properties of environment such as its frequency spectrum. In this work, the reduced dynamics of coin in a discrete-time quantum walk is characterized as a non-Markovian quantum channel. A general formalism is sketched to extract the Kraus operators for a $t$-step quantum walk. Non-Markovianity, in the sense of P-indivisibility of the reduced coin dynamics, is inferred from the non-monotonous behavior of distinguishably of two orthogonal states subjected to it. Further, we study various quantum information theoretic quantities of a qubit under the action of this channel, putting in perspective, the role such channels can play in various quantum information processing tasks.

quant-ph↗