arXiv subjects

Amit Kumar Pal

Publications and source records attributed to Amit Kumar Pal.

At least 37 records · Page 2Linked to original sources

arXiv2023

Quantum state transfer using 1D Heisenberg Hamiltonian on quasi-1D lattices

We consider transfer of single and multi-qubit states on a quasi-1D lattice, where the time evolutions involved in the state transfer protocol are generated by only 1D Hamiltonians. We use the quasi-1D isotropic Heisenberg model under a magnetic field along the $z$ direction, where the spin-spin interaction strengths along the vertical sublattices, referred to as rungs, are much stronger than the interactions along other sublattices. Tuning the field-strength to a special value, in the strong rung-coupling limit, the quasi-1D isotropic Heisenberg model can be mapped to an effective 1D XXZ model, where each rung mimics an effective two-level system. Consequently, the transfer of low-energy rung states from one rung to another can be represented by a transfer of an arbitrary single-qubit state from one lattice site to another using the 1D XXZ model. Exploiting this, we propose protocols for transferring arbitrary single-qubit states from one lattice site to another by using specific encoding of the single-qubit state into a low-energy rung state, and a subsequent decoding of the transferred state on the receiver rung. These encoding and decoding protocols involve a time evolution generated by the 1D rung Hamiltonian and single-qubit phase gates, ensuring that all time-evolutions required for transferring the single-qubit state are generated from 1D Hamiltonians. We show that the performance of the single-qubit state transfer using the proposed protocol is always better than the same when a time-evolution generated by the full quasi-1D Hamiltonian is used.

quant-ph↗

arXiv2023

Designing refrigerators in higher dimensions using quantum spin models

We design quantum refrigerators based on spin-j quantum XYZ and bilinear-biquadratic models with individual spins attached to bosonic thermal baths. By considering both local and global master equations, we illustrate an enhancement in the performance of the refrigerators with an increase in the spin dimension irrespective of the choice of the spin models. To assess the performance of the refrigerators, we introduce a distance-based measure to quantify the local temperature of a particle with arbitrary spin quantum number j. Interestingly, we find that the local temperature quantifier, defined via minimizing the distance between a spin-j thermal state and the evolved state of the spin-j particle in the steady state, coincides with the population-based definition of local temperature known in the literature for spin-1/2 particles. Moreover, we demonstrate that the qualitative behavior of the distance-based local temperature is independent of the choice of the distance measure by comparing the trace distance, Uhlmann's fidelity and relative entropy distance. We further observe by computing local master equation that the quantum refrigerator consisting of a spin-1/2 and a spin-j particle can lead to a lower local temperature compared to a refrigerator with two identical spin-j particles following the XYZ interactions.

quant-ph↗

arXiv2023

Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit

In this paper, we calculate entanglement in the isotropic Heisenberg model in a magnetic field on a two-dimensional rectangular zig-zag lattice in the strong rung-coupling limit, using the one-dimensional XXZ model as a proxy. Focusing on the leading order in perturbation, for arbitrary size of the lattice, we show how the one-dimensional effective description emerges. We point out specific states in the low-energy sector of the two-dimensional model that are well-approximated by the one-dimensional spin-1/2 XXZ model. We propose a systematic approach for mapping matrix-elements of operators defined on the two-dimensional model to their low-energy counterparts on the one-dimensional XXZ model. We also show that partial trace-based description of entanglement in the two-dimensional model can be satisfactorily approximated using the one-dimensional XXZ model as a substitute. We further show numerically that the one-dimensional XXZ model performs well in estimating entanglement quantified using a measurement-based approach in the two-dimensional model for specific choices of measured Hermitian operators.

quant-ph↗

arXiv2022

Circulating Genuine Multiparty Entanglement in Quantum Network

We propose a deterministic scheme of generating genuine multiparty entangled states in quantum networks of arbitrary size having various geometric structures -- we refer to it as entanglement circulation. The procedure involves optimization over a set of two-qubit arbitrary unitary operators and the entanglement of the initial resource state. We report that the set of unitary operators that maximize the genuine multipartite entanglement quantified via generalized geometric measure (GGM) is not unique. We prove that the GGM of the resulting state of arbitrary qubits coincides with the minimum GGM of the initial resource states. By fixing the output state as the six-qubit one, we find the optimal way to create such states according to the available resource. Moreover, we show that the method proposed here can be implemented by using logic gates, or by using the time dynamics of realizable spin Hamiltonians. In case of an ordered system, GGM varies periodically with time while the evolution via disordered models lead to a low but constant multipartite entanglement in outputs at a critical time, which decreases exponentially with the increase of the strength of the disorder.

quant-ph↗

arXiv2022

Distinguishing Phases via Non-Markovian Dynamics of Entanglement in Topological Quantum Codes under Parallel Magnetic Field

We investigate the static and the dynamical behavior of localizable entanglement and its lower bounds on nontrivial loops of topological quantum codes with parallel magnetic field. Exploiting the connection between the stabilizer states and graph states in the absence of the parallel field and external noise, we identify a specific measurement basis, referred to as the canonical measurement basis, that optimizes localizable entanglement when measurement is restricted to single-qubit Pauli measurements only, thereby providing a lower bound. We also propose an approximation of the lower bound that can be computed for larger systems according to the computational resource in hand. Additionally, we compute a lower bound of the localizable entanglement that can be computed by determining the expectation value of an appropriately designed witness operator. We study the behavior of these lower bounds in the vicinity of the topological to nontopological quantum phase transition of the system, and perform a finite-size scaling analysis. We also investigate the dynamical features of these lower bounds when the system is subjected to Markovian or non-Markovian single-qubit dephasing noise. We find that in the case of the non-Markovian dephasing noise, at large time, the canonical measurement-based lower bound oscillates with a larger amplitude when the initial state of the system undergoing dephasing dynamics is chosen from the nontopological phase, compared to the same for an initial state from the topological phase. These features can be utilized to distinguish the topological phase of the system from the nontopological phase in the presence of dephasing noise.

quant-ph↗

arXiv2022

Designing Robust Quantum Refrigerators in Disordered Spin Models

We explore a small quantum refrigerator in which the working substance is made of paradigmatic nearest-neighbor quantum spin models, the XYZ and the XY model with Dzyaloshinskii-Moriya interactions, consisting of two and three spins, each of which is in contact with a bosonic bath. We identify a specific range of interaction strengths which can be tuned appropriately to ensure a cooling of the selected spin in terms of its local temperature in the weak-coupling limit. Moreover, we report that in this domain, when one of the interaction strengths is disordered, the performance of the thermal machine operating as a refrigerator remains almost unchanged instead of degradation, thereby establishing the flexibility of this device. However, to obtain a significant amount of cooling via ordered as well as disordered spin models, we observe that one has to go beyond the weak-coupling limit and compute the figures of merits by using global master equations.

quant-ph↗

arXiv2022

Exactly Solvable 1D Quantum Models with Gamma Matrices

In this paper, we write exactly solvable generalizations of 1-dimensional quantum XY and Ising-like models by using $2^d$-dimensional Gamma ($Γ$) matrices as the degrees of freedom on each site. We show that these models result in quadratic Fermionic Hamiltonians with Jordan-Wigner like transformations. We illustrate the techniques using a specific case of 4-dimensional $Γ$ matrices and explore the quantum phase transitions present in the model.

cond-mat.stat-mech↗

arXiv2021

Relaxation times do not capture logical qubit dynamics

Quantum error correction procedures have the potential to enable faithful operation of large-scale quantum computers. They protect information from environmental decoherence by storing it in logical qubits, built from ensembles of entangled physical qubits according to suitably tailored quantum error correcting encodings. To date, no generally accepted framework to characterise the behaviour of logical qubits as quantum memories has been developed. In this work, we show that generalisations of well-established figures of merit of physical qubits, such as relaxation times, to logical qubits fail and do not capture dynamics of logical qubits. We experimentally illustrate that, in particular, spatial noise correlations can give rise to rich and counter-intuitive dynamical behavior of logical qubits. We show that a suitable set of observables, formed by code space population and logical operators within the code space, allows one to track and characterize the dynamical behaviour of logical qubits. Awareness of these effects and the efficient characterisation tools used in this work will help to guide and benchmark experimental implementations of logical qubits.

quant-ph↗

arXiv2021

Three qubits in less than three baths: Beyond two-body system-bath interactions in quantum refrigerators

We show that quantum absorption refrigerators, which have traditionally been studied as of three qubits, each of which is connected to a thermal reservoir, can also be constructed by using three qubits and two thermal baths, where two of the qubits, including the qubit to be locally cooled, are connected to a common bath. With a careful choice of the system, bath, and qubit-bath interaction parameters within the Born-Markov and rotating-wave approximations, one of the qubits attached to the common bath achieves a cooling in the steady state. We observe that the proposed refrigerator may also operate in a parameter regime where no or negligible steady-state cooling is achieved, but there is considerable transient cooling. The steady-state temperature can be lowered significantly by an increase in the strength of the few-body interaction terms existing due to the use of the common bath in the refrigerator setup. The proposed refrigerator built with three qubits and two baths is shown to provide steady-state cooling for both Markovian qubit-bath interactions between the qubits and canonical bosonic thermal reservoirs, and a simpler reset model for the qubit-bath interactions.

quant-ph↗

arXiv2021

Some results on the unique range sets

In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions.\par Also, we present some uniqueness theorems which show how two meromorphic functions are uniquely determined by their two finite shared sets. Moreover, in the last section, we make some observations that help us to construct other new classes of unique range sets.

math.CV↗

arXiv2021

Unique range sets of meromorphic functions of non-integer finite order

This paper studies the uniqueness of two non-integral finite ordered meromorphic functions with finitely many poles when they share two finite sets. Also, studies an answer to a question posed by Gross for a particular class of meromorphic functions. Moreover, some observations are made on some results due to Sahoo and Karmakar ( Acta Univ. Sapientiae, Mathematica, DOI: 10.2478/ausm-2018-0025) and Sahoo and Sarkar (Bol. Soc. Mat. Mex., DOI: 10.1007/s40590-019-00260-4).

math.CV↗

arXiv2020

Scalable characterization of localizable entanglement in noisy topological quantum codes

Topological quantum error correcting codes have emerged as leading candidates towards the goal of achieving large-scale fault-tolerant quantum computers. However, quantifying entanglement in these systems of large size in the presence of noise is a challenging task. In this paper, we provide two different prescriptions to characterize noisy stabilizer states, including the surface and the color codes, in terms of localizable entanglement over a subset of qubits. In one approach, we exploit appropriately constructed entanglement witness operators to estimate a witness-based lower bound of localizable entanglement, which is directly accessible in experiments. In the other recipe, we use graph states that are local unitary equivalent to the stabilizer state to determine a computable measurement-based lower bound of localizable entanglement. If used experimentally, this translates to a lower bound of localizable entanglement obtained from single-qubit measurements in specific bases to be performed on the qubits outside the subsystem of interest. Towards computing these lower bounds, we discuss in detail the methodology of obtaining a local unitary equivalent graph state from a stabilizer state, which includes a new and scalable geometric recipe as well as an algebraic method that applies to general stabilizer states of arbitrary size. Moreover, as a crucial step of the latter recipe, we develop a scalable graph-transformation algorithm that creates a link between two specific nodes in a graph using a sequence of local complementation operations. We develop open-source Python packages for these transformations, and illustrate the methodology by applying it to a noisy topological color code, and study how the witness and measurement-based lower bounds of localizable entanglement varies with the distance between the chosen qubits.

quant-ph↗

arXiv2020

Uniform Decoherence Effect on Localizable Entanglement in Random Multi-qubit Pure States

We investigate the patterns in distributions of localizable entanglement over a pair of qubits for random multi-qubit pure states. We observe that the mean of localizable entanglement increases gradually with increasing the number of qubits of random pure states while the standard deviation of the distribution decreases. The effects on the distributions, when the random pure multi-qubit states are subjected to local as well as global noisy channels, are also investigated. Unlike the noiseless scenario, the average value of the localizable entanglement remains almost constant with the increase in the number of parties for a fixed value of noise parameter. We also find out that the maximum strength of noise under which entanglement survives can be independent of the localizable entanglement content of the initial random pure states.

quant-ph↗

arXiv2020

Hierarchies of localizable entanglement due to spatial distribution of local noise

Complete characterization of a noisy multipartite quantum state in terms of entanglement requires full knowledge of how the entanglement content in the state is affected by the spatial distribution of noise in the state. Specifically, we find that if the measurement-basis in the protocol of computing localizable entanglement and the basis of the Kraus operator representing the local noisy channel do not commute, the information regarding the noise is retained in the system even after the qubit is traced out after measurement. Using this result and the basic properties of entanglement under noise, we present a set of hierarchies that localizable entanglement over a specific subsystem in a multiqubit state can obey when local noise acts on the subparts or on all the qubits of the whole system. In particular, we propose two types of hierarchies -- one tailored according to the number of noisy unmeasured qubits, and the other one that depends additionally on the cardinality of the set of noisy measured qubits, leading to the classification of quantum states. We report the percentage of states satisfying the proposed hierarchies in the case of random three- and four-qubit systems and show, using both analytical methods and numerical simulations, that in almost all the cases, anticipated hierarchies tend to hold with the variation of the strength of noise.

quant-ph↗

arXiv2019

Value distribution of some differential monomials

Let $f$ be a transcendental meromorphic function defined in the complex plane $\mathbb{C}$. We consider the value distribution of the differential polynomial $f^{q_{0}}(f^{(k)})^{q_{k}}$, where $q_{0}(\geq 2), q_{k}(\geq 1)$ are $k(\geq1)$ non-negative integers. We obtain a quantitative estimation of the characteristic function $T(r, f)$ in terms of $\overline{N}\left(r,\frac{1}{f^{q_{_{0}}}(f^{(k)})^{q_{k}}-1}\right)$.\par Our result generalizes the results obtained by Xu et al. (Math. Inequal. Appl., 14, 93-100, 2011) and Karmakar and Sahoo (Results Math., 73, 2018) for a particular class of transcendental meromorphic functions.

math.CV↗

arXiv2018

Scale-invariant freezing of entanglement

We show that bipartite entanglement in a one-dimensional quantum spin model undergoing time-evolution under local Markovian environments can be frozen over time. We demonstrate this by using a number of paradigmatic quantum spin models in one dimension, including the anisotropic XY model in the presence of a uniform and an alternating transverse magnetic field (ATXY), the XXZ model, the XYZ model, and the $J_1-J_2$ model involving the next-nearest-neighbor interactions. We show that the length of the freezing interval, for a chosen pair of nearest-neighbor spins, may remain independent of the length of the spin-chain, for example, in paramagnetic phases of the ATXY model, indicating a scale-invariance. Such freezing of entanglement is found to be robust against a change in the environment temperature, presence of disorder in the system, and whether the noise is dissipative, or not dissipative. Moreover, we connect the freezing of entanglement with the propagation of information through a quantum many-body system, as considered in the Lieb-Robinson theorem. We demonstrate that the variation of the freezing duration exhibits a quadratic behavior against the distance of the nearest-neighbor spin-pair from the noise-source, obtained from exact numerical simulations, in contrast to the linear one as predicted by the Lieb-Robinson theorem.

quant-ph↗

arXiv2018

Estimating localizable entanglement from witnesses

Computing localizable entanglement for noisy many-particle quantum states is difficult due to the optimization over all possible sets of local projection measurements. Therefore, it is crucial to develop lower bounds, which can provide useful information about the behaviour of localizable entanglement, and which can be determined by measuring a limited number of operators, or by performing least number of measurements on the state, preferably without performing a full state tomography. In this paper, we adopt two different yet related approaches to obtain a witness-based, and a measurement-based lower bounds for localizable entanglement. The former is determined by the minimal amount of entanglement that can be present in a subsystem of the multipartite quantum state, which is consistent with the expectation value of an entanglement witness. Determining this bound does not require any information about the state beyond the expectation value of the witness operator, which renders this approach highly practical in experiments. The latter bound of localizable entanglement is computed by restricting the local projection measurements over the qubits outside the subsystem of interest to a suitably chosen basis. We discuss the behaviour of both lower bounds against local physical noise on the qubits, and discuss their dependence on noise strength and system size. We also analytically determine the measurement-based lower bound in the case of graph states under local uncorrelated Pauli noise.

quant-ph↗

arXiv2018

Emergence of entanglement with temperature and time in factorization-surface states

There exist zero-temperature states in quantum many-body systems that are fully factorized, thereby possessing vanishing entanglement, and hence being of no use as resource in quantum information processing tasks. Such states can become useful for quantum protocols when the temperature of the system is increased, and when the system is allowed to evolve under either the influence of an external environment, or a closed unitary evolution driven by its own Hamiltonian due to a sudden change in the system parameters. Using the one-dimensional anisotropic XY model in a uniform and an alternating transverse magnetic field, we show that entanglement of the thermal states, corresponding to the factorization points in the space of the system parameters, revives once or twice with increasing temperature. We also study the closed unitary evolution of the quantum spin chain driven out of equilibrium when the external magnetic fields are turned off, and show that considerable entanglement is generated during the dynamics, when the initial state has vanishing entanglement. Interestingly, we find that creation of entanglement for a pair of spins is possible when the system is made open to an external heat bath, interacting through that spin-pair having a repetitive quantum interaction.

quant-ph↗