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Ujjwal Sen

Publications and source records attributed to Ujjwal Sen.

At least 163 records · Page 9Linked to original sources
arXiv2019

Position and momentum cannot both be lazy: Quantum reciprocity relation with Lipschitz constants

We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is, in general, independent of its spread. The spreads of the position and momentum distributions are used to obtain the celebrated Heisenberg quantum uncertainty relations. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Planck's constant.

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arXiv2019

One-shot conclusive multiport quantum dense coding capacities

We introduce a probabilistic version of the one-shot quantum dense coding protocol in both two- and multiport scenarios, and refer to it as conclusive quantum dense coding. Specifically, we analyze the corresponding capacities of two-qubit, two-qutrit, and three-qubit shared states. We identify cases where Pauli and generalized Pauli operators are not sufficient as encoders to attain the optimal one-shot conclusive quantum dense coding capacities. We find that there is a rich connection between the capacities, and the bipartite and multipartite entanglements of the shared state.

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arXiv2019

Tensor-network approach to compute genuine multisite entanglement in infinite quantum spin chains

We devise a method based on the tensor-network formalism to calculate genuine multisite entanglement in ground states of infinite spin chains containing spin-1/2 or spin-1 quantum particles. The ground state is obtained by employing an infinite time-evolving block decimation method acting upon an initial matrix product state for the infinite spin system. We explicitly show how such infinite matrix product states with translational invariance provide a natural framework to derive the generalized geometric measure, a computable measure of genuine multisite entanglement, in the thermodynamic limit of quantum many-body systems with both spin-1/2 and higher-spin particles.

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arXiv2019

Inhibition of spreading in quantum random walks due to quenched Poisson-distributed disorder

We consider a quantum particle (walker) on a line who coherently chooses to jump to the left or right depending on the result of toss of a quantum coin. The lengths of the jumps are considered to be independent and identically distributed quenched Poisson random variables. We find that the spread of the walker is significantly inhibited, whereby it resides in the near-origin region, with respect to the case when there is no disorder. The scaling exponent of the quenched-averaged dispersion of the walker is sub-ballistic but super-diffusive. We also show that the features are universal to a class of sub- and super-Poissonian distributed quenched randomized jumps.

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arXiv2019

Interference-induced localization in quantum random walk on clean cyclic graph

We quantitatively differentiate between the spreads of discrete-time quantum and classical random walks on a cyclic graph. Due to the closed nature of any cyclic graph, there is additional "collision"- like interference in the quantum random walk along with the usual interference in any such walk on any graph, closed or otherwise. We find that the quantum walker remains localized in comparison to the classical one, even in the absence of disorder, a phenomenon that is potentially attributable to the additional interference in the quantum case. This is to be contrasted with the situation on open graphs, where the quantum walker, being effectively denied the collision-like interference, garners a much higher spread than its classical counterpart. We use Shannon entropy of the position probability distribution to quantify spread of the walker in both quantum and classical cases. We find that for a given number of vertices on a cyclic graph, the entropy with respect to number of steps for the quantum walker saturates, on average, to a value lower than that for the corresponding classical one. We also analyze variations of the entropies with respect to system size, and look at the corresponding asymptotic growth rates.

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arXiv2019

Quantum Process Randomness

We study the optimization of any quantum process by minimizing the "randomness" in the measurement result at the output of that quantum process. We conceptualize and propose a measure of such randomness and inquire whether an optimization of the quantum process based on that measure, can reach the point where the process operates with maximum fidelity. We consider approximate quantum cloning and teleportation processes, and find, in particular, that the optimal approximate state-dependent quantum cloning machine obtained by maximizing the fidelity is different from that obtained by minimizing the randomness.

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arXiv2019

Universal quantum uncertainty relations: minimum-uncertainty wave packet depends on measure of spread

Based on the statistical concept of the median, we propose a quantum uncertainty relation between semi-interquartile ranges of the position and momentum distributions of arbitrary quantum states. The relation is universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We show that the median-based one is not saturated for Gaussian distributions in position. Instead, the Cauchy-Lorentz distributions in position turn out to be the one with the minimal uncertainty, among the states inspected, implying that the minimum-uncertainty state is not unique but depends on the measure of spread used. Even the ordering of the states with respect to the distance from the minimum uncertainty state is altered by a change in the measure. We invoke the completeness of Hermite polynomials in the space of all quantum states to probe the median-based relation. The results have potential applications in a variety of studies including those on the quantum-to-classical boundary and on quantum cryptography.

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arXiv2019

Universality in Distribution of Monogamy Scores for Random Multiqubit Pure States

Monogamy of quantum correlations provides a way to study restrictions on their sharability in multiparty systems. We find the critical exponent of these measures, above which randomly generated multiparty pure states satisfy the usual monogamy relation, and show that the critical power decreases with the increase in the number of parties. For three-qubit pure states, we detect that W-class states are more prone to being nonmonogamous as compared to the GHZ-class states. We also observe a different criticality in monogamy power up to which random pure states remain nonmonogamous. We prove that the "average monogamy" score asymptotically approaches its maximal value on increasing the number of parties. Analyzing the monogamy scores of random three-, four-, five- and six-qubit pure states, we also report that almost all random pure six-qubit states possess maximal monogamy score, which we confirm by evaluating statistical quantities like mean, variance and skewness of the distributions. In particular, with the variation of number of qubits, means of the distributions of monogamy scores for random pure states approach to unity -- which is the algebraic maximum -- thereby conforming to the known results of random states having maximal multipartite entanglement in terms of geometric measures.

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arXiv2019

Phase boundaries in alternating field quantum XY model with Dzyaloshinskii-Moriya interaction: Sustainable entanglement in dynamics

We report all phases and corresponding critical lines of the quantum anisotropic transverse XY model with Dzyaloshinskii-Moriya (DM) interaction along with uniform and alternating transverse magnetic fields (ATXY) by using appropriately chosen order parameters. We prove that when DM interaction is weaker than the anisotropy parameter, it has no effect at all on the zero-temperature states of the XY model with uniform transverse magnetic field which is not the case for the ATXY model. However, when DM interaction is stronger than the anisotropy parameter, we show appearance of a new gapless phase - a chiral phase - in the XY model with uniform as well as alternating field. We further report that first derivatives of nearest neighbor two-site entanglement with respect to magnetic fields can detect all the critical lines present in the system. We also observe that the factorization surface at zero-temperature present in this model without DM interaction becomes a volume on the introduction of the later. We find that DM interaction can generate bipartite entanglement sustainable at large times, leading to a proof of ergodic nature of bipartite entanglement in this system, and can induce a transition from non-monotonicity of entanglement with temperature to a monotonic one.

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arXiv2019

Fibonacci sequence and its generalizations in doped quantum spin ladders

An interesting aspect of antiferromagnetic quantum spin ladders, with complete dimer coverings, is that the wave function can be recursively generated by estimating the number of coverings in the valence bond basis, which follow the fabled Fibonacci sequence. In this work, we derive generalized forms of this sequence for multi-legged and doped quantum spin ladders, which allow the corresponding dimer-covered state to be recursively generated. We show that these sequences allow for estimation of physically and information-theoretically relevant quantities in large spin lattices without resorting to complex numerical methods. We apply the formalism to calculate the valence bond entanglement entropy, which is an important figure of merit for studying cooperative phenomena in quantum spin systems with SU(2) symmetry. We show that introduction of doping may mitigate, within the quarters of entanglement entropy, the dichotomy between odd- and even- legged quantum spin ladders.

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arXiv2019

Partial coherence and quantum correlation with fidelity and affinity distances

A fundamental task in any physical theory is to quantify certain physical quantity in a meaningful way. In this paper we show that both fidelity distance and affinity distance satisfy the strong contractibility, and the corresponding resource quantifiers can be used to characterize a large class of resource theories. Under two assumptions, namely, convexity of "free states" and closure of free states under "selective free operations", our general framework of resource theory includes quantum resource theories of entanglement, coherence, partial coherence and superposition. In partial coherence theory, we show that fidelity partial coherence of a bipartite state is equal to the minimal error probability of a mixed quantum state discrimination (QSD) task and vice versa, which complements the main result in [Xiong and Wu, J. Phys. A: Math. Theor. 51, 414005 (2018)]. We also compute the analytic expression of fidelity partial coherence for $(2,n)$ bipartite X-states. At last, we study the correlated coherence in the framework of partial coherence theory. We show that partial coherence of a bipartite state, with respect to the eigenbasis of a subsystem, is actually a measure of quantum correlation.

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arXiv2018

Adiabatic freezing of entanglement with insertion of defects in a one-dimensional Hubbard model

We report on ground state phases of a doped one-dimensional Hubbard model, which for large onsite interactions is governed by the $t$-$J$ Hamiltonian, where the extant entanglement is immutable under perturbative or sudden changes of system parameters, a phenomenon termed as adiabatic freezing. We observe that in the metallic Luttinger liquid phase of the model bipartite entanglement decays polynomially and is adiabatically frozen, in contrast to the variable, exponential decay in the phase-separation and superconducting spin-gap phases. Significantly, at low fixed electron densities, the spin-gap phase shows remarkable affinity to doped resonating valence bond gas, with multipartite entanglement frozen across all parameter space. We note that entanglement, in general, is sensitive to external perturbation, as observed in several systems, and hitherto, no such invariance or freezing behavior has been reported.

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arXiv2018

Canonical Leggett-Garg Inequality: Nonclassicality of temporal quantum correlations under energy constraint

Nonclassicality of temporal correlations pertaining to noncommutative sequential measurements is defined through the violation of macrorealistic inequalities, known as Leggett-Garg inequalities (LGI). We investigate the energy cost of the process associated with the Leggett-Garg test in the context of noiseless and Markovian noise for arbitrary initial states. We prove that in noiseless and in certain noisy scenarios, the maximal violations of LGI under the energy constraint occurs when the average energy of the process is equal to the negative of the energy of the initial state. Such a dependence of LGI on the choice of the initial state is not seen in the unconstrained case. Moreover, we find that in the presence of a moderate amount of Markovian noise, the amount of violation of LGI remains almost unaltered with a suitable choice of the evolution and dephasing operators in the neighborhood of the maximal violation line, thereby showing the robustness of temporal correlations under environmental effects.

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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.

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arXiv2018

Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better

Benford's law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A marked proportion of such analyses is restricted to the first significant digit. We employ violation of Benford's law, up to the first four significant digits, for investigating magnetization and correlation data of paradigmatic quantum many-body systems to detect cooperative phenomena, focusing on the finite-size scaling exponents thereof. We find that for the transverse field quantum XY model, behavior of the very first significant digit of an observable, at an arbitrary point of the parameter space, is enough to capture the quantum phase transition in the model with a relatively high scaling exponent. A higher number of significant digits do not provide an appreciable further advantage, in particular, in terms of an increase in scaling exponents. Since the first significant digit of a physical quantity is relatively simple to obtain in experiments, the results have potential implications for laboratory observations in noisy environments.

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arXiv2018

Response to defects in multi- and bipartite entanglement of isotropic quantum spin networks

Quantum networks are an integral component in performing efficient computation and communication tasks that are not accessible using classical systems. A key aspect in designing an effective and scalable quantum network is generating entanglement between its nodes, which is robust against defects in the network. We consider an isotropic quantum network of spin-1/2 particles with a finite fraction of defects, where the corresponding wave function of the network is rotationally invariant under the action of local unitaries, and we show that any reduced density matrix also remains unaltered under the local actions. By using quantum information-theoretic concepts like strong subadditivity of von Neumann entropy and approximate quantum telecloning, we prove analytically that in the presence of defects, caused by loss of a finite fraction of spins, the network sustains genuine multisite entanglement, and at the same time may exhibit finite moderate-range bipartite entanglement, in contrast to the network with no defects.

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arXiv2018

Response in violation of Bell inequality to imperfect photon addition and subtraction in noisy squeezed states of light

Violation of Bell inequality is a prominent detection method for quantum correlations present in composite quantum systems, both in finite and infinite dimensions. We investigate the consequence on the violation of local realism based on pseduospin operators when photons are added or subtracted in a single mode or in both the modes of the two-mode squeezed states of light in presence of noise. In the noiseless situation, we show that for addition (subtraction) of photons in a single mode, there is an overall enhancement in the maximal violation, although we observe an interplay between monotonicity and non-monotonicity in the violation of Bell inequality depending on the squeezing strength. Moreover, we report that for low squeezing or low number of photons added or subtracted, subtraction in both the modes can lead to higher violation of local realism than that in the case of addition. For any choice of parameters, such ordering is not seen if one compares their entanglement contents. In the event of a faulty twin-beam generator, we obtain a lower-than-expected squeezing in the state. In such a case, or in imperfect photon addition (subtraction), or under local noise, we find that the violation of local realism by the noise-affected two-mode squeezed states always decreases. Interestingly however, we notice that photon addition (subtraction) can in general help to conquer the ill-effects of noise by enhancing the violation of local realism or by transforming non-violating states to violating ones, thereby acting as an activating agent.

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