arXiv subjects

Namit Anand

Publications and source records attributed to Namit Anand.

30 records · Page 2Linked to original sources

arXiv2023

Scrambling of Algebras in Open Quantum Systems

Many quantitative approaches to the dynamical scrambling of information in quantum systems involve the study of out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us to study information scrambling of generalized quantum subsystems under quantum channels. For closed quantum systems, this algebraic framework was recently employed to unify quantum information-theoretic notions of operator entanglement, coherence-generating power, and Loschmidt echo. The main focus of this work is to provide a natural generalization of these techniques to open quantum systems. We first show that, for unitary dynamics, the $\mathcal{A}$-OTOC quantifies a generalized notion of information scrambling, namely between a subalgebra of observables and its commutant. For open quantum systems, on the other hand, we find a competition between the global environmental decoherence and the local scrambling of information. We illustrate this interplay by analytically studying various illustrative examples of algebras and quantum channels. To complement our analytical results, we perform numerical simulations of two paradigmatic systems: the PXP model and the Heisenberg XXX model, under dephasing. Our numerical results reveal connections with many-body scars and the stability of decoherence-free subspaces.

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arXiv2022

BROTOCs and Quantum Information Scrambling at Finite Temperature

Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.

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arXiv2021

Information Scrambling and Chaos in Open Quantum Systems

Out-of-time-ordered correlators (OTOCs) have been extensively used over the last few years to study information scrambling and quantum chaos in many-body systems. In this paper, we extend the formalism of the averaged bipartite OTOC of Styliaris et al [Phys. Rev. Lett. 126, 030601 (2021)] to the case of open quantum systems. The dynamics is no longer unitary but it is described by more general quantum channels (trace preserving, completely positive maps). This "open bipartite OTOC" can be treated in an exact analytical fashion and is shown to amount to a distance between two quantum channels. Moreover, our analytical form unveils competing entropic contributions from information scrambling and environmental decoherence such that the latter can obfuscate the former. To elucidate this subtle interplay we analytically study special classes of quantum channels, namely, dephasing channels, entanglement-breaking channels, and others. Finally, as a physical application we numerically study dissipative many-body spin-chains and show how the competing entropic effects can be used to differentiate between integrable and chaotic regimes.

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arXiv2021

Quantum coherence as a signature of chaos

We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos. We quantify this connection at two different levels: quantum states and quantum channels. At the level of states, we show how several well-studied quantifiers of chaos are, in fact, quantum coherence measures in disguise (or closely related to them). We further this connection for all quantum coherence measures by using tools from majorization theory. Then, we numerically study the coherence of chaotic-vs-integrable eigenstates and find excellent agreement with random matrix theory in the bulk of the spectrum. At the level of channels, we show that the coherence-generating power (CGP) -- a measure of how much coherence a dynamical process generates on average -- emerges as a subpart of the out-of-time-ordered correlator (OTOC), a measure of information scrambling in many-body systems. Via numerical simulations of the (nonintegrable) transverse-field Ising model, we show that the OTOC and CGP capture quantum recurrences in quantitatively the same way. Moreover, using random matrix theory, we analytically characterize the CGP-OTOC connection for the Haar and Gaussian ensembles. In closing, we remark on how our coherence-based signatures of chaos relate to other diagnostics, namely the Loschmidt echo, OTOC, and the Spectral Form Factor.

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arXiv2021

Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality

In recent years, the out-of-time-order correlator (OTOC) has emerged as a diagnostic tool for information scrambling in quantum many-body systems. Here, we present exact analytical results for the OTOC for a typical pair of random local operators supported over two regions of a bipartition. Quite remarkably, we show that this "bipartite OTOC" is equal to the operator entanglement of the evolution and we determine its interplay with entangling power. Furthermore, we compute long-time averages of the OTOC and reveal their connection with eigenstate entanglement. For Hamiltonian systems, we uncover a hierarchy of constraints over the structure of the spectrum and elucidate how this affects the equilibration value of the OTOC. Finally, we provide operational significance to this bipartite OTOC by unraveling intimate connections with average entropy production and scrambling of information at the level of quantum channels.

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arXiv2019

Quantum coherence and the localization transition

A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation precise, we study the localization transition via quantum coherence measures arising from the resource theory of coherence. We show that the escape probability, which is known to show distinct behavior in the ergodic and localized phases, arises naturally as the average of a coherence measure. Moreover, using the theory of majorization, we argue that broad families of coherence measures can detect the uniformity of the transition matrix (between the Hamiltonian and configuration bases) and hence act as probes to localization. We provide supporting numerical evidence for Anderson and Many-Body Localization (MBL). For infinitesimal perturbations of the Hamiltonian, the differential coherence defines an associated Riemannian metric. We show that the latter is exactly given by the dynamical conductivity, a quantity of experimental relevance which is known to have a distinctively different behavior in the ergodic and in the many-body localized phases. Our results suggest that the quantum information-theoretic notion of coherence and its associated geometrical structures can provide useful insights into the elusive nature of the ergodic-MBL transition.

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arXiv2019

Quantifying non-Markovianity: a quantum resource-theoretic approach

The quantification and characterization of non-Markovian dynamics in quantum systems is an essential endeavor both for the theory of open quantum systems and for a deeper understanding of the effects of non-Markovian noise on quantum technologies. Here, we introduce the robustness of non-Markovianity, an operationally-motivated, optimization-free measure that quantifies the minimum amount of Markovian noise that can be mixed with a non-Markovian evolution before it becomes Markovian. We show that this quantity is a bonafide non-Markovianity measure, since it is faithful, convex, and monotonic under composition with Markovian channels. A two-fold operational interpretation of this measure is provided, with the robustness measure quantifying an advantage in both a state discrimination and a channel discrimination task. Furthermore, we provide a closed-form analytical expression for this measure and show that, quite remarkably, the robustness measure is exactly equal to half the Rivas-Huelga-Plenio (RHP) measure [Phys. Rev. Lett. \textbf{105}, 050403 (2010)]. As a result, we provide a direct operational meaning to the RHP measure while endowing the robustness measure with the physical characterizations of the RHP measure.

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arXiv2018

Demonstration of fidelity improvement using dynamical decoupling with superconducting qubits

Quantum computers must be able to function in the presence of decoherence. The simplest strategy for decoherence reduction is dynamical decoupling (DD), which requires no encoding overhead and works by converting quantum gates into decoupling pulses. Here, using the IBM and Rigetti platforms, we demonstrate that the DD method is suitable for implementation in today's relatively noisy and small-scale cloud based quantum computers. Using DD, we achieve substantial fidelity gains relative to unprotected, free evolution of individual superconducting transmon qubits. To a lesser degree, DD is also capable of protecting entangled two-qubit states. We show that dephasing and spontaneous emission errors are dominant in these systems, and that different DD sequences are capable of mitigating both effects. Unlike previous work demonstrating the use of quantum error correcting codes on the same platforms, we make no use of post-selection and hence report unconditional fidelity improvements against natural decoherence.

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arXiv2018

Asymmetry and coherence weight of quantum states

The asymmetry of quantum states is an important resource in quantum information processing tasks such as quantum metrology and quantum communication. In this paper, we introduce the notion of $asymmetry~weight$ --- an operationally motivated asymmetry quantifier in the resource theory of asymmetry. We study the convexity and monotonicity properties of asymmetry weight and focus on its interplay with the corresponding semidefinite programming (SDP) forms along with its connection to other asymmetry measures. Since the SDP form of asymmetry weight is closely related to asymmetry witnesses, we find that the asymmetry weight can be regarded as a (state-dependent) asymmetry witness. Moreover, some specific entanglement witnesses can be viewed as a special case of an asymmetry witness --- which indicates a potential connection between asymmetry and entanglement. We also provide an operationally meaningful coherence measure, which we term $coherence~weight$, and investigate its relationship to other coherence measures like the robustness of coherence and the $l_1$ norm of coherence. In particular, we show that for Werner states in any dimension $d$, all three coherence quantifiers, namely, the coherence weight, the robustness of coherence, and the $l_1$ norm of coherence, are equal and are given by a single letter formula.

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arXiv2016

Coherence and Entanglement Monogamy in the Discrete Analogue of Analog Grover Search

Grover's search algorithm is the optimal quantum algorithm that can search an unstructured database quadratically faster than any known classical algorithm. The role of entanglement and correlations in the search algorithm have been studied in great detail and it is known that entanglement between the qubits is necessary to gain a quadratic speedup, for pure state implementation of the Grover search algorithm. Here, we systematically investigate the behavior of quantum coherence and monogamy of entanglement in the discrete analogue of the $\textit{analog analogue of Grover search algorithm}$. The analog analogue of Grover search is a continuous time quantum algorithm based on the adiabatic Hamiltonian evolution that gives a quadratic speedup, similar to the original Grover search algorithm. We show that the decrease of quantum coherence, quantified using various coherence monotones, is a clear signature of attaining the maximum success probability in the analog Grover search. We also show that for any two qubit reduced density matrix of the system, the concurrence evolves in close vicinity to the increasing rate of success probability. Furthermore, we show that the system satisfies a $n$-party monogamy inequality for arbitrary times, hence bounding the amount of $n$-qubit entanglement during the quantum search.

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arXiv2015

Do quantum strategies always win?

In a seminal paper, Meyer [David Meyer, Phys. Rev. Lett. 82, 1052 (1999)] described the advantages of quantum game theory by looking at the classical penny flip game. A player using a quantum strategy can win against a classical player almost 100\% of the time. Here we make a slight modification to the quantum game, with the two players sharing an entangled state to begin with. We then analyze two different scenarios, first in which quantum player makes unitary transformations to his qubit while the classical player uses a pure strategy of either flipping or not flipping the state of his qubit. In this case the quantum player always wins against the classical player. In the second scenario we have the quantum player making similar unitary transformations while the classical player makes use of a mixed strategy wherein he either flips or not with some probability "p". We show that in the second scenario, 100\% win record of a quantum player is drastically reduced and for a particular probability "p" the classical player can even win against the quantum player. This is of possible relevance to the field of quantum computation as we show that in this quantum game of preserving versus destroying entanglement a particular classical algorithm can beat the quantum algorithm.

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arXiv2015

Comment on Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

This is a comment to the paper, Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics by C Cisneros et al 1998 Eur. J. Phys. 19 237. doi:10.1088/0143-0807/19/3/005. The proof that the authors construct for the limitation on the superposition of state vectors corresponding to different sectors of the Hilbert space, partitioned by a superoperator has a flaw as outlined below.

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