arXiv subjects

Varun Narasimhachar

Publications and source records attributed to Varun Narasimhachar.

At least 19 recordsLinked to original sources

arXiv2026

Time-ordered free energy in correlated quantum systems: An agentic approach

How much work can an agent extract from a temporal sequence of quantum states when it can only operate online under causal constraints---deciding which energy extraction method to use with knowledge of what it has observed before? Here, we study this problem in the context of quantum state sequences that are potentially non-Markovian---generated by some underlying hidden Markov machine that the agent cannot observe. Using techniques from dynamic programming and computational mechanics, we present a method to identify the provably optimal agent strategy, with time complexity that scales linearly with sequence length. This motivates us to introduce the maximum work such agents can extract---time-ordered free energy(TOFE)---as a fundamental measure of free energy available in a temporally correlated quantum system subject to causal considerations.

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arXiv2026

Approximate virtual quantum broadcasting

The no-broadcasting theorem, a fundamental limitation on the communication of quantum information, holds that a physical process cannot broadcast copies of an unknown quantum state to two or more receivers. Recent work has explored ways of circumventing this limitation using "virtual" implementations of non-physical processes using measurement and data-processing on statistical samples of the unknown input. However, the statistical fluctuations of this data degrades the virtual copies so much that the protocol effectively depletes, rather than proliferate, the sample size -- thereby rendering it worse than the "naive" approach of splitting the given sample and sending a subsample to each receiver. In this work, we circumvent this flaw by allowing a small amount of systematic bias in the broadcast data, resulting in approximate virtual copies. We provide efficient semidefinite programs (SDP's) to determine the minimum sample size required to keep the approximation error below a desired threshold and vice versa. For reasonably small error values, we find approximate virtual broadcasting to be viable with sample sizes smaller than naive sample-splitting would demand. Along the way, we prove several symmetry-based simplifications to the problem, allowing optimal approximate broadcasting to be characterized in terms of the simple class of depolarizing channels.

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arXiv2025

The Dirac--Bergmann approach to optimal control theory

We present a novel framework for optimal control in both classical and quantum systems. Our approach leverages the Dirac--Bergmann algorithm: a systematic method for formulating and solving constrained dynamical systems. In contrast to the standard Pontryagin Principle, which is used in control theory, our approach bypasses the need to perform a variation to obtain the optimal solution. Instead, the Dirac--Bergmann algorithm generates the optimal solution automatically, through the closure of the Poission Bracket algebra of the full set of constraints and the Hamiltonian. The efficacy of our framework is demonstrated through two quintessential examples: (1) the classical brachistochrone problem and (2) the time-optimal control of a generic quantum system, relevant for quantum technological applications. In the latter example, both closed and open quantum systems are discussed.

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arXiv2025

The coherent measurement cost of coherence distillation

Quantum coherence -- an indispensable resource for quantum technologies -- is known to be distillable from a noisy form using operations that cannot create it. However, distillation exacts a hidden coherent measurement cost, which has not previously been examined. We devise the target effect construction to characterize this cost through detailed conditions on the coherence-measuring structure necessary in any process realizing exact (maximal or non-maximal) or approximate distillation. As a corollary, we lower-bound the requisite measurement coherence, as quantified by operationally-relevant measures. We then consider the asymptotic limit of distilling from many copies of a given noisy coherent state, where we offer rigorous arguments to support the conjecture that the (necessary and sufficient) coherent measurement cost scales extensively in the number of copies. We also show that this cost is no smaller than the coherence of measurements saturating the scaling law in the generalized quantum Stein's lemma. Our results and conjectures apply to any task whereof coherence distillation is an incidental outcome (e.g., incoherent randomness extraction). But if pure coherence is the only desired outcome, our conjectures would have the cautionary implication that the measurement cost is often higher than the distilled yield, in which case coherence should rather be prepared afresh than distilled from a noisy input.

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arXiv2025

Optimized circuits for windowed modular arithmetic with applications to quantum attacks against RSA

Windowed arithmetic [Gidney, 2019] is a technique for reducing the cost of quantum arithmetic circuits with space--time tradeoffs using memory queries to precomputed tables. It can reduce the asymptotic cost of modular exponentiation from $O\left(n^3\right)$ to $O\left(n^3/\log^2 n\right)$ operations, resulting in the current state-of-the-art compilations of quantum attacks against modern cryptography. In this work we introduce four optimizations to windowed modular exponentiation. We (1) show how the cost of unlookups can be reduced by $66\%$ asymptotically in the number of bits, (2) illustrate how certain addresses can be bypassed, reducing both circuit depth and the overall lookup cost, (3) demonstrate that multiple lookup--addition operations can be merged into a single, larger lookup at the start of the modular exponentiation circuit, and (4) reduce the depth of the unary conversion for unlookups. On a logical level, this leads to a $3\%$ improvement in Toffoli count and Toffoli depth for modular exponentiation circuits relevant to cryptographic applications. This translates to some improvements on [Gidney and Ekerå, 2021]'s factoring algorithm: for a given number of physical qubits, our improvements show a reduction in the expected runtime from $2\%$ to $6\%$ for factoring $\mathsf{RSA}$-$2048$ integers.

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arXiv2024

Causal classification of spatiotemporal quantum correlations

From correlations in measurement outcomes alone, can two otherwise isolated parties establish whether such correlations are atemporal? That is, can they rule out that they have been given the same system at two different times? Classical statistics says no, yet quantum theory disagrees. Here, we introduce the necessary and sufficient conditions by which such quantum correlations can be identified as atemporal. We demonstrate the asymmetry of atemporality under time reversal, and reveal it to be a measure of spatial quantum correlation distinct from entanglement. Our results indicate that certain quantum correlations possess an intrinsic arrow of time, and enable classification of general quantum correlations across space-time based on their (in)compatibility with various underlying causal structures.

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arXiv2024

Measurement-based uncomputation of quantum circuits for modular arithmetic

Measurement-based uncomputation (MBU) is a technique used to perform probabilistic uncomputation of quantum circuits. We formalize this technique for the case of single-qubit registers, and we show applications to modular arithmetic. First, we present formal statements for several variations of quantum circuits performing non-modular addition: controlled addition, addition by a constant, and controlled addition by a constant. We do the same for subtraction and comparison circuits. This addresses gaps in the current literature, where some of these variants were previously unexplored. Then, we shift our attention to modular arithmetic, where again we present formal statements for modular addition, controlled modular addition, modular addition by a constant, and controlled modular addition by a constant, using different kinds of plain adders and combinations thereof. We introduce and prove a "MBU lemma" in the context of single-qubit registers, which we apply to all aforementioned modular arithmetic circuits. Using MBU, we reduce the Toffoli count and depth by $10\%$ to $15\%$ for modular adders based on the architecture of [VBE96], and by almost $25\%$ for modular adders based on the architecture of [Bea02]. Our results have the potential to improve other circuits for modular arithmetic, such as modular multiplication and modular exponentiation, and can find applications in quantum cryptanalysis.

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arXiv2023

Quantum-optimal information encoding using noisy passive linear optics

The amount of information that a noisy channel can transmit has been one of the primary subjects of interest in information theory. In this work we consider a practically-motivated family of optical quantum channels that can be implemented without an external energy source. We optimize the Holevo information over procedures that encode information in attenuations and phase-shifts applied by these channels on a resource state of finite energy. It is shown that for any given input state and environment temperature, the maximum Holevo information can be achieved by an encoding procedure that uniformly distributes the channel's phase-shift parameter. Moreover for large families of input states, any maximizing encoding scheme has a finite number of channel attenuation values, simplifying the codewords to a finite number of rings around the origin in the output phase space. The above results and numerical evidence suggests that this property holds for all resource states. Our results are directly applicable to the quantum reading of an optical memory in the presence of environmental thermal noise.

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arXiv2023

Engines for predictive work extraction from memoryful quantum stochastic processes

Quantum information-processing techniques enable work extraction from a system's inherently quantum features, in addition to the classical free energy it contains. Meanwhile, the science of computational mechanics affords tools for the predictive modeling of non-Markovian classical and quantum stochastic processes. We combine tools from these two sciences to develop a technique for predictive work extraction from non-Markovian stochastic processes with quantum outputs. We demonstrate that this technique can extract more work than non-predictive quantum work extraction protocols, on one hand, and predictive work extraction without quantum information processing, on the other. We discover a phase transition in the efficacy of memory for work extraction from quantum processes, which is without classical precedent. Our work opens up the prospect of machines that harness environmental free energy in an essentially quantum, essentially time-varying form.

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arXiv2023

Amplification, Mitigation and Energy Storage via Constrained Thermalization

Amplification (mitigation) is the increase (decrease) in the change of thermodynamic quantities when an initial thermal state is thermalized to a different temperature in the presence of constraints, studied thus far only for permutationally invariant baths. In this manuscript, we generalize amplification and mitigation to accommodate generic strong symmetries of open quantum systems and connect the phenomenon to Landauer's erasure. We exemplify our general theory with a new bath-induced battery charging protocol that overcomes the passivity of KMS-preserving transitions.

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arXiv2021

Fisher information universally identifies quantum resources

We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states with and without a given resource. This shows that all quantum resources confer an advantage in metrology, and establishes the Fisher information as a universal tool to probe the resourcefulness of quantum states. We provide bounds on the extent of this advantage, as well as a simple criterion to test whether different resources are useful for the estimation of unitarily encoded parameters. Finally, we extend the results to show that the Fisher information is also able to identify the dynamical resourcefulness of quantum operations.

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arXiv2021

Thermodynamic resources in continuous-variable quantum systems

Thermodynamic resources, beyond their well-known usefulness in work extraction and other thermodynamic tasks, are often important also in tasks that are not evidently thermodynamic. Here we develop a framework for identifying such resources in diverse applications of bosonic continuous-variable systems. Introducing the class of bosonic linear thermal operations to model operationally-feasible processes, we apply this model to identify uniquely quantum properties of bosonic states that refine classical notions of thermodynamic resourcefulness. Among these are (1) a suite of temperature-like quantities generalizing the equilibrium temperature to quantum, non-equilibrium scenarios; (2) signal-to-noise ratios quantifying a system's capacity to carry information in phase-space displacement; and (3) well-established non-classicality measures quantifying the resolution in sensing and parameter estimation tasks.

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arXiv2020

Agents governed by quantum mechanics can use it intersubjectively and consistently

Following Frauchiger and Renner's discovery of a conflict between quantum mechanics and certain commonsense reasoning axioms, much work has gone into finding alternative axiomatizations that can avoid the conflict. However, this body of work is largely based on specific interpretations of quantum mechanics, and at times employs specialized formalism that may be inaccessible to mainstream quantum information experts. Taking an interpretation-agnostic approach, we propose a simple operational principle called superpositional solipsism to aid rational agents in making situational inferences. We show that the principle leads to sound inferences in all operationally-relevant instances. Along the way, we discuss certain subtleties about the Frauchiger--Renner result that may have gone hithertofore unnoticed.

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arXiv2019

Coherence manipulation with dephasing-covariant operations

We characterize the operational capabilities of quantum channels which can neither create nor detect quantum coherence vis-à-vis efficiently manipulating coherence as a resource. We study the class of dephasing-covariant operations (DIO), unable to detect the coherence of any input state, as well as introduce an operationally-motivated class of channels $ρ$-DIO which is tailored to a specific input state. We first show that pure-state transformations under DIO are completely governed by majorization, establishing necessary and sufficient conditions for such transformations and adding to the list of operational paradigms where majorization plays a central role. We then show that $ρ$-DIO are strictly more powerful: although they cannot detect the coherence of the input state $ρ$, the operations $ρ$-DIO can distill more coherence than DIO. However, the advantage disappears in the task of coherence dilution as well as generally in the asymptotic limit, where both sets of operations achieve the same rates in all transformations.

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arXiv2019

Quantifying memory capacity as a quantum thermodynamic resource

The information-carrying capacity of a memory is known to be a thermodynamic resource facilitating the conversion of heat to work. Szilard's engine explicates this connection through a toy example involving an energy-degenerate two-state memory. We devise a formalism to quantify the thermodynamic value of memory in general quantum systems with nontrivial energy landscapes. Calling this the thermal information capacity, we show that it converges to the non-equilibrium Helmholtz free energy in the thermodynamic limit. We compute the capacity exactly for a general two-state (qubit) memory away from the thermodynamic limit, and find it to be distinct from known free energies. We outline an explicit memory--bath coupling that can approximate the optimal qubit thermal information capacity arbitrarily well.

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arXiv2019

Matrix Product States for Quantum Stochastic Modelling

In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states (MPS) are known as a particularly efficient representation of 1D spin chains. In this Letter, we associate each stochastic process with a suitable quantum state of a spin chain. We then show that the optimal predictive model for the process leads directly to an MPS representation of the associated quantum state. Conversely, MPS methods offer a systematic construction of the best known quantum predictive models. This connection allows an improved method for computing the quantum memory needed for generating optimal predictions. We prove that this memory coincides with the entanglement of the associated spin chain across the past-future bipartition.

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arXiv2018

Operational resource theory of continuous-variable nonclassicality

Genuinely quantum states of a harmonic oscillator may be distinguished from their classical counterparts by the Glauber-Sudarshan P-representation -- a state lacking a positive P-function is said to be nonclassical. In this paper, we propose a general operational framework for studying nonclassicality as a resource in networks of passive linear elements and measurements with feed-forward. Within this setting, we define new measures of nonclassicality based on the quantum fluctuations of quadratures, as well as the quantum Fisher information of quadrature displacements. These lead to fundamental constraints on the manipulation of nonclassicality, especially its concentration into subsystems, that apply to generic multi-mode non-Gaussian states. Special cases of our framework include no-go results in the concentration of squeezing and a complete hierarchy of nonclassicality for single mode Gaussian states.

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arXiv2018

Understanding quantum physics through simple experiments: from wave-particle duality to Bell's theorem

Quantum physics, which describes the strange behavior of light and matter at the smallest scales, is one of the most successful descriptions of reality, yet it is notoriously inaccessible. Here we provide an approachable explanation of quantum physics using simple thought experiments. We derive all relevant quantum predictions using minimal mathematics, without introducing the advanced calculations that are typically used to describe quantum physics. We focus on the two key surprises of quantum physics, namely wave-particle duality, a term that was introduced to capture the fact that single quantum particles in some respects behave like waves and in other respects like particles, and entanglement, which applies to two or more quantum particles and brings out the inherent contradiction between quantum physics and seemingly obvious assumptions regarding the nature of reality. Following arguments originally made by John Bell and Lucien Hardy, we show that the so-called local hidden variables are inadequate at explaining the behavior of entangled quantum particles. This means that one either has to give up on hidden variables, i.e., the idea that the outcomes of measurements on quantum particles are determined before an experiment is actually carried out, or one has to relinquish the principle of locality, which requires that no causal influences should be faster than the speed of light and is a cornerstone of Einstein's theory of relativity. Finally, we describe how these remarkable predictions of quantum physics have been confirmed in experiments. We have successfully used the present approach in a course that is open to all undergraduate students at the University of Calgary, without any prerequisites in mathematics or physics.

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