arXiv subjects

Twesh Upadhyaya

Publications and source records attributed to Twesh Upadhyaya.

15 recordsLinked to original sources

arXiv2026

Fast GHZ encoding with $1-o(1)$ fidelity

We prove that $(1-o(1))$-fidelity $N$-qubit Greenberger--Horne--Zeilinger (GHZ) encoding can be performed in time $O(\log N/N)$ using all-to-all 2-local Hamiltonians with bounded 2-qubit interaction terms. This saturates the theoretical lower bound $Ω(\log N/N)$, and by rescaling, also saturates the lower bound on signaling time for Hamiltonians with power-law interaction strengths $1/r^γ$, $γ<d$ in dimension $d$. The protocol uses spin-squeezing dynamics combined with quantum signal processing.

quant-ph↗

arXiv2026

Majorization theory for quasiprobabilities

The question of how to characterize disorder arises in a wide variety of settings, including information theory, economics, and quantum thermodynamics. The theory of majorization provides an elegant answer, playing a central role in these fields. However, the existing majorization framework is inapplicable to functions that both take negative values and are defined on infinite spaces. Yet such functions, in the form of quasiprobability distributions, are ubiquitous in fields such as quantum optics, signal analysis, and bosonic quantum computation. Here we develop a notion of majorization that is applicable to such functions, proving that it admits four equivalent characterizations that naturally reduce to the finite case, thereby generalizing a seminal theorem by Hardy, Littlewood, and Pólya. Moreover, we extend this equivalence to the setting where majorization is considered relative to an arbitrary positive distribution. We give several applications of our results in the context of quantum resource theories. These include deriving families of resource monotones and constraining quantum state conversions. We analytically and numerically study examples using the Wigner and Husimi functions, which feature prominently in quantum optics. Our results provide a comprehensive majorization framework for assessing the disorder of integrable functions over infinite measure spaces.

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arXiv2026

Thermal Throttling of Quantum State Transfer

Quantum state transfer on qubit lattices is a crucial step in a panoply of quantum information processing tasks. Understanding its fundamental limits in the presence of practical imperfections remains a pressing open question. In particular, it is unclear how thermal noise in the intermediate ancilla sites impedes transfer. In this work, we derive tight lower bounds on the necessary growth of commutator norms to achieve approximate state transfer. Specializing to 1D power-law systems with thermal ancilla states, we demonstrate that state transfer runtimes depend sensitively on the scaling of temperature with system size, improving logarithmic bounds to algebraic ones. Our work extends previous results on exact state transfer to the qualitatively different and more practically relevant regime of approximate state transfer.

quant-ph↗

arXiv2026

Numerical security framework for quantum key distribution with bypass channels

Satellite based quantum key distribution (QKD) aims to establish secure key exchange over long distances despite significant technological challenges. To alleviate some of these challenges, Ghalaii et al. [PRX Quantum 4, 040320 (2023)] proposed that any airborne eavesdropper up to a certain size can be detected by classical monitoring techniques, limiting the transmission efficiencies of any undetected Eve. This creates a new QKD scenario in which some of the transmitted signal from Alice to Bob bypasses Eve entirely. In this manuscript, we develop a general framework for computing key rates in this "bypass" scenario for discrete variable protocols. We first numerically support a conjecture that the performance of BB84 with single photons does not improve under bypass constraints, and go on to find new regimes that do. Specifically, we find improvements when the receiver's detectors have an efficiency mismatch and when BB84 is implemented using weak coherent pulses under certain squashing assumptions. Technically, our framework is realized by including marginal constraints on the source to account for bypass effects, combined with existing numerical approaches for minimizing the key rate and squashing and dimension reduction techniques to handle photonic states of unbounded dimension.

quant-ph↗

arXiv2026

Robustness-Runtime Tradeoff for Quantum State Transfer

Quantum state transfer is the primitive of transporting an unknown state on one site of a lattice to another. Using power-law interactions, recent state transfer protocols achieve speedup by utilizing the intermediate ancilla sites. However, these protocols require the ancillas to be in a perfectly initialized state, which, due to noise or imperfect control, may not be the case. In this work we introduce the $\textit{robustness}$ of a state transfer protocol, which quantifies the protocol's tolerance to error in the initial ancilla state. In the Heisenberg picture, state transfer grows operators supported on the final site such that they no longer commute with all operators on the starting site. We prove that this robustness tightly bounds the Schatten $p$-norms of these commutators between initial and final-site operators. This generalizes the known cases of $p=\infty$ and $p=2$, which govern completely state-dependent and state-independent state transfer respectively, demonstrating that intermediate values of $p$ govern partially state-dependent state transfer. In conjunction with existing power-law light cones, our result gives new minimum runtimes for partially state-dependent protocols which, in certain regimes, are parametrically better than existing bounds. We introduce new robust state transfer protocols, charting the landscape between complete state-dependence and state-independence.

quant-ph↗

arXiv2026

Bosonic statistics enhance Maxwell's demon in photonic experiment

Maxwell's demon elucidates the value of information in thermodynamics, using measurement and feedback: he evolves an equilibrated gas into a nonequilibrium state, from which one might extract work. The demon can evolve the system farther from equilibrium, on average, if the particles obey Bose-Einstein statistics than if they are distinguishable. We experimentally support this decade-and-a-half-old prediction by comparing indistinguishable with distinguishable photons. We use a fully programmable linear-optics platform, whose local photon statistics were shown recently to behave thermally. Our demon nondestructively measures the number of photons in a subset of the modes. Guided by the outcome, he conditionally interchanges the measured and unmeasured modes. This interchange creates a positive temperature difference between a mode in a particular subset and a mode in the other. The temperature difference is greater, on average, if the photons are indistinguishable. This result bolsters a long-standing prediction about the interplay among thermodynamics, information, and quantum particle statistics. Additionally, this work suggests a thermodynamic means of weakly validating boson-sampling platforms.

quant-ph↗

arXiv2024

Composable free-space continuous-variable quantum key distribution using discrete modulation

Continuous-variable (CV) quantum key distribution (QKD) allows for quantum secure communication with the benefit of being close to existing classical coherent communication. In recent years, CV QKD protocols using a discrete number of displaced coherent states have been studied intensively, as the modulation can be directly implemented with real devices with a finite digital resolution. However, the experimental demonstrations until now only calculated key rates in the asymptotic regime. To be used in cryptographic applications, a QKD system has to generate keys with composable security in the finite-size regime. In this paper, we present a CV QKD system using discrete modulation that is especially designed for urban atmospheric channels. For this, we use polarization encoding to cope with the turbulent but non-birefringent atmosphere. This will allow to expand CV QKD networks beyond the existing fiber backbone. In a first laboratory demonstration, we implemented a novel type of security proof allowing to calculate composable finite-size key rates against i.i.d. collective attacks without any Gaussian assumptions. We applied the full QKD protocol including a QRNG, error correction and privacy amplification to extract secret keys. In particular, we studied the impact of frame errors on the actual key generation.

quant-ph↗

arXiv2024

Non-Abelian transport distinguishes three usually equivalent notions of entropy production

We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities ("charges") between two systems initialized in thermal states. Three common formulae model the entropy produced. They respectively cast entropy as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number). Yet quantum charges can fail to commute. Noncommutation invites generalizations, which we posit and justify, of the three formulae. Charges' noncommutation, we find, breaks the formulae's equivalence. Furthermore, different formulae quantify different physical effects of charges' noncommutation on entropy production. For instance, entropy production can signal contextuality - true nonclassicality - by becoming nonreal. This work opens up stochastic thermodynamics to noncommuting - and so particularly quantum - charges.

quant-ph↗

arXiv2023

Finite-Size Security for Discrete-Modulated Continuous-Variable Quantum Key Distribution Protocols

Discrete-Modulated (DM) Continuous-Variable Quantum Key Distribution (CV-QKD) protocols are promising candidates for commercial implementations of quantum communication networks due to their experimental simplicity. While tight security analyses in the asymptotic limit exist, proofs in the finite-size regime are still subject to active research. We present a composable finite-size security proof against independently and identically distributed collective attacks for a general DM CV-QKD protocol. We introduce a new energy testing theorem to bound the effective dimension of Bob's system and rigorously prove security within Renner's epsilon-security framework and address the issue of acceptance sets in protocols and their security proof. We want to highlight, that our method also allows for nonunique acceptance statistics, which is necessary in practise. Finally, we extend and apply a numerical security proof technique to calculate tight lower bounds on the secure key rate. To demonstrate our method, we apply it to a quadrature phase-shift keying protocol, both for untrusted, ideal and trusted nonideal detectors. The results show that our security proof method yields secure finite-size key rates under experimentally viable conditions up to at least 72km transmission distance.

quant-ph↗

arXiv2023

Noncommuting conserved charges in quantum thermodynamics and beyond

Thermodynamic systems typically conserve quantities ("charges") such as energy and particle number. The charges are often assumed implicitly to commute with each other. Yet quantum phenomena such as uncertainty relations rely on observables' failure to commute. How do noncommuting charges affect thermodynamic phenomena? This question, upon arising at the intersection of quantum information theory and thermodynamics, spread recently across many-body physics. Charges' noncommutation has been found to invalidate derivations of the thermal state's form, decrease entropy production, conflict with the eigenstate thermalization hypothesis, and more. This Perspective surveys key results in, opportunities for, and work adjacent to the quantum thermodynamics of noncommuting charges. Open problems include a conceptual puzzle: Evidence suggests that noncommuting charges may hinder thermalization in some ways while enhancing thermalization in others.

quant-ph↗

arXiv2023

Imperfect Phase-Randomisation and Generalised Decoy-State Quantum Key Distribution

Decoy-state methods [1-3] are essential to perform quantum key distribution (QKD) at large distances in the absence of single photon sources. However, the standard techniques apply only if laser pulses are used that are independent and identically distributed (iid). Moreover, they require that the laser pulses are fully phase-randomised. However, realistic high-speed QKD setups do not meet these stringent requirements [4]. In this work, we generalise decoy-state analysis to accommodate laser sources that emit imperfectly phase-randomised states. We also develop theoretical tools to prove the security of protocols with lasers that emit pulses that are independent, but not identically distributed. These tools can be used with recent work [5] to prove the security of laser sources with correlated phase distributions as well. We quantitatively demonstrate the effect of imperfect phase-randomisation on key rates by computing the key rates for a simple implementation of the three-state protocol.

quant-ph↗

arXiv2022

An Improved Correction Term for Dimension Reduction in Quantum Key Distribution

The dimension reduction method enables security proofs of quantum key distribution (QKD) protocols that are originally formulated in infinite dimensions via reduction to a tractable finite-dimensional optimization. The reduction of dimensions is associated with a correction term in the secret key rate calculation. The previously derived correction term is loose when the protocol measurements are nearly block-diagonal with respect to the projection onto the reduced finite-dimensional subspace. Here, we provide a tighter correction term. It interpolates between the two extreme cases where all measurement operators are block-diagonal, and where at least one has maximally large off-diagonal blocks. This new correction term can reduce the computational overhead of applying the dimension reduction method by reducing the required dimension of the chosen subspace.

quant-ph↗

arXiv2021

Dimension Reduction in Quantum Key Distribution for Continuous- and Discrete-Variable Protocols

We develop a method to connect the infinite-dimensional description of optical continuous-variable quantum key distribution (QKD) protocols to a finite-dimensional formulation. The secure key rates of the optical QKD protocols can then be evaluated using recently-developed reliable numerical methods for key rate calculations. We apply this method to obtain asymptotic key rates for discrete-modulated continuous-variable QKD protocols, which are of practical significance due to their experimental simplicity and potential for large-scale deployment in quantum-secured networks. Importantly, our security proof does not require the photon-number cutoff assumption relied upon in previous works. We also demonstrate that our method can provide practical advantages over the flag-state squasher when applied to discrete-variable protocols.

quant-ph↗

arXiv2020

Lift & Project Systems Performing on the Partial-Vertex-Cover Polytope

We study integrality gap (IG) lower bounds on strong LP and SDP relaxations derived by the Sherali-Adams (SA), Lovasz-Schrijver-SDP (LS+), and Sherali-Adams-SDP (SA+) lift-and-project (L&P) systems for the t-Partial-Vertex-Cover (t-PVC) problem, a variation of the classic Vertex-Cover problem in which only t edges need to be covered. t-PVC admits a 2-approximation using various algorithmic techniques, all relying on a natural LP relaxation. Starting from this LP relaxation, our main results assert that for every epsilon > 0, level-Theta(n) LPs or SDPs derived by all known L&P systems that have been used for positive algorithmic results (but the Lasserre hierarchy) have IGs at least (1-epsilon)n/t, where n is the number of vertices of the input graph. Our lower bounds are nearly tight. Our results show that restricted yet powerful models of computation derived by many L&P systems fail to witness c-approximate solutions to t-PVC for any constant c, and for t = O(n). This is one of the very few known examples of an intractable combinatorial optimization problem for which LP-based algorithms induce a constant approximation ratio, still lift-and-project LP and SDP tightenings of the same LP have unbounded IGs. We also show that the SDP that has given the best algorithm known for t-PVC has integrality gap n/t on instances that can be solved by the level-1 LP relaxation derived by the LS system. This constitutes another rare phenomenon where (even in specific instances) a static LP outperforms an SDP that has been used for the best approximation guarantee for the problem at hand. Finally, one of our main contributions is that we make explicit of a new and simple methodology of constructing solutions to LP relaxations that almost trivially satisfy constraints derived by all SDP L&P systems known to be useful for algorithmic positive results (except the La system).

cs.DS↗

arXiv2019

Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution

Continuous-variable quantum key distribution (CV QKD) protocols with discrete modulation are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks, but their security analysis is less advanced than that of Gaussian modulation schemes. In this work, we apply a numerical method to analyze the security of discrete-modulation protocols against collective attacks in the asymptotic limit, paving the way for a full security proof with finite-size effects. While our method is general for discrete-modulation schemes, we focus on two variants of the CV QKD protocol with quaternary modulation. Interestingly, thanks to the tightness of our proof method, we show that this protocol is capable of achieving much higher key rates over significantly longer distances with experimentally feasible parameters compared with previous security proofs of binary and ternary modulation schemes and also yielding key rates comparable to Gaussian modulation schemes. Furthermore, as our security analysis method is versatile, it allows us to evaluate variations of the discrete-modulated protocols, including direct and reverse reconciliation, and postselection strategies. In particular, we demonstrate that postselection of data in combination with reverse reconciliation can improve the key rates.

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