arXiv subjects

Shibdas Roy

Publications and source records attributed to Shibdas Roy.

At least 19 recordsLinked to original sources

arXiv2026

Estimation of trace distance between two arbitrary quantum states

When it comes to discriminating between two quantum states, trace distance is one of the well-known metrics used in quantum computation and quantum information theory. While there are several quantum algorithms for calculating the trace distance between two quantum states, computing it for any two general density matrices remains computationally demanding. In this paper, we propose a quantum algorithm based on the exponentiation of the density matrix and the improved quantum phase estimation (IQPE) to determine the trace distance for both pure and mixed states, with a time complexity of $O(N^2/\varepsilon^6)$ where $N$ is the number of qubits of the given states and $\varepsilon$ is the simulation or estimation precision error. We demonstrate its ability to predict the quantity with proof-of-principle simulations and also quantum hardware computations on the IBM quantum computers, confirming its promise for near-term quantum devices.

quant-ph↗

arXiv2025

Efficient algorithm for fidelity estimation of two quantum states

The fidelity estimation between two quantum states is crucial for quantum computation and information science. However, an efficacious method for this, especially for mixed states and higher-dimensional density matrices, remains elusive. While there are many existing algorithms on computing the fidelity between two pure states, there is not much work on how to obtain the fidelity between two mixed states. Here, an efficient quantum algorithm for the fidelity estimation is proposed, based primarily on the density matrix exponentiation and interferometeric scheme for mixed states, with a time complexity of $O(\kappa^2N^2/\epsilon^7)$, where $N$ is the system size, $\kappa$ is the larger of the condition number of the density matrices and $\epsilon$ is a precision error. This algorithm may serve as a resource-efficient technique to deduce fidelity of any two (pure or mixed) unknown or known quantum states, when the density matrices of the quantum states commute with each other.

quant-ph↗

arXiv2025

P-divisibility conditions on subsystems in quantum dynamics

We investigate the constraints imposed by global unitary dynamics on the P-divisibility of local subsystems in a bipartite system-environment setting. Using the trace distance as a measure of state distinguishability and exploiting its conservation under unitary evolution, we develop a fully symmetric framework that simultaneously tracks information flow in both the open system $S$ and its environment $E$. We first show that for initially uncorrelated states the maximum net non-Markovian gain in one subsystem is rigidly bounded by the initial distinguishability of the other (Theorem~1). We then establish a two-sided Correlation Window (Theorem~2) that confines the sum of net changes in local distinguishability: the upper edge is set by the total initial marginal distinguishability, while the lower edge is governed exactly by the dynamically generated bipartite correlation norm, proving that any mutual loss of local distinguishability is necessarily encoded into correlations. Finally, we generalize both results to initially correlated states (Theorem~3), showing that initial bipartite correlations augment the capacity for non-Markovian gain and that simultaneous P-indivisibility of both subsystems is funded by the degradation of the initial correlation reservoir. These results are validated on four-qubit GHZ and W circuit examples, demonstrating subsystem locking, asymmetric single-subsystem backflow, and correlation-funded simultaneous back-flow.

quant-ph↗

arXiv2025

Complete Positivity of Subsystems in Quantum Dynamics

Although many quantum channels satisfy Completely Positive Trace Preserving (CPTP) condition, there are valid quantum channels that can be non-completely positive (NCP). As memory effects can provide advantages in the dynamics of noisy quantum systems, we investigate the relative CP condition and the CP-divisibility condition of the system and environment subsystems of a joint system-environment quantum state evolving noiselessly. We show that the system and environment channels must be both CP (NCP) or CP-divisible (CP-indivisible) for the evolution in the joint system-environment space to be unitary. We illustrate our results with examples of Bell state created from $|00\rangle$, GHZ state created from $|000\rangle$, W state created from $|100\rangle$, and the partial transpose (PT) operation acting on the Bell state

quant-ph↗

arXiv2025

Unitality Conditions on Subsystems in Quantum Dynamics

It is known that non-unital noise such as the amplitude damping can sometimes increase quantum correlations, while unital noise such as the dephasing usually decreases quantum correlations. It is, therefore, important to delineate the conditions, when noise can enhance the quantumness of the system. Here, we show that if the noise acting on the system is unital (non-unital), then the noise acting on the environment must also be unital (non-unital), for the evolution to be unitary in the joint system-environment space. For example, if the first two qubits are treated as system and the third qubit is treated as environment, then both the system and the environment evolve unitally in case of a three-qubit GHZ state, and both of them evolve non-unitally in case of a three-qubit W state. Our result may be of interest in quantum information, and we anticipate it to be useful in various contexts, such as to better tackle noise in quantum computing and quantum information processing.

quant-ph↗

arXiv2023

Efficient learning of arbitrary single-copy quantum states

Quantum state tomography is the problem of estimating a given quantum state. Usually, it is required to run the quantum experiment - state preparation, state evolution, measurement - several times to be able to estimate the output quantum state of the experiment, because an exponentially high number of copies of the state is required. In this work, we present an efficient algorithm to estimate with a small but non-zero probability of error the output state of the experiment using a single copy of the state, without knowing the evolution dynamics of the state. It also does not destroy the original state, which can be recovered easily for any further quantum processing. As an example, it is usually required to repeat a quantum image processing experiment many times, since many copies of the state of the output image are needed to extract the information from all its pixels. The information from $\mathcal{N}$ pixels of the image can be inferred from a single run of the image processing experiment in our algorithm, to efficiently estimate the density matrix of the image state.

physics.gen-ph↗

arXiv2023

BQP $=$ PSPACE

The complexity class $PSPACE$ includes all computational problems that can be solved by a classical computer with polynomial memory. All $PSPACE$ problems are known to be solvable by a quantum computer too with polynomial memory and are, thus, known to be in $BQPSPACE$. Here, we present a polynomial time quantum algorithm for a $PSPACE$-complete problem, implying that $PSPACE$ is equal to the class $BQP$ of all problems solvable by a quantum computer in polynomial time. In particular, we outline a $BQP$ algorithm for the $PSPACE$-complete problem of evaluating a full binary $NAND$ tree. An existing best of quadratic speedup is achieved using quantum walks for this problem, so that the complexity is still exponential in the problem size. By contrast, we achieve an exponential speedup for the problem, allowing for solving it in polynomial time. There are many real-world applications of our result, such as strategy games like chess or Go. As an example, in quantum sensing, the problem of quantum illumination, that is treated as that of channel discrimination, is $PSPACE$-complete. Our work implies that quantum channel discrimination, and so, quantum illumination, can be performed efficiently by a quantum computer.

cs.CC↗

arXiv2022

Adapting the HHL algorithm to quantum many-body theory

Rapid progress in developing near- and long-term quantum algorithms for quantum chemistry has provided us with an impetus to move beyond traditional approaches and explore new ways to apply quantum computing to electronic structure calculations. In this work, we identify the connection between quantum many-body theory and a quantum linear solver, and implement the Harrow-Hassidim-Lloyd (HHL) algorithm to make precise predictions of correlation energies for light molecular systems via the (non-unitary) linearised coupled cluster theory. We alter the HHL algorithm to integrate two novel aspects- (a) we prescribe a novel scaling approach that allows one to scale any arbitrary symmetric positive definite matrix A, to solve for Ax = b and achieve x with reasonable precision, all the while without having to compute the eigenvalues of A, and (b) we devise techniques that reduce the depth of the overall circuit. In this context, we introduce the following variants of HHL for different eras of quantum computing- AdaptHHLite in its appropriate forms for noisy intermediate scale quantum (NISQ), late-NISQ, and the early fault-tolerant eras, as well as AdaptHHL for the fault-tolerant quantum computing era. We demonstrate the ability of the NISQ variant of AdaptHHLite to capture correlation energy precisely, while simultaneously being resource-lean, using simulation as well as the 11-qubit IonQ quantum hardware.

quant-ph↗

arXiv2018

Fundamental noisy multiparameter quantum bounds

Quantum multiparameter estimation involves estimating multiple parameters simultaneously and can be more precise than estimating them individually. Our interest here is to determine fundamental quantum limits to the achievable multiparameter estimation precision in the presence of noise. We present a lower bound to the estimation error covariance for a noisy initial probe state evolving via a noiseless quantum channel. We then present a lower bound to the estimation error covariance in the most general form for a noisy initial probe state evolving via a noisy quantum channel. We show conditions and accordingly measurements to attain these estimation precision limits for noisy systems. We see that the Heisenberg precision scaling of $1/N$ can be achieved with a probe comprising $N$ particles even in the presence of noise. In fact, some noise in the initial probe state or the quantum channel can serve as a feature rather than a bug, since the estimation precision scaling achievable in the presence of noise in the initial state or the channel in some situations is impossible in the absence of noise in the initial state or the channel. However, a lot of noise harms the quantum advantage achievable with $N$ parallel resources, and allows for a best precision scaling of $1/\sqrt{N}$. Moreover, the Heisenberg precision limit can be beaten with noise in the channel, and we present a super-Heisenberg precision limit with scaling of $1/N^2$ for optimal amount of noise in the channel, characterized by one-particle evolution operators. Further, using $γ$-particle evolution operators for the noisy channel, where $γ>1$, the best precision scaling attainable is $1/N^{2γ}$, which is otherwise known to be only possible using $2γ$-particle evolution operators for a noiseless channel.

quant-ph↗

arXiv2017

Robust Guaranteed-Cost Adaptive Quantum Phase Estimation

Quantum parameter estimation plays a key role in many fields like quantum computation, communication and metrology. Optimal estimation allows one to achieve the most precise parameter estimates, but requires accurate knowledge of the model. Any inevitable uncertainty in the model parameters may heavily degrade the quality of the estimate. It is therefore desired to make the estimation process robust to such uncertainties. Robust estimation was previously studied for a varying phase, where the goal was to estimate the phase at some time in the past, using the measurement results from both before and after that time within a fixed time interval up to current time. Here, we consider a robust guaranteed-cost filter yielding robust estimates of a varying phase in real time, where the current phase is estimated using only past measurements. Our filter minimizes the largest (worst-case) variance in the allowable range of the uncertain model parameter(s) and this determines its guaranteed cost. It outperforms in the worst case the optimal Kalman filter designed for the model with no uncertainty, that corresponds to the center of the possible range of the uncertain parameter(s). Moreover, unlike the Kalman filter, our filter in the worst case always performs better than the best achievable variance for heterodyne measurements, that we consider as the tolerable threshold for our system. Furthermore, we consider effective quantum efficiency and effective noise power, and show that our filter provides the best results by these measures in the worst case.

quant-ph↗

arXiv2016

Robust $H_\infty$ Coherent-Classical Estimation of Linear Quantum Systems

We study robust $H_\infty$ coherent-classical estimation for a class of physically realizable linear quantum systems with parameter uncertainties. Such a robust coherent-classical estimator, with or without coherent feedback, can yield better disturbance-to-error performance than the corresponding robust purely-classical estimator for an uncertain plant. Moreover, coherent feedback allows for such a robust coherent-classical estimator to be more robust to uncertainty in comparison to the robust classical-only estimator.

eess.SY↗

arXiv2015

Robust $H_\infty$ Estimation of Uncertain Linear Quantum Systems

We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust $H_\infty$ estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled $H_\infty$ control problem. The solution is obtained in the form of two algebraic Riccati equations. Relevant examples involving dynamic squeezers are presented to illustrate the efficacy of our method.

eess.SY↗

arXiv2015

Coherent-Classical Estimation for Linear Quantum Systems

We study a coherent-classical estimation scheme for a class of linear quantum systems, where the estimator is a mixed quantum-classical system that may or may not involve coherent feedback. We show that when the quantum plant or the quantum part of the estimator (coherent controller) is an annihilation operator only system, coherent-classical estimation without coherent feedback can provide no improvement over purely-classical estimation. Otherwise, coherent-classical estimation without feedback can be better than classical-only estimation for certain homodyne detector angles, although the former is inferior to the latter for the best choice of homodyne detector angle. Moreover, we show that coherent-classical estimation with coherent feedback is no better than classical-only estimation, when both the plant and the coherent controller are annihilation operator only systems. Otherwise, coherent-classical estimation with coherent feedback can be superior to purely-classical estimation, and in this case, the former is better than the latter for the optimal choice of homodyne detector angle.

math.OC↗

arXiv2014

Robust Adaptive Quantum Phase Estimation

Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is possible when we have very precise knowledge of and control over the model. However, uncertainties in key parameters underlying the system are unavoidable and may impact the quality of the estimate. We show here how quantum optical phase estimation of a squeezed state of light exhibits improvement when using a robust fixed-interval smoother designed with uncertainties explicitly introduced in parameters underlying the phase noise.

quant-ph↗

arXiv2014

Coherent-Classical Estimation versus Purely-Classical Estimation for Linear Quantum Systems

We consider a coherent-classical estimation scheme for a class of linear quantum systems. It comprises an estimator that is a mixed quantum-classical system without involving coherent feedback. The estimator yields a classical estimate of a variable for the quantum plant. We demonstrate that for a passive plant that can be characterized by annihilation operators only, such coherent-classical estimation provides no improvement over purely-classical estimation. An example is also given which shows that if the plant is not assumed to be an annihilation operator only quantum system, it is possible to get better estimates with such coherent-classical estimation compared with purely-classical estimation.

quant-ph↗

arXiv2013

Robust Smoothing for Estimating Optical Phase Varying as a Continuous Resonant Process

Continuous phase estimation is known to be superior in accuracy as compared to static estimation. The estimation process is, however, desired to be made robust to uncertainties in the underlying parameters. Here, homodyne phase estimation of coherent and squeezed states of light, evolving continuously under the influence of a second-order resonant noise process, are made robust to parameter uncertainties using a robust fixed-interval smoother, designed for uncertain systems satisfying a certain integral quadratic constraint. We observe that such a robust smoother provides improved worst-case performance over the optimal smoother and also performs better than a robust filter for the uncertain system.

math.OC↗

arXiv2013

Robust Estimation of Optical Phase Varying as a Continuous Resonant Process

It is well-known that adaptive homodyne estimation of continuously varying optical phase provides superior accuracy in the phase estimate as compared to adaptive or non-adaptive static estimation. However, most phase estimation schemes rely on precise knowledge of the underlying parameters of the system under measurement, and performance deteriorates significantly with changes in these parameters; hence it is desired to develop robust estimation techniques immune to such uncertainties. In related works, we have already shown how adaptive homodyne estimation can be made robust to uncertainty in an underlying parameter of the phase varying as a simplistic Ornstein-Uhlenbeck stochastic noise process. Here, we demonstrate robust phase estimation for a more complicated resonant noise process using a guaranteed cost robust filter.

math.OC↗

arXiv2013

Robust Phase Estimation of Squeezed State

Optimal phase estimation of a phase-squeezed quantum state of light has been recently shown to beat the coherent-state limit. Here, the estimation is made robust to uncertainties in underlying parameters using a robust fixed-interval smoother.

quant-ph↗