arXiv subjects

Chandan Datta

Publications and source records attributed to Chandan Datta.

At least 19 recordsLinked to original sources

arXiv2026

Polytopic Quantum Resource Theories: Geometry and Structures

Quantum resource theories provide a unifying framework to quantify, compare, and manipulate quantum resources under well-defined operational constraints. Here, we consider any resource theory where the set of free states can be expressed as a convex combination of a set of quantum states, referred to as extremal states and name them as polytopic quantum resource theories (PQRT). These include some of the most studied resource theories, such as coherence and magic. We formulate a novel tensorial representation of PQRTs that reveals the underlying geometry of these theories and provides insight into the origin of the resources. We further address a fundamental question in resource theories that when two theories should be regarded as physically equivalent, and to this purpose we introduce notions of homomorphism and isomorphism that compare both the structure of free states and the allowed transformations. Using the tools we develop, we find results revealing the geometrical and structural foundations of such theories. Interestingly, we find that all polytopic resource theories with a fixed number of pure extremal points are equivalent under a physical map, up to normalisation. Additionally, we introduce linearly independent polytopic resource theories (resource theory of ``basis-non-convexity''), where the set of extremal free states forms a basis of the quantum density operators. We further study the categorical structures of PQRTs beyond single systems.

quant-ph↗

arXiv2026

Robustness as a thermodynamic currency: work advantages and preparation costs of nonclassical states

Understanding whether uniquely quantum features can provide concrete advantages in thermodynamic processes is a central objective of quantum thermodynamics. A key challenge is quantifying how different forms of non-classicality can be systematically harnessed to enhance thermodynamic tasks. In light of this, we prove that any form of non-classicality can serve as a thermodynamic resource. In particular, any system that possesses quantum magic, coherence, or non-classical correlations can be leveraged to extract higher amounts of work than if the system does not possess such resources. The quantum thermodynamic advantages--quantified by the ratio between work extractable from a resource state and work extractable in its absence--increase with the resource robustness. We show that for any convex quantum resource theory, any resourceful state can yield a work-extraction advantage over all free states via a cyclic quench/thermalization protocol whose Hamiltonian is engineered from an optimal robustness witness. We illustrate concrete examples in which the robustness measures increase with the system's dimension, yielding quantum thermodynamic advantages that scale with it. In contrast, we also show that preparing a resource state (e.g., one with magic, coherence, or non-classical correlations) can be significantly more thermodynamically costly than preparing any state without such a resource. Concretely, there always exists a protocol that can prepare any non-resourceful state at significantly less work than it takes to prepare a resourceful state. Overall, our results provide operational meaning to robustness measures of quantum resources in terms of their thermodynamic costs and advantages.

quant-ph↗

arXiv2026

Violation of Bell Monogamy Relations

The entangled multipartite systems, specially in pure states, exhibit the phenomenon of entanglement monogamy. Such systems also display the phenomenon of Bell nonlocality. Like entanglement monogamy relations, there are Bell monogamy relations. These relations suggest a sharing of nonlocality across the subsystems. The nonlocality, as characterized by Bell inequalities, of one subsystem limits the nonlocality exhibited by another subsystem. We show that the Bell monogamy relations can be violated by using local filtering operations. We consider permutation-symmetric multipartite pure states, in particular $W$ states, to demonstrate the violation.

quant-ph↗

arXiv2025

Deterministic distribution of W-class states in quantum networks

Multipartite entangled states possess a number of non-intuitive properties, making them a useful resource for various quantum information-processing tasks. The three-qubit W-state is one such example where every state is robust to single-qubit loss. However, this state is not suitable for deterministic distribution, and deterministic communication protocols. Here, we focus on the distribution of a non-symmetric version of such states, namely $W_{\mathrm{mod}}$ states. These states belong to the W-class, and have one ebit of entanglement across a specific bipartition, enabling deterministic teleportation and superdense coding. In particular, we describe a few protocols through which these multipartite entangled states can be distributed {\it deterministically} in a quantum network by first preparing them locally in a central node and then transmitting individual qubits to the end nodes. We analyse the performance of these protocols based on the fidelity of the final distributed state, considering all types of noises that can act during the distribution. Finally, we compare the performance of the protocols to the case where the distribution is performed without any central node.

quant-ph↗

arXiv2025

All steerable quantum correlations can provide thermodynamic advantages in cooling

The removal of heat generated during computation poses a major challenge for both classical and quantum information processing. In particular, heat removal is directly linked to a fundamental requirement of quantum computation: the ability to reset a system to a pure state before computation. Efficient cooling is therefore crucial both for advancing our understanding of thermodynamics in the quantum regime and for enabling the development of modern quantum technologies. In this work, we devise a cooling task that exploits steerability, a fundamental form of quantum correlations, to demonstrate a provable quantum advantage over classically correlated scenarios in which steerability is absent. We quantify this advantage by the ratio between the heat removed using steerable quantum correlations and the heat removed using unsteerable classical correlations. Specifically, we show that steerable quantum correlations always provide a thermodynamic advantage in the cooling task. Remarkably, we further establish that the maximum achievable advantage is directly related to a geometric measure of steerability known as steerability robustness. Our results suggest that this thermodynamic advantage can serve as a witness of steerability. Finally, we present examples showing that the advantage can increase with the dimension of the underlying system.

quant-ph↗

arXiv2025

Quantum thermodynamic advantage in work extraction from steerable quantum correlations

Inspired by the primary goal of quantum thermodynamics -- to characterize quantum signatures and leverage their benefits in thermodynamic scenarios -- , we design a work extraction game within a bipartite framework that exhibits a quantum thermodynamic advantage. The steerability of quantum correlations between the two parties is the key resource enabling such an advantage. In designing the game, we exploit the correspondence between steerability and the incompatibility of observables. Our work extraction protocol involves mutually unbiased bases, which exhibit maximum incompatibility and therefore maximum steerability, showcased in maximally entangled quantum states. We derive upper bounds on the extractable work for unsteerable and steerable correlations and devise a protocol that saturates the latter. The ratio between the extractable work in steerable and unsteerable scenarios, which encapsulates the quantum advantage, increases with the dimension of the underlying system (sometimes referred to as an unbounded advantage). This proves a quantum thermodynamic advantage arising from steerable quantum correlations.

quant-ph↗

arXiv2024

Detecting quantum resources in a semi-device independent framework

We investigate whether one can detect the presence of a quantum resource in some operational task or equivalently whether every quantum resource provides an advantage over its free counterpart in some black box scenarios where one does not have much information about the devices. For any dimension $d$, we find that for any resource theory with less than $d^2$ number of linearly independent free states or free operations, there exist correlations that can detect the presence of a quantum resource. For this purpose, we introduce the framework for detecting quantum resources semi-device independently by considering the prepare-and-measure scenario with the restriction on the dimension of the quantum channel connecting the preparation box with the measurement box. We then explicitly construct witnesses to observe the presence of various quantum resources. We expect these results will open avenues for detecting and finding uses of quantum resources in general operational tasks.

quant-ph↗

arXiv2024

Optimal performance of a three stroke heat engine in the microscopic regime

We consider a three-stroke engine in the microscopic regime, where the working body of the engine is composed of a two-level system. The working body of the engine aims to withdraw heat from the hot heat bath, generate work, and discharge the surplus heat into the cold heat bath through the successive execution of three strokes. In this process, the interaction of the working body with the heat baths is assumed to be energy-conserving and thus can be described by thermal operations. While earlier studies analyzed the optimal performance of this engine when the working body could be transformed by any arbitrary thermal operation, we present closed expressions for the maximum work produced by the engine and the maximum efficiency of the engine when only a restricted class of thermal operations can be implemented on the working body. Furthermore, we explore the engine's optimal performance under two well-studied classes of restrictions: thermal operations realized via Jaynes-Cummings interaction and thermal operations realizable with finite-sized heat baths. Therefore, on one hand, our results are general, as they reproduce the optimal performance achieved when any arbitrary thermal operation can be implemented on the working body once the restriction is relaxed. On the other hand, our results allow us to determine the engine's maximum work production and efficiency in a more realistic scenario, where only a restricted class of thermal operations are possible, thereby bringing our findings closer to experimental feasibility.

quant-ph↗

arXiv2023

Scalable noisy quantum circuits for biased-noise qubits

In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to design a class of noisy Hadamard-tests involving entangling and certain non-Clifford gates, which can be conducted reliably with only a polynomial overhead in algorithm repetitions. On the flip side we also found classical algorithms able to efficiently simulate both the noisy and noiseless versions of our specific variants of Hadamard test. We propose to use these algorithms as a simple benchmark of the biasness of the noise at the scale of large circuits. The bias being checked on a full computational task, it makes our benchmark sensitive to crosstalk or time-correlated errors, which are usually invisible from individual gate tomography. For realistic noise models, phase-flip will not be negligible, but in the Pauli-Twirling approximation, we show that our benchmark could check the correctness of circuits containing up to $10^6$ gates, several orders of magnitudes larger than circuits not exploiting a noise-bias. Our benchmark is applicable for an arbitrary noise-bias, beyond Pauli models.

quant-ph↗

arXiv2023

Self-testing composite measurements and bound entangled state in a single quantum network

Within the quantum networks scenario we introduce a single scheme allowing to certify three different types of composite projective measurements acting on a three-qubit Hilbert space: one constructed from genuinely entangled GHZ-like states, one constructed from fully product vectors that exhibit the phenomenon of nonlocality without entanglement (NLWE), and a hybrid measurement obtained from an unextendible product basis (UPB). Noticeably, we certify a basis exhibiting NLWE in the smallest dimension capable of supporting this phenomenon. On the other hand, the possibility of certification of a measurement obtained from a UPB has an interesting implication that one can also self-test a bound entangled state in the considered quantum network. Such a possibility does not seem to exist in the standard Bell scenario. Furthermore, we also analyse the robustness of our scheme towards experimental errors.

quant-ph↗

arXiv2022

Is there a finite complete set of monotones in any quantum resource theory?

Entanglement quantification aims to assess the value of quantum states for quantum information processing tasks. A closely related problem is state convertibility, asking whether two remote parties can convert a shared quantum state into another one without exchanging quantum particles. Here, we explore this connection for quantum entanglement and for general quantum resource theories. For any quantum resource theory which contains resource-free pure states, we show that there does not exist a finite set of resource monotones which completely determines all state transformations. We discuss how these limitations can be surpassed, if discontinuous or infinite sets of monotones are considered, or by using quantum catalysis. We also discuss the structure of theories which are described by a single resource monotone and show equivalence with totally ordered resource theories. These are theories where a free transformation exists for any pair of quantum states. We show that totally ordered theories allow for free transformations between all pure states. For single-qubit systems, we provide a full characterization of state transformations for any totally ordered resource theory.

quant-ph↗

arXiv2022

Real quantum operations and state transformations

Resource theory of imaginarity provides a useful framework to understand the role of complex numbers, which are essential in the formulation of quantum mechanics, in a mathematically rigorous way. In the first part of this article, we study the properties of ``real'' (quantum) operations both in single-party and bipartite settings. As a consequence, we provide necessary and sufficient conditions for state transformations under real operations and show the existence of ``real entanglement'' monotones. In the second part of this article, we focus on the problem of single copy state transformation via real quantum operations. When starting from pure initial states, we completely solve this problem by finding an analytical expression for the optimal fidelity of transformation, for a given probability of transformation and vice versa. Moreover, for state transformations involving arbitrary initial states and pure final states, we provide a semidefinite program to compute the optimal achievable fidelity, for a given probability of transformation.

quant-ph↗

arXiv2022

Inferred-variance uncertainty relations in the presence of quantum entanglement

Uncertainty relations play a significant role in drawing a line between classical physics and quantum physics. Since the introduction by Heisenberg, these relations have been considerably explored. However, the effect of quantum entanglement on uncertainty relations was not probed. Berta et al. [Nature Physics 6, 659-662 (2010)] removed this gap by deriving a conditional-entropic uncertainty relation in the presence of quantum entanglement. In the same spirit, using inferred-variance, we formulate uncertainty relations in the presence of entanglement for general two-qubit systems and arbitrary observables. We derive lower bounds for the sum and product inferred-variance uncertainty relations. Strikingly, we can write the lower bounds of these inferred-variance uncertainty relations in terms of measures of entanglement of two-qubit states, as characterized by concurrence, or $G$ function. Presumably, the presence of entanglement in the lower bound of inferred-variance uncertainty relation is new and unique. We also explore the violation of local uncertainty relations in this context and an interference experiment. Furthermore, we discuss possible applications of these uncertainty relations.

quant-ph↗

arXiv2022

Catalysis of entanglement and other quantum resources

In chemistry, a catalyst is a substance which enables a chemical reaction or increases its rate, while remaining unchanged in the process. Instead of chemical reactions, quantum catalysis enhances our ability to convert quantum states into each other under physical constraints. The nature of the constraints depends on the problem under study and can arise, e.g., from energy preservation. This article reviews the most recent developments in quantum catalysis and gives a historical overview of this research direction. We focus on the catalysis of quantum entanglement and coherence, and also discuss this phenomenon in quantum thermodynamics and general quantum resource theories. We review applications of quantum catalysis and also discuss the recent efforts on universal catalysis, where the quantum state of the catalyst does not depend on the states to be transformed. Catalytic embezzling is also considered, a phenomenon that occurs if the catalyst's state can change in the transition.

quant-ph↗

arXiv2022

Entanglement catalysis for quantum states and noisy channels

Many applications of the emerging quantum technologies, such as quantum teleportation and quantum key distribution, require singlets, maximally entangled states of two quantum bits. It is thus of utmost importance to develop optimal procedures for establishing singlets between remote parties. As has been shown very recently, singlets can be obtained from other quantum states by using a quantum catalyst, an entangled quantum system which is not changed in the procedure. In this work we take this idea further, investigating properties of entanglement catalysis and its role for quantum communication. For transformations between bipartite pure states, we prove the existence of a universal catalyst, which can enable all possible transformations in this setup. We demonstrate the advantage of catalysis in asymptotic settings, going beyond the typical assumption of independent and identically distributed systems. We further develop methods to estimate the number of singlets which can be established via a noisy quantum channel when assisted by entangled catalysts. For various types of quantum channels our results lead to optimal protocols, allowing to establish the maximal number of singlets with a single use of the channel.

quant-ph↗

arXiv2021

Stochastic approximate state conversion for entanglement and general quantum resource theories

Quantum resource theories provide a mathematically rigorous way of understanding the nature of various quantum resources. An important problem in any quantum resource theory is to determine how quantum states can be converted into each other within the physical constraints of the theory. The standard approach to this problem is to study approximate or probabilistic transformations. Here, we investigate the intermediate regime, providing limits on both, the fidelity and the probability of state transformations. We derive limitations on the transformations, which are valid in all quantum resource theories, by providing bounds on the maximal transformation fidelity for a given transformation probability. As an application, we show that these bounds imply an upper bound on the asymptotic rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels, which goes beyond the previously known bounds of channel manipulations. Furthermore, we completely solve the question of stochastic-approximate state conversion via local operations and classical communication in the following two cases: (i) Both initial and target states are pure bipartite entangled states of arbitrary dimensions. (ii) The target state is a two-qubit entangled state and the initial state is a pure bipartite state.

quant-ph↗

arXiv2021

Sub-Rayleigh characterization of a binary source by spatially demultiplexed coherent detection

We investigate theoretically coherent detection implemented simultaneously on a set of mutually orthogonal spatial modes in the image plane as a method to characterize properties of a composite thermal source below the Rayleigh limit. A general relation between the intensity distribution in the source plane and the covariance matrix for the complex field amplitudes measured in the image plane is derived. An algorithm to estimate parameters of a two-dimensional symmetric binary source is devised and verified using Monte Carlo simulations to provide super-resolving capability for high ratio of signal to detection noise (SNR). Specifically, the separation between two point sources can be meaningfully determined down to $\textrm{SNR}^{-1/2}$ in the units determined by the spatial spread of the transfer function of the imaging system. The presented algorithm is shown to make a nearly optimal use of the measured data in the sub-Rayleigh region.

physics.optics↗

arXiv2021

Catalytic Transformations of Pure Entangled States

Quantum entanglement of pure states is usually quantified via the entanglement entropy, the von Neumann entropy of the reduced state. Entanglement entropy is closely related to entanglement distillation, a process for converting quantum states into singlets, which can then be used for various quantum technological tasks. The relation between entanglement entropy and entanglement distillation has been known only for the asymptotic setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Here we close this gap by considering entanglement catalysis. We prove that entanglement entropy completely characterizes state transformations in the presence of entangled catalysts. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving asymptotic results an operational meaning also in the single-copy setup.

quant-ph↗