arXiv subjects

Shubhayan Sarkar

Publications and source records attributed to Shubhayan Sarkar.

At least 19 recordsLinked to original sources

arXiv2026

Network steering with arbitrarily low detection efficiency of any entangled measurement

Quantum nonlocality and its asymmetric counterpart, quantum steering, are among the most intriguing manifestations of quantum mechanics. From a theoretical perspective, they are not only of fundamental significance but also hold promise for a wide range of applications. However, the stringent technological requirements for their experimental observation in a loophole-free way have largely restricted their realization to foundational demonstrations. A major challenge in these setups is the limited detection efficiency of current detectors as to observe nonlocality or steering in the standard scenarios, one requires detectors above a certain critical efficiency which can only be achieved with superconducting detectors. Considering the simplest quantum network, we demonstrate here that quantum steering between two parties, can be demonstrated for any non-zero detection efficiency, if the sources in the network generate states above a critical visibility well-within the current practical limits. This form of quantum steering in networks, is termed swap-steering. Moreover, when the sources are perfect, swap-steering can be observed using any entangled measurement on the untrusted side, even with arbitrarily low detection efficiency. Consequently, two major loopholes, the detection-loophole as well as free-will loophole can be closed easily in quantum steering experiments, when implemented using networks.

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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.

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arXiv2026

Predictive supremacy of informationally-restricted quantum perceptron

In the current world, the use of artificial intelligence is penetrating every aspect of human life. The basic element of any artificial intelligence is a digital neuron, called a perceptron, while its quantum analogue is called a quantum perceptron. Here, we introduce a model of perceptron called the informationally-restricted measurement-based perceptron (IMP), where each input is composed of two bits, while at the node, depending on a free input variable, the perceptron decides which bit to evaluate. Additionally, the states transmitted from the input to the node are restricted to a bit (qubit). We establish that under this restriction, the quantum IMP predicts better than a classical IMP. This means that under dimensional restriction of the transmitted states, when both the classical and quantum perceptrons learn the same, the quantum perceptron predicts better than the classical perceptron. For our purpose, we find specific learned values of the perceptron that can display the advantage of a quantum perceptron over its classical counterpart. Restricting to discrete binary inputs, we establish that the observed quantum advantage is universal, that is, for any non-trivial function implementable by both the quantum and classical IMP, one can always find a quantum implementation that outperforms the predictive capability of every classical one. This points to the fact that, given identical learning and resources, a quantum perceptron would predict better than any classical one.

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arXiv2026

Entanglement is not sufficient for most practical entanglement-based QKD protocols

Quantum key distribution (QKD) is the most explored application of quantum information theory. A central problem in entanglement-based QKD (EB-QKD), is whether every entangled state can be used to extract a key. We observe that entanglement is not sufficient for standard practical EB-QKD protocols where the input choices are announced by the parties that want to share a secure key, such as E91 or entanglement-based BB84 type protocols, when even an arbitrarily small amount of leakage of classical side information occurs. We do this by identifying a class of two-qubit isotropic states that are entangled but cannot be used to distil the key under such protocols for any possible measurement by the parties. Counter-intuitively, this gap persists even when the leakage occurs from the "junk" rounds of the protocol, i.e, rounds that cannot be used to generate any key. We then extend this result to arbitrary dimensions and parties by identifying a class of isotropic states that are not useful to extract a secure key under such protocols, even if they are entangled. Finally, we demonstrate that our approach provides a tool to upper-bound the scalability of repeater-based QKD architectures in a protocol-independent manner. Interestingly, we find that allowing for even a tiny noise in the preparation drastically reduces the scalability of the QKD network.

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arXiv2026

Classifying the simplest Bell inequalities beyond qubits and their applications towards self-testing

Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum behaviour. This is useful for the geometric characterisation of the set of nonlocal correlations achievable within quantum theory. Moreover, it provides a systematic way to construct Bell inequalities that are tailored to specific quantum information processing tasks. This characterisation is well understood in the simplest $(2,2,2)$ scenario, namely two parties performing two binary outcome measurements. However, beyond this setting, relatively few Bell inequalities are known, and the situation becomes particularly scarce in scenarios involving a greater number of outcomes. Here, we consider the $(2,2,3)$ scenario, or two parties performing two three-outcome measurements, and characterise all Bell inequalities that can arise from the simplest sum-of-squares decomposition and are maximally violated by the maximally entangled state of local dimension three. We then utilise them to self-test this state, along with a class of three-outcome measurements.

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arXiv2025

Any gate of a quantum computer can be certified device-independently

Device-independent (DI) certification allows the verification of quantum systems based solely on observed statistics, without assumptions about their internal structure. While self-testing, the strongest DI certification, of a wide range of quantum states and measurements is done, the self-testing of quantum operations remains underdeveloped. Here, we show in a proof-of-principle way that any quantum unitary can be self-tested within the DI paradigm. For our purpose, we utilise the framework of quantum networks with multiple independent sources. Our work provides a fundamental step toward certifying quantum interactions directly from data, without detailed modelling assumptions. Moreover, the result also serves as a crucial ingredient for quantum computation, where verifying that quantum gates perform as intended is essential for building secure and reliable quantum processors.

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arXiv2025

Topologically noise robust network steering without inputs

Quantum networks with independent sources allow observing quantum nonlocality or steering with just a single measurement per node of the network, or without any inputs. Inspired by the recently introduced notion of swap-steering, we consider here the triangle network scenario without inputs, where one of the parties is trusted to perform a well-calibrated measurement. In this scenario, we first propose a linear witness to detect triangle network swap-steering. Then, by using the correlations that achieve the maximum value of this inequality, and assuming that all the sources are the same, we can self-test the state generated by the sources and the measurements of the untrusted party. We then extend this framework to ring networks with an arbitrary number of nodes with one of them being trusted. Interestingly, this is the first example of a topologically robust, that is, one can observe steerability without assuming the network structure of the network, as well as noise-robust quantum advantage in a network. Additionally, by allowing the trusted party to perform tomography of their subsystems, we demonstrate that every bipartite entangled state will result in swap-steerable correlations in the ring network. For this purpose, we construct linear witnesses to detect ring network swap-steering corresponding to every bipartite entangled state.

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arXiv2025

Gap between quantum theory based on real and complex numbers is arbitrarily large

Quantum Information Theory, the standard formalism used to represent information contained in quantum systems, is based on complex Hilbert spaces (CQT). It was recently shown that it predicts correlations in quantum networks which cannot be explained by Real Quantum Theory (RQT), a quantum theory with real Hilbert spaces instead of complex ones, when three parties are involved in a quantum network with non-trivial locality constraints. In this work, we study a scenario with $N+1$ parties sharing quantum systems in a star network. Here, we construct a "conditional" multipartite Bell inequality that exhibits a gap between RQT and CQT, which linearly increases with $N$ and is thus arbitrarily large in the asymptotic limit. This implies, that, as the number of parties grows, Hilbert space formalism based on real numbers becomes exceedingly worse at describing complex networks of quantum systems. Furthermore, we also compute the tolerance of this gap to experimental errors.

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arXiv2025

Detecting entanglement in any measurement using quantum networks

Entanglement is a key resource to demonstrate quantum advantage over classical strategies. Entanglement in quantum states is one of the most well-explored areas in quantum physics. However, a rigorous approach to understanding and detecting entanglement in composite quantum measurements is lacking. In this work, we focus on composite quantum measurements and classify them into two classes: entangled and separable measurements. As done for quantum states, we define analogously a notion of witness that can be used to detect entanglement in composite quantum measurements. Here, one does not need to trust the measurement to witness its entanglement but must trust the quantum states. We then further extend this approach to show that any entangled measurement provides an advantage in network quantum steering without inputs, also known as swap steering. Consequently, this provides a way to witness entanglement in any quantum measurement in a one-sided device-independent way. Finally, we consider the star network scenario and show that any rank-one projective entangled quantum measurement gives a quantum advantage. Thus, one can detect the entanglement in any rank-one projective measurement in a device-independent way.

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arXiv2025

Using quantum nonlocality for device-independent confirmation of relativistic effects

Synchronizing clocks to measure time is a fundamental process underpinning every practical communication task from GPS to parallel computation. However, as the current protocols are based on classical communication between the sender and receiver, they are prone to simple attacks that could cause a slight delay in the signal which would then cause a massive error in further operations. In this work, we first explain a simple attack that in principle can cause an arbitrary delay in the signal between sender and receiver. We then propose a way to overcome this problem by using a recently contrived idea of device-independent certification which utilises quantum nonlocality. Consequently, clocks can be synchronized in a highly secure way without trusting any devices in the setup. We then extend this proposal to observe relativistic time dilation in a device-independent manner.

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arXiv2024

Network quantum steering enables randomness certification without seed randomness

Quantum networks with multiple sources allow the observation of quantum nonlocality without inputs. Consequently, the incompatibility of measurements is not a necessity for observing quantum nonlocality when one has access to multiple quantum sources. Here we investigate the minimal scenario without inputs where one can observe any form of quantum nonlocality. We show that even two parties with two sources that might be classically correlated can witness a form of quantum nonlocality, in particular quantum steering, in networks without inputs if one of the parties is trusted, that is, performs a fixed known measurement. We term this effect as swap-steering. The scenario presented in this work is minimal to observe such an effect. Consequently, a scenario exists where one can observe quantum steering but not Bell non-locality. We further construct a linear witness to observe swap-steering. Interestingly, this witness enables self-testing of the quantum states generated by the sources and the local measurement of the untrusted party. This in turn allows certifying two bits of randomness that can be obtained from the measurement outcomes of the untrusted device without the requirement of initially feeding the device with randomness.

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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.

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arXiv2024

Witnessing network steerability of every bipartite entangled state without inputs

Quantum steering is an asymmetric form of quantum nonlocality where one can detect whether a measurement on one system can steer or change another distant system. It is well-known that there are quantum states that are entangled but unsteerable in the standard quantum steering scenario. Consequently, a long-standing open problem in this regard is whether the steerability of every entangled state can be activated in some way. In this work, we consider quantum networks and focus on the swap-steering scenario without inputs and find linear witnesses of network steerability corresponding to any negative partial transpose (NPT) bipartite state and a large class of bipartite states that violate the computable cross-norm (CCN) criterion. Furthermore, by considering that the trusted party can perform tomography of the incoming subsystems, we construct linear inequalities to witness swap-steerability of every bipartite entangled state. Consequently, for every bipartite entangled state one can now observe a form of quantum steering.

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arXiv2024

Operationally independent events can influence each other in quantum theory

In any known description of nature, two physical systems are considered independent of each other if any action on one of the systems does not change the other system. From our classical intuitions about the world, we further conclude that these two systems are not affecting each other in any possible way, and thus these two systems are causally disconnected or they do not influence each other. Building on this idea, we show that in quantum theory such a notion of classical independence is not satisfied, that is, two quantum systems can still influence each other even if any operation on one of the systems does not create an observable effect on the other. For our purpose, we consider the framework of quantum networks and construct a linear witness utilizing the Clauser-Horne-Shimony-Holt inequality. We also discuss one of the interesting applications resulting from the maximal violation of classical independence towards device-independent certification of quantum states and measurements.

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arXiv2024

One-sided DI-QKD secure against coherent attacks over long distances

Quantum Key Distribution (QKD) is a technique enabling provable secure communication but faces challenges in device characterization, posing potential security risks. Device-Independent (DI) QKD protocols overcome this issue by making minimal device assumptions but are limited in distance because they require high detection efficiencies, which refer to the ability of the experimental setup to detect quantum states. It is thus desirable to find quantum key distribution protocols that are based on realistic assumptions on the devices as well as implementable over long distances. In this work, we consider a one-sided DI QKD scheme with two measurements per party and show that it is secure against coherent attacks up to detection efficiencies greater than 50.1% specifically on the untrusted side. This is almost the theoretical limit achievable for protocols with two untrusted measurements. Interestingly, we also show that, by placing the source of states close to the untrusted side, our protocol is secure over distances comparable to standard QKD protocols.

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arXiv2024

Almost device-independent certification of GME states with minimal measurements

Device-independent certification of quantum states enables the characterization of states within a device under minimal physical assumptions. A major problem in this regard is to certify quantum states using minimal resources. Aiming to address this problem, we consider a multipartite quantum steering scenario involving an arbitrary number of parties, of which only one is trusted, meaning that the measurements performed by this party are known. Consequently, the self-testing scheme is almost device-independent. Importantly, all the parties can only perform two measurements each, which is the minimal number of measurements required to observe any form of quantum nonlocality. Then, we propose steering inequalities that are maximally violated by three major classes of genuinely multipartite entangled (GME) states: graph states of arbitrary local dimension, Schmidt states of arbitrary local dimension, and $N$-qubit generalized W states. Using the proposed inequalities, we then provide an almost device-independent certification of the above GME states. Restricting to qubits, we also lift our almost device-independent scheme to device-independent self-testing.

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arXiv2024

Model-independent inference of quantum interaction from statistics

Any physical theory aims to establish the relationship between physical systems in terms of the interaction between these systems. However, any known approach in the literature to infer this interaction is dependent on the particular modelling of the physical systems involved. Here, we propose an alternative approach where one does not need to model the systems involved but only assume that these systems behave according to quantum theory. We first propose a setup to infer a particular entangling quantum interaction between two systems from the statistics. For our purpose, we utilise the framework of Bell inequalities. We then extend this setup where an arbitrary number of quantum systems interact via some entangling interaction.

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arXiv2023

A universal scheme to self-test any quantum state or measurement

The emergence of quantum devices has raised a significant issue: how to certify the quantum properties of a device without placing trust in it. To characterise quantum states and measurements in a device-independent way, up to some degree of freedom, we can make use of a technique known as self-testing. While schemes have been proposed to self-test all pure multipartite entangled states (up to complex conjugation) and real local projective measurements, little has been done to certify mixed entangled states, composite or non-projective measurements. By employing the framework of quantum networks, we propose a scheme for self-testing (up to complex conjugation) arbitrary extremal measurements, including the projective ones, but also, in an indirect way, any quantum state, including the mixed ones and any quantum measurement, including non-extremal ones. The quantum network considered in this work is the simple star network, which is implementable using current technologies. For our purposes, we also construct a scheme that can be used to self-test the two-dimensional tomographically complete set of measurements with an arbitrary number of parties.

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