arXiv subjects

Farid Shahandeh

Publications and source records attributed to Farid Shahandeh.

At least 19 recordsLinked to original sources

arXiv2026

Linear Algebra of Generalized Contextuality in All Prepare-Transform-Measure Scenarios

Generalized contextuality is a canonical distinguishing property of nonclassical generalized probabilistic theories, in particular quantum mechanics. Methods for certification and characterization of generalized contextuality of a given generalized probabilistic theory are well developed for prepare-measure and single-stage prepare-transform-measure scenarios. In a recent work [arXiv:2512.10000], a bottom-up, statistics-first linear-algebraic framework for contextuality in prepare-measure scenarios was introduced. We extend this approach to operational scenarios with sequential transformations with an arbitrary number of stages. We give a full decision procedure for contextuality of such scenarios within operational theories and analyze its computational complexity. In particular, our decision procedure has a complexity linearly exponential in the minimum generalized probabilistic theory (GPT) dimension, and polynomial in the number of procedures. We demonstrate our framework and approach through multiple examples, including Spekkens' toy theory and the 8-state single-qubit stabilizer theory. In particular, we construct an operational theory in which contextuality manifests itself only in the sequential structure of the transformations. Our findings thus shed new light on the significant role of compositional structures in the phenomenon of generalized contextuality.

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arXiv2026

A Unified Linear Algebraic Framework for Physical Models and Generalized Contextuality

We develop a bottom-up, statistics-first framework in which the full probabilistic content of an operational theory is encoded in its matrix of conditional outcome probabilities of events (COPE). Within this setting, five model classes (preGPTs, GPTs, quasiprobabilistic, ontological, and noncontextual ontological) are unified as constrained factorizations of the COPE matrix. We identify equirank factorizations as the structural core of GPTs and noncontextual ontological models and establish their relation to tomographic completeness. This yields a simple, model-agnostic criterion for noncontextuality: an operational theory admits a noncontextual ontological model if and only if its COPE matrix admits an equirank nonnegative matrix factorization (ENMF). Failure of the equirank condition in all ontological models therefore establishes contextuality. We operationalize rank separation via two complementary methods provided by the linear-algebraic framework. First, we use ENMF to interpret noncontextual ontological models as nested polytopes. This allows us to establish that the boxworld operational theory is ontologically contextual. Second, we apply techniques from discrete mathematics to derive a lower bound on the ontological dimensionality of COPE matrices exhibiting sparsity patterns, and use this bound to establish a new proof that a discrete version of qubit theory exhibits ontological contextuality. By reframing contextuality as a problem in matrix analysis, our work provides a unified structure for its systematic study and opens new avenues for exploring nonclassical resources.

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arXiv2026

Contextuality in Sequential State Discrimination

Generalized contextuality is known to be required in optimal strategies for quantum state discrimination protocols. More recently, sequential discrimination tasks have been studied; n players attempt to determine in which state a qubit was prepared, in such a way that they all have a finite probability of success. We consider the extent to which contextuality plays a role in sequential versions of both unambiguous and minimum error discrimination. In the standard nonsequential case where n = 1, we use the COPE formalism to demonstrate that the presence of contextuality is guaranteed not only for the optimal measurement, but for a specific set of nonoptimal measurements as well. In the sequential case n > 1, we show that the presence of contextuality depends on which states are prepared, and on the protocol (unambiguous or minimum error) selected.

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arXiv2026

Sheaf-Theoretic Preparation Contextuality

We introduce a preparation-dual notion of contextuality, formulated as an obstruction to stochastic extension. In parallel with the sheaf-theoretic formulation of measurement contextuality, preparation contextuality arises when locally specified preparation statistics cannot be extended to a single global response matrix compatible with all source contexts. Whereas measurement contextuality concerns the incompatibility of restriction maps (marginalisation), the preparation setting requires stochastic extension of partial conditioning data, which is inherently non-unique. We identify minimal structural and preparation compatibility conditions on admissible extension matrices and show that they enforce a rigid product form. This leads to a notion of preparation contextuality in which the absence of any admissible global response representation witnesses contextuality, while preparation compatibility identifies the cases in which this obstruction is nontrivial. The framework is formulated explicitly in matrix form and illustrated by a quantum-mechanical example exhibiting preparation contextuality.

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arXiv2026

Contextuality of all optimal quantum cloning

Quantum contextuality is a key nonclassical feature underlying advantages in quantum computation and communication. We introduce a new method to study contextuality in quantum information-processing tasks and protocols, relying solely on observed information-processing statistics. Building on the framework of Shahandeh, Yianni and Doosti in arXiv:2512.10000 and employing rank separation techniques, we prove that contextuality is the necessary resource in both phase-covariant and universal optimal quantum cloning, thereby establishing its role as a fundamental source of nonclassicality in all known optimal cloning scenarios and resolving an open problem on the connection between cloning and contextuality. As a second application, we demonstrate the power of our method by providing a new, streamlined proof of contextuality in minimum-error quantum state discrimination.

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arXiv2025

Complexity of Contextuality

Generalized contextuality is a hallmark of nonclassical theories like quantum mechanics. Yet, three fundamental computational problems concerning its decidability and complexity remain open. First, determining the complexity of deciding if a theory admits a noncontextual ontological model; Second, determining the complexity of deciding if such a model is possible for a specific dimension $k$; Third, efficiently computing the smallest such model when it exists, given that finding the smallest ontological model is NP-hard. We address the second problem by presenting an algorithm derived from a geometric formulation and its reduction to the intermediate simplex problem in computational geometry. We find that the complexity of deciding the existence of a noncontextual ontological model of dimension $k$ is at least exponential in the dimension of the theory and at most exponential in $k$. This, in turn, implies that computing the smallest noncontextual ontological model is inefficient in general. Finally, we demonstrate the fundamental difference between finding the smallest noncontextual ontological model and the smallest ontological model using an explicit example wherein the respective minimum ontic sizes are five and four.

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arXiv2023

Witnessing entanglement in trapped-ion quantum error correction under realistic noise

Quantum Error Correction (QEC) exploits redundancy by encoding logical information into multiple physical qubits. In current implementations of QEC, sequences of non-perfect two-qubit entangling gates are used to codify the information redundantly into multipartite entangled states. Also, to extract the error syndrome, a series of two-qubit gates are used to build parity-check readout circuits. In the case of noisy gates, both steps cannot be performed perfectly, and an error model needs to be provided to assess the performance of QEC. We present a detailed microscopic error model to estimate the average gate infidelity of two-qubit light-shift gates used in trapped-ion platforms. We analytically derive leading-error contributions in terms of microscopic parameters and present effective error models that connect the error rates typically used in phenomenological accounts to the microscopic gate infidelities hereby derived. We then apply this realistic error model to quantify the multipartite entanglement generated by circuits that act as QEC building blocks. We do so by using entanglement witnesses, complementing in this way the recent studies by exploring the effects of a more realistic microscopic noise.

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arXiv2021

Quantum computational advantage implies contextuality

We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum algorithms. Our result subsumes versions of Gottesman-Knill theorem as special cases.

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arXiv2021

Incoherent witnessing of quantum coherence

Theoretical and experimental studies have suggested the relevance of quantum coherence to the performance of photovoltaic and light-harvesting complex molecular systems. However, there are ambiguities regarding the validity of statements we can make about the coherence in such systems. Here we analyze the general procedure for coherence detection in quantum systems and show the counterintuitive phenomenon of detecting a quantum system's initial coherence when both the input and output probe states are completely incoherent. Our analysis yields the necessary and sufficient conditions for valid claims regarding the coherence of directly inaccessible systems. We further provide a proof-of-principle protocol that uses entangled probes to detect quantum coherence satisfying these conditions, and discuss its potency for detecting coherence.

physics.chem-ph↗

arXiv2020

Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits

Ensuring the correct functioning of quantum error correction (QEC) circuits is crucial to achieve fault tolerance in realistic quantum processors subjected to noise. The first checkpoint for a fully operational QEC circuit is to create genuine multipartite entanglement across all subsystems of physical qubits. We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) that is efficient in the number of subsystems and, importantly, robust against experimental noise and imperfections. Specifically, we prove that the detection of entanglement in a linear number of bipartitions by a number of measurements that also scales linearly, suffices to certify GME. Moreover, our method goes beyond the standard procedure of separating the state from the convex hull of biseparable states, yielding an improved finesse and robustness compared to previous techniques. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version. In particular, we subject the circuits to combinations of three types of noise, namely, uniform depolarizing noise, two-qubit gate depolarizing noise, and bit-flip measurement noise. We numerically compare our method with the standard, yet generally inefficient, fidelity test and to a pair of efficient witnesses, verifying the increased robustness of our method. Last but not least, we provide the full translation of our analysis to a trapped-ion native gate set that makes it suitable for experimental applications.

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arXiv2020

Contextuality of general probabilistic theories

Generalized contextuality refers to our inability of explaining measurement statistics using a context-independent probabilistic and ontological model. On the other hand, measurement statistics can also be modeled using the framework of general probabilistic theories (GPTs). Here, starting from a construction of GPTs based on a Gleason-type theorem, we fully characterize these structures with respect to their permission and rejection of generalized (non)contextual ontological models. It follows that in any GPT construction the three insistence of (i) the no-restriction hypothesis, (ii) the ontological noncontextuality, and (iii) multiple nonrefinable measurements for any fixed number of outcomes are incompatible. Hence, any GPT satisfying the no-restriction hypothesis is ontologically noncontextual if and only if it is simplicity. We give a detailed discussion of GPTs for which the no-restriction hypothesis is violated, and show that they can always be considered as subtheories (subGPTs) of GPTs satisfying the hypothesis. It is shown that subGPTs are ontologically noncontextual if and only if they are subtheories of simplicial GPTs of the same dimensionality. Finally, we establish as a corollary the necessary and sufficient condition for a single resourceful measurement or state to promote an ontologically noncontextual (i.e. classical) general probabilistic theory to an ontologically contextual (i.e. nonclassical) one under the no-restriction hypothesis.

quant-ph↗

arXiv2019

Assisted Macroscopic Quantumness

It is commonly expected that quantum theory is universal, in that it describes the world at all scales. Yet, quantum effects at the macroscopic scale continue to elude our experimental observation. This fact is commonly attributed to decoherence processes affecting systems of sufficiently large number of constituent subsystems leading to an effective macro-scale beyond which a quantum description of the whole system becomes superfluous. Here, we show both theoretically and experimentally that the existence of such a scale is unjustifiable from an information-theoretic perspective. We introduce a variant of the Wigner's friend experiment in which a multiparticle quantum system is observed by the friend. The friend undergoes rapid decoherence through her interactions with the environment. In the usual version of this thought experiment, decoherence removes the need for Wigner to treat her as a quantum system. However, for our variant we prove theoretically and observe experimentally that there exist partitions of the subsystems in which the friend is entangled with one of the particles in assistance with the other particle, as observed by Wigner. Importantly, we show that the friend is indispensable for the entanglement to be observed. Hence Wigner is compelled to treat the friend as part of a larger quantum system. By analyzing our scenario in the context of a quantum key distribution protocol, we show that a semi-classical description of the experiment is suboptimal for security analysis, highlighting the significance of the quantum description of the friend.

quant-ph↗

arXiv2019

Optomechanical state reconstruction and nonclassicality verification beyond the resolved-sideband regime

Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices. Yet, the challenge of reconstructing and verifying the quantum state of mechanical systems has remained a major roadblock in the field. Here, we present a novel approach that allows for tomographic reconstruction of the quantum state of a mechanical system without the need for extremely high quality optical cavities. We show that, without relying on the usual state transfer presumption between light an mechanics, the full optomechanical Hamiltonian can be exploited to imprint mechanical tomograms on a strong optical coherent pulse, which can then be read out using well-established techniques. Furthermore, with only a small number of measurements, our method can be used to witness nonclassical features of mechanical systems without requiring full tomography. By relaxing the experimental requirements, our technique thus opens a feasible route towards verifying the quantum state of mechanical resonators and their nonclassical behaviour in a wide range of optomechanical systems.

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arXiv2018

Quantum Correlations and Global Coherence in Distributed Quantum Computing

Deviations from classical physics when distant quantum systems become correlated are interesting both fundamentally and operationally. There exist situations where the correlations enable collaborative tasks that are impossible within the classical formalism. Here, we consider the efficiency of quantum computation protocols compared to classical ones as a benchmark for separating quantum and classical resources and argue that the computational advantage of collaborative quantum protocols in the discrete variable domain implies the nonclassicality of correlations. By analysing a toy model, it turns out that this argument implies the existence of quantum correlations distinct from entanglement and discord. We characterize such quantum correlations in terms of the net global coherence resources inherent within quantum states and show that entanglement and discord can be understood as special cases of our general framework. Finally, we provide an operational interpretation of such correlations as those allowing two distant parties to increase their respective local quantum computational resources only using locally incoherent operations and classical communication.

quant-ph↗

arXiv2017

Quantum Correlations in Nonlocal BosonSampling

Determination of the quantum nature of correlations between two spatially separated systems plays a crucial role in quantum information science. Of particular interest is the questions of if and how these correlations enable quantum information protocols to be more powerful. Here, we report on a distributed quantum computation protocol in which the input and output quantum states are considered to be classically correlated in quantum informatics. Nevertheless, we show that the correlations between the outcomes of the measurements on the output state cannot be efficiently simulated using classical algorithms. Crucially, at the same time, local measurement outcomes can be efficiently simulated on classical computers. We show that the only known classicality criterion violated by the input and output states in our protocol is the one used in quantum optics, namely, phase-space nonclassicality. As a result, we argue that the global phase-space nonclassicality inherent within the output state of our protocol represents true quantum correlations.

quant-ph↗

arXiv2016

Ultrafine Entanglement Witnessing

Entanglement witnesses are invaluable for efficient quantum entanglement certification without the need for expensive quantum state tomography. Yet, standard entanglement witnessing requires multiple measurements and its bounds can be elusive as a result of experimental imperfections. Here we introduce and demonstrate a novel procedure for entanglement detection which seamlessly and easily improves any standard witnessing procedure by using additional available information to tighten the witnessing bounds. Moreover, by relaxing the requirements on the witness operators, our method removes the general need for the difficult task of witness decomposition into local observables. We experimentally demonstrate entanglement detection with our approach using a separable test operator and a simple fixed measurement-device for each agent. Finally we show that the method can be generalized to higher-dimensional and multipartite cases with a complexity that scales linearly with the number of parties.

quant-ph↗

arXiv2016

Measurement-Device-Independent Approach to Entanglement Measures

Within the context of semiquantum nonlocal games, the trust can be removed from the measurement devices in an entanglement-detection procedure. Here we show that a similar approach can be taken to quantify the amount of entanglement. To be specific, first, we show that in this context a small subset of semiquantum nonlocal games is necessary and sufficient for entanglement detection in the LOCC paradigm. Second, we prove that the maximum pay-off for these games is a universal measure of entanglement which is convex and continuous. Third, we show that for the quantification of negative-partial-transpose entanglement, this subset can be further reduced down to a single arbitrary element. Importantly, our measure is operationally accessible in a measurement-device-independent way by construction. Finally, our approach is simply extended to quantify the entanglement within any partitioning of multipartite quantum states.

quant-ph↗

arXiv2016

Arbitrary Multi-Qubit Generation

We propose and analyse a scheme for single-rail-encoded arbitrary multi-qubit quantum-state generation to provide a versatile tool for quantum optics and quantum information applications. Our scheme can be realized, for small numbers of qubits, with current technologies using single photon inputs, passive linear optics, and heralding measurements. The particular examples of two- and three-qubit cluster states are studied in detail. We show that such states can be prepared with a high probability of success. Our analysis quantifies the effects of experimentally relevant imperfections and inefficiencies. The general case of arbitrary N-qubit preparation is discussed and some interesting connections to the boson sampling problem are given.

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