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Armin Tavakoli

Publications and source records attributed to Armin Tavakoli.

At least 19 recordsLinked to original sources
arXiv2026

Detecting high-dimensional entanglement with simple measurements

The standard benchmark for high-dimensional entanglement is the number of dimensions in which entanglement must be present in order to generate the state. This is called the Schmidt number and its detection is usually based on implementing an appropriate set of local basis measurements. However, as quantum technology brings increasingly large physical dimensions within reach, the implementation of such measurements typically becomes more costly. Here, we develop a scheme for detecting Schmidt numbers based only on sequences of single-qubit observables. These measurements are simpler to implement as they require only low-depth quantum circuits. Using up to sixteen-dimensional photonic spatial mode entanglement and multi-plane light conversion technology, we demonstrate how it simplifies setup complexity and successfully detects the maximal (or close-to-maximal) Schmidt number. Our results reveal that simple and more scalable measurements are sufficient to detect high-dimensional entanglement properties.

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arXiv2026

Semidefinite block-matrix relaxations for computing quantum correlations

Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today's leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant types of constraints. Here, we propose a semidefinite relaxation methodology that can incorporate a breadth of constraints needed in various quantum correlation problems, thereby generalising the seminal Navascués-Pironio-Acín hierarchy. It yields useful results at reasonable computational cost. We showcase the methodology and its features by using it to address five different quantum information problems. These are (i) entanglement witnessing from imperfect measurement devices, (ii) certifying measurements from fidelity-constrained sources, (iii) computing dimensionality in genuine multi-particle entangled states, (iv) benchmarking dimensionality for state preparation devices, and (v) finding uncertainty relations for nearly anti-commuting observables. These applications reflect both the usefulness and versatility of the methodology, as well as its potential for broader relevance in the field.

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arXiv2026

Robust certification of non-projective measurements: theory and experiment

Determining the conditions under which positive operator-valued measures (POVMs), the most general class of quantum measurements, outperform projective measurements remains a challenging and largely unresolved problem. Of particular interest are projectively simulable POVMs, which can be realized through probabilistic mixtures of projective measurements, and therefore offer no advantage over projective schemes. Characterizing the boundary between simulable and non-simulable POVMs is, however, a difficult task, and existing tools either fail to scale efficiently, provide limited experimental feasibility or work only for specific POVMs. Here, we introduce and demonstrate a general method to certify non-simulability of a POVM by introducing a complete hierarchy of semidefinite programs. It provides upper bounds on the non-simulability measure of critical visibility of arbitrary POVMs which are tight in many cases and outperform previously known criteria. We experimentally certify the non-simulability of two- and three-dimensional POVMs using a trapped-ion qudit quantum processor by constructing non-simulability witnesses and introduce a modification of our framework that makes them robust against state preparation errors. Finally, we extend our results to the setting where an additional ancilla system is available.

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arXiv2026

Simulating quantum measurements without superposition devices

Superposition is the core feature that sets quantum theory apart from classical physics. Here, we investigate whether sets of quantum measurements can be modelled by using only devices that are classical, in the sense that they only resolve orthogonal measurement outcomes. This leads us to introduce classical measurement models, which we show to be intermediate between the notion of commutative measurements and joint measurability. Towards understanding these models we (i) identify exact noise and loss rates at which all projective measurements admit a classical model, (ii) propose numerical methods to construct classical models for finite sets of measurements, and (iii) show how to construct witnesses of genuine superposition properties in quantum measurements. In addition, we show that classical measurement models also have operational implications in non-disturbance tasks where sequential quantum measurements are implemented with classical side-information. Our work provides a new approach to the role of superposition in quantum measurements.

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arXiv2026

Resource theory of interactive quantum instruments

Quantum instruments describe both the classical outcome and the updated quantum state in a measurement process. To do this in a non-trivial way, instruments must have the capability to interact coherently with the state that they measure. Here, we develop a resource theory for instruments. We consider a relevant quantifier of the separation between interactive and non-interactive instruments and show that it admits three distinct operational interpretations in terms of quantum information tasks. These concern (i) the preservation of maximally entangled states after a local measurement, (ii) the average ability to preserve random states after measurement, and (iii) the ability to recover the classical information generated from measuring half of a maximally entangled state. We also introduce a natural set of allowed operations and show that the third task fully characterises the resource content of instruments. Our general framework reproduces as special cases established resource theories for channels and measurements.

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arXiv2026

Efficient Energy-Constrained Semi-Device-Independent QRNG with an Integrated Heterodyne Receiver

Semi-device-independent QRNG frameworks represent a particularly attractive approach, combining strong security guarantees with high randomness generation rates while relying only on reduced and practical physical assumptions. A recently proposed approach based on photon-number constraints is particularly suited to photonic implementations, where these assumptions can be easily assessed experimentally. Here, we experimentally demonstrate a quantum random number generator within this framework, enabling the direct computation of lower bounds on the certifiable Shannon entropy via semidefinite relaxation techniques. When combined with entropy accumulation methods, this approach enables finite-size randomness certification without assuming independent and identically distributed rounds. We realize the protocol using a four-state coherent-state constellation symmetrically distributed in phase space and measured by heterodyne detection, certifying 0.223 bit per measurement, which is the highest value reported to date for a continuous-variable semi-device-independent QRNG. The implementation combines a low-loss integrated photonic heterodyne receiver with a simple transmitter assembled from commercial components, providing a practical and high-speed architecture for semi-device-independent randomness generation.

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arXiv2026

Faking entanglement with imperceptible measurement deviations

Quantum entanglement is a central resource underpinning emerging quantum technologies, enabling capabilities beyond those of classical systems. Accurate verification of entanglement is therefore crucial. However, experimental schemes usually rely on the assumption that quantum measurements can be realized exactly. As the complexity of a quantum system grows, this assumption typically becomes increasingly unrealistic, therefore leading to a widening mismatch between theoretical models and experimental implementations. Here we demonstrate that arbitrarily small measurement errors, when adversarially encoded in the measurement apparatus, can lead to the false certification of high-dimensional entanglement in systems that are, in fact, separable. This is achieved by introducing explicit hacking attacks to measurement devices in well-established entanglement verification tests. We further experimentally demonstrate this effect using classical photonic states encoded in the spatial degree of freedom, spanning up to 61 dimensions with measurement fidelity errors as low as 0.23%. Our results uncover a fundamental vulnerability in current methods for high-dimensional entanglement detection, highlighting the susceptibility of complex quantum devices to small adversarial perturbations. The findings underscore the need for developing secure verification of quantum information that is robust to bounded discrepancies between theory and experiment.

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arXiv2026

Certifying coherence in quantum devices under classical control

Quantum states that do not commute exhibit coherence, but only when the device preparing them is assumed to be unaffected by classical parameters inaccessible to the experimenter. Such hidden classical control arises both in fundamental tests of quantum phenomena and in quantum information protocols that operate under limited control assumptions. Here, we address the problem of coherence certification by developing complete and practically efficient methods. First, we prove that coherence can be fully characterised through a hierarchy of semidefinite programs. Second, we introduce a practical semidefinite programming approach that achieves useful accuracy while remaining computationally efficient even for preparation devices generating many, potentially high-dimensional, quantum states. For the important special case of qubits, we further exploit conceptual connections with the theory of joint measurability to obtain highly accurate coherence characterisation that scales to more than one thousand qubits. Finally, we apply these methods to determine whether quantum channels are able to preserve coherence or are inherently coherence-breaking. Together, these results provide a powerful toolbox for analysing quantum superposition in the presence of hidden classical control.

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arXiv2026

High-Dimensional Quantum Photonics: Roadmap

The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.

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arXiv2026

Quantum inputs in the prepare-and-measure scenario and stochastic teleportation

We investigate prepare-and-measure scenarios in which a sender and a receiver use entanglement to send quantum information over a channel with limited capacity. We formalise this framework, identify its basic properties and provide numerical tools for optimising quantum protocols for generic communication tasks. The seminal protocol for sending quantum information over a classical channel is teleportation. We study a natural stochastic generalisation in which the sender holds $N$ qubits from which the receiver can recover one on demand. We show that with two bits of communication alone, this task can be solved exactly for all $N$, if the sender and receiver have access to stronger-than-quantum nonlocality. We then consider entanglement-based protocols and show that these can be constructed systematically by leveraging connections to several well-known quantum information primitives, such as teleportation, cloning machines and random access coding. In particular, we show that by using genuine multi-particle entangled measurements, one can construct a universal stochastic teleportation machine, i.e.~a device whose teleportation fidelity is independent of the quantum input.

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arXiv2026

Entanglement in prepare-and-measure scenarios without receiver inputs

The most elementary prepare-and-measure scenarios have no independent measurement inputs. No inputs mean that quantum advantages require two indispensable ingredients: shared entanglement and measurements that can be adapted to the communicated messages. Understanding these scenarios is therefore conceptually natural, but also practically relevant, since they act as testbeds for black-box certification of adaptive one-way LOCC. Here, we study them systematically and reveal several of their basic features. For classical messages, we first identify the minimal scenario with a quantum advantage and show that it is maximised by high-dimensional entanglement. Then, we identify the next-to-minimal scenario, and show that quantum advantages can be propelled by nonlocality of the Clauser-Horne-Shimony-Holt type, which makes this an appropriate setting for certification experiments. Proceeding further, we replace classical messages with quantum messages, but require the receiver to read the message before measuring the entangled particle. We show that this leads to amplified quantum advantages, that are made possible only thanks to non-projective message read-out. This in dispensable role of non-projective measurements challenges the common wisdom that they play a secondary role in revealing the power of quantum correlations in black-box experiments.

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arXiv2026

Quantum correlations in prepare-and-measure scenarios and their semi-device-independent applications

A key aspect in quantum information is to understand the advantage offered by quantum systems over classical ones in communication tasks. In recent years, a fundamental approach to this problem has been developed, focusing on quantum correlations in prepare-and-measure scenarios. Inspired by the developments in Bell nonlocality and device-independent information processing, this line of research aims to characterize the possibilities and limits of quantum systems for communication, in particular to precisely capture the advantage they offer over classical systems. In addition to fundamental insights, these ideas also underpin the concept of semi-device-independent quantum information processing. Exploring trade-offs between security, performance and ease-of-implementation, this approach opens promising directions for novel quantum information processing technologies and devices. A number of protocols and proof-of-principle demonstrations have been reported in recent years, in particular for quantum randomness certification and key distribution. Here, we provide a comprehensive introduction to quantum prepare-and-measure correlations and semi-device independent applications.

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arXiv2026

A single programmable photonic circuit for universal quantum measurements

Programmable photonic quantum processors face a critical challenge: despite significant advances in quantum state preparation and manipulation, measurements remain limited to projective techniques. Here, we demonstrate a programmable measurement processor that overcomes this limitation by enabling arbitrary quantum measurements within a scalable circuit framework. Our large-scale integrated photonic architecture achieves precise coherent control of ancillary quantum systems, realizing a universal four-dimensional quantum measurement device. We benchmark the processor by performing measurement tomography on 100 randomly selected measurements, achieving an average fidelity of 97.7%. The processor's performance exceeds the theoretical limits of projective measurements in three key quantum information tasks: state discrimination (with 23 times lower error), state estimation (with 10.6% higher fidelity), and randomness generation (with 37% more randomness yield), demonstrating its high operational quality. This work establishes a fully programmable quantum measurement processor, advancing the development of universal quantum operations for photonic quantum information processing by providing the key missing component.

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arXiv2026

Maximally non-projective measurements are not always symmetric informationally complete

Standard quantum measurements are projective. However, the full scope of quantum measurements is represented by positive operator-valued measures (POVMs) and many of these break the limitations of projective measurements as resources in quantum information. It is therefore natural to consider how accurately an experimenter with access only to projective measurements and classical processing can simulate POVMs. The most well-known class of non-projective measurements is called symmetric informationally complete (SIC). Such measurements are both ubiquitous in the broader scope of quantum information theory and known to be the most strongly non-projective measurements in qubit systems. Here, we show that beyond qubit systems, the SIC property is in general not associated with the most non-projective measurement. For this, we put forward a semidefinite programming criterion for detecting genuinely non-projective measurements. This method allows us to determine quantitative simulability thresholds for generic POVMs and to put forward a conjecture on which qutrit and ququart measurements that are most strongly non-projective.

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arXiv2026

Bell and EPR experiments with signalling data

The no-signalling principle is a fundamental assumption in Bell-inequality and quantum-steering experiments. Nonetheless, experimental imperfections can lead to apparent violations beyond those expected from finite-sample statistics. Here, we propose extensions of local hidden variable and local hidden state theories that allow for bounded, operationally quantifiable, amounts of signalling. We show how non-classicality tests can be developed for these models, both through exact methods based on the full set of observed statistics and through corrections to the standard Bell and steering inequalities. We demonstrate the applicability of these methods via two scenarios that feature apparent signalling: an IBM quantum processor and post-selected data from inefficient detectors.

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arXiv2026

Operationally classical simulation of quantum states

A classical state-preparation device cannot generate states in relative superposition. We introduce classical models in which devices that are individually unable to generate states with relative superposition can be stochastically coordinated to simulate sets of quantum states. These models have natural operational interpretation in prepare-and-measure scenarios and they can account for many non-commuting quantum state sets. We develop systematic methods both for classically simulating quantum sets and for showing that no such simulation exists, thereby certifying quantum coherence. In particular, we determine the exact noise rates required to classically simulate the entire state space of quantum theory. We also reveal connections between the operational classicality of sets and the well-known fundamental concepts of joint measurability and Einstein-Podolsky-Rosen steering. Here, we present an avenue to understand how and to what extent quantum states defy generic models based on classical devices, which also has relevant implications for quantum information applications.

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arXiv2026

Binarisation-loophole-free observation of high-dimensional quantum nonlocality

Bell inequality tests based on high-dimensional entanglement usually require measurements that can resolve multiple possible outcomes. However, the implementation of high-dimensional multi-outcome measurements is often only emulated via a collection of ``click or no-click'' measurements. This reduction of multi-outcome measurements to binary-outcome measurements opens a loophole in high-dimensional tests Bell inequalities which can be exploited by local hidden variable models [Tavakoli et al., Phys. Rev. A 111, 042433 (2025)]. Here, we close this loophole by using four-dimensional photonic path-mode entanglement and multi-outcome detection. We test both the well-known Collins-Gisin-Linden-Massar-Popescu inequality and a related Bell inequality tailored for maximally entangled states in high-dimension. We observe violations that are large enough to also rule out any quantum model based on entanglement of lower dimension, thereby demonstrating genuinely high-dimensional nonlocality free of the binarisation loophole.

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arXiv2025

The role of entanglement in energy-restricted communication and randomness generation

A promising platform for semi-device-independent quantum information is prepare-and-measure experiments restricted only by a bound on the energy of the communication. Here, we investigate the role of shared entanglement in such scenarios. For classical communication, we derive a general correlation criterion for nonlocal resources and use it to show that entanglement can fail to be a resource in standard tasks. For quantum communication, we consider the basic primitive for energy-constrained communication, namely the probabilistic transmission of a bit, and show that the advantages of entanglement only can be unlocked by non-unitary encoding schemes that purposefully decohere the entangled state. We also find that these advantages can be increased by using entanglement of higher dimension than qubit. We leverage these insights to investigate the impact of entanglement for quantum random number generation, which is a standard application of these systems but whose security so far only has been established against classical side information. In the low-energy regime, our attacks on the protocol indicate that the security remains largely intact, thereby paving the way for strengthened security without more complex setups and with negligible performance reductions.

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