arXiv subjects

Carles Roch i Carceller

Publications and source records attributed to Carles Roch i Carceller.

12 recordsLinked to original sources

arXiv2026

MoMPy: automated construction of moment matrices for semidefinite programming relaxations

We present MoMPy, an open-source Python package that provides a unified, declarative construction of moment matrices for semidefinite programming (SDP) hierarchies. The user declares operator labels together with a small set of structural relations, and MoMPy returns a matrix of SDP variable indices in which every implied identification has already been made, ready for CVXPY or any other modelling layer. Internally, the identification problem is recast as a word-rewriting problem on tuples of integers and solved with a memoised breadth-first closure coupled to a disjoint-set forest, so that each distinct monomial is processed exactly once per build, however many matrix entries it eventually labels. The central abstraction is independent of the physical scenario: the same construction handles tracial, state (NPA), and block-valued moments, with no notion of parties, settings or preparations. We demonstrate this generality on a tripartite Mermin inequality, the bipartite CHSH inequality, measurement compatibility in a steering scenario, state discrimination and dimension witnessing in prepare-and-measure scenarios, device-independent randomness certification, and certification of deterministic correlations from known ensembles. The construction is validated against an independent brute-force implementation and benchmarked across eight structurally distinct scenarios, spanning bipartite and tripartite Bell tests, heterogeneous-outcome, steering-type, jointly-measurable and network configurations.

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arXiv2026

Characterising the set of deterministic quantum correlations in prepare-and-measure scenarios

Correlations that do not admit a deterministic explanation are a central feature of quantum theory and a key resource for quantum information processing. Identifying and certifying such correlations, however, remains a fundamental challenge. In this work, we advance on this problem by considering deterministic correlations in the prepare-and-measure scenario consistent with a wide range of communication restrictions. To certify correlations incompatible with such deterministic models, we ask whether they admit a scenario in which measurement outcomes can be perfectly predicted by an adversary equipped with classical side-information. We show the usefulness of this approach and propose semidefinite programming relaxations tailored to three representative communication restrictions: fixed ensemble, bounded overlaps and restricted observables.

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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

Quantum randomness certification with untrusted measurements and few probe states

We present a scheme for semi-device-independent quantum randomness certification from an untrusted measurement device and a trusted source and demonstrate it experimentally. No assumptions about noise or imperfections in the measurement are required and the scheme is simple to implement with existing technology. The measurement device is probed with a few trusted states and the output entropy can be lower bounded conditioned on the observed outcome distribution. The protocol can be applied to measurements with any finite number of outcomes and in particular can be realised by homodyne measurements of the vacuum using a detector probed by coherent states, as we experimentally demonstrate by intensity modulation of a telecom-wavelength pilot laser followed by homodyne detection and discretisation by analog-to-digital conversion. We show that randomness can be certified in the presence of both Gaussian additive noise and non-Gaussian imperfections.

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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

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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arXiv2025

Unlimited quantum correlation advantage from bound entanglement

Entangled states that cannot be distilled to maximal entanglement are called bound entangled and they are often viewed as too weak to break the limitations of classical models. Here, we show a strongly contrasting result: that bound entangled states, when deployed as resources between two senders who communicate with a receiver, can generate correlation advantages of unlimited magnitude. The proof is based on using many copies of a bound entangled state to assist quantum communication. We show that in order to simulate the correlations predicted by bound entanglement, one requires in the many-copy limit either an entanglement visibility that tends to zero or a diverging amount of overhead communication. This capability of bound entanglement is unlocked by only using elementary single-qubit operations. The result shows that bound entanglement can be a scalable resource for breaking the limitations of physical models without access to entanglement.

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arXiv2025

Semidefinite relaxations for high-dimensional entanglement in the steering scenario

We introduce semidefinite programming hierarchies for benchmarking relevant entanglement properties in the high-dimensional steering scenario. Firstly, we provide a general method for detecting the entanglement dimensionality through certification of the Schmidt number. Its key feature is that the computational cost is independent of the Schmidt number under consideration. Secondly, we provide a method to estimate the fidelity of the source with any maximally entangled state. Using only basic computational means, we demonstrate the usefulness of these methods, which can be directly used to analyse experiments on high-dimensional systems.

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arXiv2024

Prepare-and-measure scenarios with photon-number constraints

We study correlations in the prepare-and-measure scenario when quantum communication is constrained by photon-number statistics. Such constraints are natural and practical control parameters for semi-device-independent certification in optical platforms. To analyse these scenarios, we show how semidefinite programming relaxations for non-commutative polynomial optimization can be used to bound the set of quantum correlations under restrictions on the photon-number distribution. The practicality of this method is demonstrated by computing optimal performance bounds on several well-known communication tasks. We then apply the method to the certification of semi-device-inpependent random number generation protocols and show how to bound the conditional Shannon entropy. We showcase this versatile tool by improving randomness extraction in established protocols based on coherent states and homodyne measurements.

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arXiv2024

Scalable entanglement certification via quantum communication

Harnessing the advantages of shared entanglement for sending quantum messages often requires the implementation of complex two-particle entangled measurements. We investigate entanglement advantages in protocols that use only the simplest two-particle measurements, namely product measurements. For experiments in which only the dimension of the message is known, we show that robust entanglement advantages are possible, but that they are fundamentally limited by Einstein-Podolsky-Rosen steering. Subsequently, we propose a natural extension of the standard scenario for these experiments and show that it circumvents this limitation. This leads us to prove entanglement advantages from every entangled two-qubit Werner state, evidence its generalisation to high-dimensional systems and establish a connection to quantum teleportation. Our results reveal the power of product measurements for generating quantum correlations in entanglement-assisted communication and they pave the way for practical semi-device-independent entanglement certification well-beyond the constraints of Einstein-Podolsky-Rosen steering.

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arXiv2022

Maximum confidence measurement for qubit states

In quantum state discrimination, one aims to identify unknown states from a given ensemble by performing measurements. Different strategies such as minimum-error discrimination or unambiguous state identification find different optimal measurements. Maximum-confidence measurements (MCMs) maximise the confidence with which inputs can be identified given the measurement outcomes. This unifies a range of discrimination strategies including minimum-error and unambiguous state identification, which can be understood as limiting cases of MCM. In this work, we investigate MCMs for general ensembles of qubit states. We present a method for finding MCMs for qubit-state ensembles by exploiting their geometry and apply it to several interesting cases, including ensembles two and four mixed states and ensembles of an arbitrary number of pure states. We also compare MCMs to minimum-error and unambiguous discrimination for qubits. Our results provide interpretations of various qubit measurements in terms of MCM and can be used to devise qubit protocols.

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arXiv2021

Contextual advantages and certification for maximum confidence discrimination

One of the most fundamental results in quantum information theory is that no measurement can perfectly discriminate between non-orthogonal quantum states. In this work, we investigate quantum advantages for discrimination tasks over noncontextual theories by considering a maximum confidence measurement that unifies different strategies of quantum state discrimination, including minimum-error and unambiguous discrimination. We first show that maximum confidence discrimination, as well as unambiguous discrimination, contains contextual advantages. We then consider a semi-device independent scenario of certifying maximum confidence measurement. The scenario naturally contains undetected events, making it a natural setting to explore maximum confidence measurements. We show that the certified maximum confidence in quantum theory also contains contextual advantages. Our results establish how the advantages of quantum theory over a classical model may appear in a realistic scenario of a discrimination task.

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