arXiv subjects

Ramon Muñoz-Tapia

Publications and source records attributed to Ramon Muñoz-Tapia.

14 recordsLinked to original sources

arXiv2026

Neural Network Learning of One-Bit Protocols for Qubit Measurement Simulation

Communication complexity provides a natural framework for quantifying the classical resources required to reproduce quantum statistics. In the qubit prepare-and-measure scenario, two classical bits have been shown to be necessary and sufficient to simulate arbitrary qubit states and arbi- trary quantum measurements exactly. However, this result does not exclude the possibility that restricted families of measurements may admit accurate 1-bit classical approximations. We use a neural network procedure to demonstrate that a single bit can achieve high average accuracy for specific measurement families. A performance analysis of our neural network reveals that symmet- ric measurements with uniformly weighted elements, such as those forming regular polyhedra, are particularly amenable to this restricted communication. By analyzing the patterns learned by the neural network, we derive an analytical protocol that is extremely accurate for finite information- ally complete symmetric configurations and becomes exact in the limit of a continuous isotropic measurement.

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arXiv2026

Exact identification of unknown unitary processes

The accurate identification of faulty hardware is a fundamental requirement for reliable quantum information processing. We address this problem in a quantum setting, where a series of $n$ devices is intended to apply the same unitary operation, but $k$ malfunctioning devices among them apply a different, unknown unitary action. Under the assumption of complete ignorance regarding the specific unitary transformation applied, we model our hypotheses using representation-theoretic tools and study the zero-error protocol for identifying these faulty devices. We derive the optimal success probability for the single- and two-anomaly scenarios, demonstrating that it is independent of the total number of devices in the series. Furthermore, we present a simple protocol that makes use of ancillary systems that achieves this optimal limit. Notably, this protocol offers significant operational advantages, such as allowing us to test each device independently. Finally, we extend our analysis to the general scenario in which both the number of anomalies and the local dimension of the systems are arbitrary, evaluating our protocol's performance and conjecturing its global optimality in the general case.

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arXiv2026

Quantum state exclusion for group-generated ensembles of pure states

Quantum state exclusion is the task of determining which states from a given set a system was not prepared in. We provide a complete solution to optimal quantum state exclusion for arbitrary sets of pure states generated by finite groups, establishing necessary and sufficient conditions for perfect (zero-error conclusive) exclusion. When perfect exclusion is impossible, we introduce two natural extensions: minimum-error and unambiguous exclusion. For both, we derive the optimal protocols and present analytical expressions for the corresponding failure probabilities and measurements, providing additional insight into how quantum states encode information.

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arXiv2025

Prepare-and-measure and entanglement simulation beyond qubits

For two non-communicating parties, quantum theory can give rise to probability distributions of outcomes that no local classical model can reproduce without communication. However, in the case of two-dimensional systems ($d=2$), it is known that allowing a finite amount of classical communication to shared classical resources makes it possible to simulate these quantum correlations. Whether such a simulation remains possible in higher dimensions is still an open question. In this work, we identify the key features of the exact classical protocol in $d=2$, and use them to construct robust approximate protocols in higher dimensions. We assess their performance through a randomized numerical study based on the Total Variation Distance. Our approach exactly reproduces the quantum probability distributions for $d=2$, and performs very well compared to existing protocols for higher dimensions, being the most robust protocol in all cases studied. These results offer new insights into the analytical structure of classical protocols in higher dimensions.

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arXiv2025

Quantum Edge Detection

This paper introduces quantum edge detection, aimed at locating boundaries of quantum domains where all particles share the same pure state. Focusing on the 1D scenario of a string of particles, we develop an optimal protocol for quantum edge detection, efficiently computing its success probability through Schur-Weyl duality and semidefinite programming techniques. We analyze the behavior of the success probability as a function of the string length and local dimension, with emphasis in the limit of long strings. We present a protocol based on square root measurement, which proves asymptotically optimal. Additionally, we explore a mixed quantum change point detection scenario where the state of particles transitions from known to unknown, which may find practical applications in detecting malfunctions in quantum devices

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arXiv2024

Quantum multi-anomaly detection

A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of $n$ preparations with $k$ anomalies. We analyze the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the observer and anomalies can appear equally likely in any position of the preparation series. We find the solution using results from association schemes theory, thus establishing a connection between graph theory and quantum hypothesis testing. In particular, we use the Johnson association scheme which arises naturally from the Gram matrix of this problem. We also study the regime of large $n$ and obtain the expression of the success probability that is non-vanishing. Finally, we address the case in which the observer is blind to the reference and the anomalous states. This scenario requires a universal protocol for which we prove that in the asymptotic limit, the success probability corresponds to the average of the known state scenario.

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arXiv2022

Universal algorithms for quantum data learning

Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this Perspective, we review a line of works dealing with measurements that reveal structural properties of quantum datasets given in the form of product states. These algorithms are universal, meaning that their performances do not depend on the reference frame in which the dataset is provided. Requiring the universality property implies a characterization of optimal measurements via group representation theory.

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arXiv2022

Volumes of parent Hamiltonians for benchmarking quantum simulators

We investigate the relative volume of parent Hamiltonians having a target ground state up to some fixed error $ε$, a quantity which sets a benchmark on the performance of quantum simulators. For vanishing error, this relative volume is of measure zero, whereas for a generic $ε$ we show that it increases with the dimension of the Hilbert space. We also address the volume of parent Hamiltonians when they are restricted to be local. For translationally invariant Hamiltonians, we provide an upper bound to their relative volume. Finally, we estimate numerically the relative volume of parent Hamiltonians when the target state is the ground state of the Ising chain in a transverse field.

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arXiv2022

Online identification of symmetric pure states

We consider online strategies for discriminating between symmetric pure states with zero error when $n$ copies of the states are provided. Optimized online strategies involve local, possibly adaptive measurements on each copy and are optimal at each step, which makes them robust in front of particle losses or an abrupt termination of the discrimination process. We first review previous results on binary minimum and zero error discrimination with local measurements that achieve the maximum success probability set by optimizing over global measurements, highlighting their online features. We then extend these results to the case of zero error identification of three symmetric states with constant overlap. We provide optimal online schemes that attain global performance for any $n$ if the state overlaps are positive, and for odd $n$ if overlaps have a negative value. For arbitrary complex overlaps, we show compelling evidence that online schemes fail to reach optimal global performance. The online schemes that we describe only require to store the last outcome obtained in a classical memory, and adaptiveness of the measurements reduce to at most two changes, regardless of the value of $n$.

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arXiv2021

Quantum Sequential Hypothesis Testing

We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error threshold, $ε$, when copies of the states can be required on demand. We obtain ultimate lower bounds on the average number of copies needed to accomplish the task. We give a block-sampling strategy that allows to achieve the lower bound for some classes of states. The bound is optimal in both the symmetric as well as the asymmetric setting in the sense that it requires the least mean number of copies out of all other procedures, including the ones that fix the number of copies ahead of time. For qubit states we derive explicit expressions for the minimum average number of copies and show that a sequential strategy based on fixed local measurements outperforms the best collective measurement on a predetermined number of copies. Whereas for general states the number of copies increases as $\log 1/ε$, for pure states sequential strategies require a finite average number of samples even in the case of perfect discrimination, i.e., $ε=0$.

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arXiv2020

Reinforcement learning for optimal error correction of toric codes

We apply deep reinforcement learning techniques to design high threshold decoders for the toric code under uncorrelated noise. By rewarding the agent only if the decoding procedure preserves the logical states of the toric code, and using deep convolutional networks for the training phase of the agent, we observe near-optimal performance for uncorrelated noise around the theoretically optimal threshold of 11%. We observe that, by and large, the agent implements a policy similar to that of minimum weight perfect matchings even though no bias towards any policy is given a priori.

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arXiv2019

Unsupervised classification of quantum data

We introduce the problem of unsupervised classification of quantum data, namely, of systems whose quantum states are unknown. We derive the optimal single-shot protocol for the binary case, where the states in a disordered input array are of two types. Our protocol is universal and able to automatically sort the input under minimal assumptions, yet partially preserving information contained in the states. We quantify analytically its performance for arbitrary size and dimension of the data. We contrast it with the performance of its classical counterpart, which clusters data that has been sampled from two unknown probability distributions. We find that the quantum protocol fully exploits the dimensionality of the quantum data to achieve a much higher performance, provided data is at least three-dimensional. For the sake of comparison, we discuss the optimal protocol when the classical and quantum states are known.

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arXiv2018

Online optimal exact identification of a quantum change point

We consider online detection strategies for identifying a change point in a stream of quantum particles allegedly prepared in identical states. We show that the identification of the change point can be done without error via sequential local measurements while attaining the optimal performance bound set by quantum mechanics. In this way, we establish the task of exactly identifying a quantum change point as an instance where local protocols are as powerful as global ones. The optimal online detection strategy requires only one bit of memory between subsequent measurements, and it is amenable to experimental realization with current technology.

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arXiv2018

Experimentally detecting a quantum change point via Bayesian inference

Detecting a change point is a crucial task in statistics that has been recently extended to the quantum realm. A source state generator that emits a series of single photons in a default state suffers an alteration at some point and starts to emit photons in a mutated state. The problem consists in identifying the point where the change took place. In this work, we consider a learning agent that applies Bayesian inference on experimental data to solve this problem. This learning machine adjusts the measurement over each photon according to the past experimental results finds the change position in an online fashion. Our results show that the local-detection success probability can be largely improved by using such a machine learning technique. This protocol provides a tool for improvement in many applications where a sequence of identical quantum states is required.

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