arXiv subjects

Edgar A. Aguilar

Publications and source records attributed to Edgar A. Aguilar.

10 recordsLinked to original sources

arXiv2026

Thermal Operations in general are not memoryless

So-called Thermal Operations seem to describe the most fundamental and reasonable set of operations allowable for state transformations at an ambient inverse temperature $β$. However, a priori, they require experimentalists to manipulate very complex environments and have control over their internal degrees of freedom. For this reason, the community has been working on creating more experimentally-friendly operations. In [Perry, et al., Phys. Rev. X 8, 041049], it was shown that for states diagonal in the energy basis, Thermal Operations can be performed by so-called Coarse Operations, which need just one auxiliary qubit but are otherwise Markovian and classical in spirit. In this work, by providing an explicit counterexample, we show that this one qubit of memory is necessary. We also provide almost full characterization (i.e., full, but with one intriguing exception that remains open) of possible transitions that do not require memory in the case where the system is a qubit. We do this by analyzing arbitrary control sequences comprising level energy changes and partial thermalizations in each step.

quant-ph↗

arXiv2023

Specification-Guided Critical Scenario Identification for Automated Driving

To test automated driving systems, we present a case study for finding critical scenarios in driving environments guided by formal specifications. To that aim, we devise a framework for critical scenario identification, which we base on open-source libraries that combine scenario specification, testing, formal methods, and optimization.

math.OC↗

arXiv2022

Hierarchical Potential-based Reward Shaping from Task Specifications

The automatic synthesis of policies for robotic-control tasks through reinforcement learning relies on a reward signal that simultaneously captures many possibly conflicting requirements. In this paper, we in\-tro\-duce a novel, hierarchical, potential-based reward-shaping approach (HPRS) for defining effective, multivariate rewards for a large family of such control tasks. We formalize a task as a partially-ordered set of safety, target, and comfort requirements, and define an automated methodology to enforce a natural order among requirements and shape the associated reward. Building upon potential-based reward shaping, we show that HPRS preserves policy optimality. Our experimental evaluation demonstrates HPRS's superior ability in capturing the intended behavior, resulting in task-satisfying policies with improved comfort, and converging to optimal behavior faster than other state-of-the-art approaches. We demonstrate the practical usability of HPRS on several robotics applications and the smooth sim2real transition on two autonomous-driving scenarios for F1TENTH race cars.

cs.LG↗

arXiv2022

Model-Free Reinforcement Learning for Symbolic Automata-encoded Objectives

Reinforcement learning (RL) is a popular approach for robotic path planning in uncertain environments. However, the control policies trained for an RL agent crucially depend on user-defined, state-based reward functions. Poorly designed rewards can lead to policies that do get maximal rewards but fail to satisfy desired task objectives or are unsafe. There are several examples of the use of formal languages such as temporal logics and automata to specify high-level task specifications for robots (in lieu of Markovian rewards). Recent efforts have focused on inferring state-based rewards from formal specifications; here, the goal is to provide (probabilistic) guarantees that the policy learned using RL (with the inferred rewards) satisfies the high-level formal specification. A key drawback of several of these techniques is that the rewards that they infer are sparse: the agent receives positive rewards only upon completion of the task and no rewards otherwise. This naturally leads to poor convergence properties and high variance during RL. In this work, we propose using formal specifications in the form of symbolic automata: these serve as a generalization of both bounded-time temporal logic-based specifications as well as automata. Furthermore, our use of symbolic automata allows us to define non-sparse potential-based rewards which empirically shape the reward surface, leading to better convergence during RL. We also show that our potential-based rewarding strategy still allows us to obtain the policy that maximizes the satisfaction of the given specification.

cs.AI↗

arXiv2021

Optimized detection of high-dimensional entanglement

Entanglement detection is one of the most conventional tasks in quantum information processing. While most experimental demonstrations of high-dimensional entanglement rely on fidelity-based witnesses, these are powerless to detect entanglement within a large class of entangled quantum states, the so-called unfaithful states. In this paper, we introduce a highly flexible automated method to construct optimal tests for entanglement detection given a bipartite target state of arbitrary dimension, faithful or unfaithful, and a set of local measurement operators. By restricting the number or complexity of the considered measurement settings, our method outputs the most convenient protocol which can be implemented using a wide range of experimental techniques such as photons, superconducting qudits, cold atoms or trapped ions. With an experimental quantum optics setup that can prepare and measure arbitrary high-dimensional mixed states, we implement some $3$-setting protocols generated by our method. These protocols allow us to experimentally certify 2- and 3-unfaithful entanglement in 4-dimensional photonic states, some of which contain well above 50% of noise.

quant-ph↗

arXiv2021

Quantum Preparation Games

A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. The measurement setting in each round, as well as the final score of the game, are decided by the referee based on the past history of settings and measurement outcomes. Many experimental tasks in quantum information, such as entanglement quantification or magic state detection, can be cast as preparation games. In this paper, we introduce general methods to design $n$-round preparation games, with tight bounds on the average game scores achievable by players subject to constraints on their preparation devices. We illustrate our results by devising new adaptive measurement protocols for entanglement detection and quantification. Surprisingly, we find that the standard procedure in entanglement detection, namely, estimating $n$ times the average value of a given entanglement witness, is in general sub-optimal for detecting the entanglement of a specific quantum state. On the contrary, there exist $n$-round experimental scenarios where detecting the entanglement of a known state optimally requires adaptive measurement schemes.

quant-ph↗

arXiv2021

Semi-Device-Independent Random Number Generation with Flexible Assumptions

Our ability to trust that a random number is truly random is essential for fields as diverse as cryptography and fundamental tests of quantum mechanics. Existing solutions both come with drawbacks -- device-independent quantum random number generators (QRNGs) are highly impractical and standard semi-device-independent QRNGs are limited to a specific physical implementation and level of trust. Here we propose a new framework for semi-device-independent randomness certification, using a source of trusted vacuum in the form of a signal shutter. It employs a flexible set of assumptions and levels of trust, allowing it to be applied in a wide range of physical scenarios involving both quantum and classical entropy sources. We experimentally demonstrate our protocol with a photonic setup and generate secure random bits under three different assumptions with varying degrees of security and resulting data rates.

quant-ph↗

arXiv2020

Entanglement Detection Beyond Measuring Fidelities

One of the most widespread methods to determine if a quantum state is entangled, or to quantify its entanglement dimensionality, is by measuring its fidelity with respect to a pure state. In this Letter we find a large class of states whose entanglement cannot be detected in this manner; we call them unfaithful. We find that unfaithful states are ubiquitous in information theory. For small dimensions, we check numerically that most bipartite states are both entangled and unfaithful. Similarly, numerical searches in low dimensions show that most pure entangled states remain entangled but become unfaithful when a certain amount of white noise is added. We also find that faithfulness can be self-activated, i.e., there exist instances of unfaithful states whose tensor powers are faithful. To explore how the fidelity approach limits the quantification of entanglement dimensionality, we generalize the notion of an unfaithful state to that of a D-unfaithful state, one that cannot be certified as D-dimensionally entangled by measuring its fidelity with respect to a pure state. For describing such states, we additionally introduce a hierarchy of semidefinite programming relaxations that fully characterizes the set of states of Schmidt rank at most D.

quant-ph↗

arXiv2018

Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses

We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using non-coupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.

quant-ph↗

arXiv2018

Connections Between Mutually Unbiased Bases and Quantum Random Access Codes

We present a new quantum communication complexity protocol, the promise--Quantum Random Access Code, which allows us to introduce a new measure of unbiasedness for bases of Hilbert spaces. The proposed measure possesses a clear operational meaning and can be used to investigate whether a specific number of mutually unbiased bases exist in a given dimension by employing Semi--Definite Programming techniques.

quant-ph↗