arXiv subjects

Esteban Martínez-Vargas

Publications and source records attributed to Esteban Martínez-Vargas.

11 recordsLinked to original sources

arXiv2026

Fixed Point Engineering of Quantum Batteries

We develop, in the context of open quantum systems, a general formalism to build completely positive and unital (CPU) maps that have a desired fixed point. In contrast to quantum channels, these maps act on observables, not on states. As the CPU maps will have a known observable as their fixed point, we know by construction that in the asymptotic limit the map will yield a constant observable. Therefore, if we implement this in a differential equation, we have a linear growth of a quantity with respect to time. Applying these ideas to the charging of quantum batteries, we obtain an upper bound on the charging power of batteries by allowing interchanges of multiple states every time the CPU map is applied.

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arXiv2024

Relativistic time dilation from a quantum mechanism

One of the concepts of Relativity theory that challenges conventional intuition the most is time dilation and length contraction. Usual approaches for describing relativistic effects in quantum systems merely postulate the consequences of these effects as physical constraints. Here, we propose to rebuild Special Relativity from quantum mechanical considerations. This is done by dropping one of its fundamental postulates: the universality of the speed of light. Lorentz transformations are obtained by a quantum mechanism. We use the fact that quantum states depend on the Galilean reference frame where they are defined. In other words, quantum states outside an observer's Galilean reference frame are distorted. Then, we show in a theorem the existence of time-dependent observables that are sensible to this distortion in such a way that their expectation value is a Lorentz-covariant function of time. We then postulate this mechanism as the source of the phenomena of Special Relativity. As a corollary of the main theorem, we show the existence of a Lorentz covariant momentum and mass operators which yield the relativistic momentum and mass. In this theory, the fundamental limit of the speed of light imposes a transparency condition for faster-than-light particles: they are allowed but they are not observable. The transparency effect could explain dark matter in a more general theory following this quantum formalism.

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arXiv2023

Classicality from Quantum Stochastic Processes

I develop a theory of classicality from quantum systems. This theory stems from the study of classical and quantum stationary stochastic processes. The stochastic processes are characterized by polyhedral (classical) and semidefinite representative (quantum) cones. Based on a previous result by the author I expand the study of fixed points from quantum channels. I give a semidefinite program that characterizes a quantum channel separating into a core and a part that decays with many iterations. In general, the solution is non-separable in the space it is defined. I present a characterization of channels in terms of their fixed points for the separable case. A quantum simulation of a polyhedral cone can then be constructed.

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arXiv2023

Stability Verification of Quantum non-i.i.d. sources

We introduce the problem of stability verification of quantum sources which are non-i.i.d.. The problem consists in ascertaining whether a given quantum source is stable or not, in the sense that it produces always a desired quantum state or if it suffers deviations. Stability is a statistical notion related to the sparsity of errors. This problem is closely related to the problem of quantum verification first proposed by Pallister et. al. [1], however, it extends the notion of the original problem. We introduce a family of states that come from these non-i.i.d. sources which we call a Markov state. These sources are more versatile than the i.i.d. ones as they allow statistical deviations from the norm instead of the more coarse previous approach. We prove in theorem 1 that the Markov states are not well described with tensor products over a changing source. In theorem 2 we further provide a lower bound on the trace distance between two Markov states, or conversely, an upper bound on the fidelity between these states. This is a bound on the capacity of determining the stability property of the source, which shows that it is exponentially easier to ascertain this with respect to n, the number of outcomes from the source.

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arXiv2023

Quantum Stabilizer Channel for Thermalization

We study the problem of quantum thermalization from a very recent perspective: via discrete interactions with thermalized systems. We thus extend the previously introduced scattering thermalization program by studying not only a specific channel but allowing any possible one. We find a channel that solves a fixed point condition using the Choi matrix approach that is in general non-trace-preserving. We also find a general way to complement the found channel so that it becomes trace-preserving. Therefore we find a general way of characterizing a family of channels with the same desired fixed point. From a quantum computing perspective, the results thus obtained can be interpreted as a condition for quantum error correction that also reminds of quantum error avoiding.

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arXiv2022

Sequential Analysis of a finite number of Coherent states

We investigate an advantage for information processing of ordering a set of states over making a global quantum processing with a fixed number of copies of coherent states. Suppose Alice has $N$ copies of one of two quantum states $σ_0$ or $σ_1$ and she gives these states to Bob. Using the optimal sequential test, the SPRT, we ask if processing the states in batches of size $l$ is advantageous to optimally distinguish the two hypotheses. We find that for the symmetric case $\{|γ\rangle,|-γ\rangle\}$ there is no advantage of taking any batch size $l$. We give an expression for the optimal batch size $l_\text{opt}$ in the assymetric case. We give bounds $l_\text{min}$ and $l_\text{max}$ for when $P_S\approx 1$.

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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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arXiv2019

Certified answers for ordered quantum discrimination problems

We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is, answers that never deviate from the true value more than a specified distance and hence a control of the desired quality of the results. We obtain an efficient semidefinite program and also find a general lower bound valid for any error distance that only requires the knowledge of optimal minimum error scheme. We apply our results to the quantum change point and quantum state anomaly detection cases.

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arXiv2019

Quantum measurement optimization by decomposition of measurements into extremals

Using the convex structure of positive operator value measurements and of several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to find the best strategy allowed by quantum mechanics to estimate a parameter. This method explores extremal measurements thus providing a significant advantage over previously used methods. We exemplify the method for different cost functions in a qubit and in a harmonic oscillator and find a strong numerical advantage when the desired target error is sufficiently small.

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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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