arXiv subjects

J. A. López-Saldívar

Publications and source records attributed to J. A. López-Saldívar.

4 recordsLinked to original sources

arXiv2025

Geometric properties of qudit systems

We discuss in general how to geometrically visualize a qudit system, with a particular interest in thermal states. The principle of maximum entropy is used to study the geometric properties of an ensemble of finite dimensional Hamiltonian systems with known average energy. These geometric characterizations are given in terms of the generalized diagonal Bloch vectors and the invariants of the special unitary group in $n$ dimensions. As examples, Hamiltonians written in terms of linear and quadratic generators of the angular momentum algebra are considered with $J= 1$ and $J=3/2$. For these cases, paths as functions of the temperature are established in the corresponding simplex representations, which show first- and second-order quantum phase transitions, as well as the adiabatic evolution of the interaction strengths (control parameters) of the Hamiltonian models. For the Lipkin-Meshkov-Glick Hamiltonian the quantum phase diagram is explicitly shown for different temperature values in parameter space.

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arXiv2024

Dynamic violation of Bell's inequalities in the angular momentum representation

A parametrization of density matrices of $d$ dimensions in terms of the raising $J_+$ and lowering $J_-$ angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann parameters. A general expression for the density matrix of the composite system of angular momenta $j_1$ and $j_2$ is obtained. In this matrix representation violations of the Bell-Clauser-Horne-Shimony-Holt inequalities are established for the $X$-states of a qubit-qubit, pure and mixed, composite system, as well as for a qubit-qutrit density matrix. In both cases maximal violation of the Bell inequalities can be reached, i.e., the Cirel'son limit. A correlation between the entanglement measure and a strong violation of the Bell factor is also given. For the qubit-qutrit composite system a time-dependent convex combination of the density matrix of the eigenstates of a two-particle Hamiltonian system is used to determine periodic maximal violations of the Bell's inequality.

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arXiv2023

Continuous monitoring for noisy intermediate-scale quantum processors

We present a continuous monitoring system for intermediate-scale quantum processors that allows extracting estimates of noisy native gate and read-out measurements based on the set of executed quantum circuits and resulting measurement outcomes. In contrast to standard approaches for calibration and benchmarking quantum processors, the executed circuits, which are input to the monitoring system, are assumed to be out of any control. We provide the results of applying our system to the synthetically generated data obtained from a quantum emulator, as well as to the experimental data collected from a publicly accessible cloud-based quantum processor. In the both cases, we demonstrate that the developed approach provides valuable results about inherent noises of emulators/processors. Considering that our approach uses only already accessible data from implemented circuits without the need to run additional algorithms, the monitoring system can complement existing approaches. We expect that our monitoring system can become a useful tool for various quantum computers in the near-term horizon, including publicly accessible cloud-based platforms, and reduce resources that are required for their benchmarking and calibration.

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arXiv2017

New entropic inequalities for qubit and unimodal Gaussian states

The Tsallis relative entropy $S_q (\hatρ,\hatσ)$ measures the distance between two arbitrary density matrices $\hatρ$ and $\hatσ$. In this work the approximation to this quantity when $q=1+δ$ ($δ\ll 1$) is obtained. It is shown that the resulting series is equal to the von Neumann relative entropy when $δ=0$. Analyzing the von Neumann relative entropy for arbitrary $\hatρ$ and a thermal equilibrium state $\hatσ=e^{- β\hat{H}}/{\rm Tr}(e^{- β\hat{H}})$ is possible to define a new inequality relating the energy, the entropy, and the partition function of the system. From this inequality, a parameter that measures the distance between the two states is defined. This distance is calculated for a general qubit system and for an arbitrary unimodal Gaussian state. In the qubit case, the dependence on the purity of the system is studied for $T \geq 0$ and also for $T<0$. In the Gaussian case, the general partition function given a unimodal quadratic Hamiltonian is calculated and the comparison of the thermal light state as a thermal equilibrium state of the parametric amplifier is presented.

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