arXiv subjects

Marco Enriquez

Publications and source records attributed to Marco Enriquez.

10 recordsLinked to original sources

arXiv2026

Entanglement Generation through Coherent and Non-Coherent Control

The controlled generation of quantum entanglement from separable states remains a central challenge in quantum information science. Here, we investigate entanglement generation using two related control paradigms: coherent path superposition of local unitary operations and stochastic implementations of Pauli channels under coherent control. We show that entangled states belonging to the Bell, GHZ and W classes, can be deterministically generated from fully separable inputs by coherently superposing alternative sets of local unitary transformations. Conditions on the local operators for entanglement generation are derived, and the resulting states are shown to be locally unitary equivalent to standard multipartite entangled states. We further extend the analysis to noisy scenarios, where separable mixed states evolve through pairs of Pauli channels arranged in path-superposition and indefinite causal order configurations. Closed-form expressions for the output states are obtained, and entanglement is quantified using concurrence. By exploring representative channel families across their parameter space, we identify regimes where stochastic entanglement emerges, determine the associated success probabilities, and characterize trade-offs between entanglement and purity.

quant-ph↗

arXiv2024

A geometric formulation to measure global and genuine entanglement in three-qubit systems

We introduce a purely geometric formulation for two different measures addressed to quantify the entanglement between different parts of a tripartite qubit system. Our approach considers the entanglement-polytope defined by the smallest eigenvalues of the reduced density matrices of the qubit-components. The measures identify global and genuine entanglement, and are respectively associated with the projection and rejection of a given point of the polytope on the corresponding biseparable segments. Solving the so called `inverse problem', we also discuss a way to force the system to behave in a particular form, which opens the possibility of controlling and manipulating entanglement for practical purposes.

quant-ph↗

arXiv2021

Multifold behavior of the information transmission by the quantum 3-switch

We uncover new behaviors of the transmission of information by three quantum channels in superposition of causal orders subject to some level of noise. We find that the transmission can exhibit three different behaviors as the level of noise is varied. This multifold behavior can be explained by the different equivalence classes of quantum switch matrices related to specific combinations of causal orders. We classify these matrices using their characteristic polynomials and matrix invariants, and we calculate analytical expressions for the Holevo information in three representative cases. Our results are a step forward to understand and harness quantum control of causal orders with different levels of noise. We also study the Holevo information as function of a continuous order parameter and analyse transitions at integer values.

quant-ph↗

arXiv2019

Communication Enhancement Through Quantum Coherent Control of $N$ Channels in an Indefinite Causal-order Scenario

In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e. using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number $N$ of channels with arbitrary individual capacity i.e. information preservation characteristics in the case of indefinite causal order. We propose a formalism to assess information transmission in the most general case of $N$ channels in an indefinite causal order scenario yielding the output of such transmission. Then we explicitly derive the quantum switch output and the associated Holevo limit of the information transmission for $N=2$, $N=3$ as a function of all involved parameters. We find in the case $N=3$ that the transmission of information for three channels is twice of transmission of the two channel case when a full superposition of all possible causal orders is used.

quant-ph↗

arXiv2019

Sending classical information via three noisy channels in superposition of causal orders

In this work, we study the transmission of classical information through three completely depolarizing channels in superposition of different causal orders. We thus introduce the quantum 3-switch as a resource for quantum communications. We perform a new kind of quantum control that was not accessible to the previously treated two-channel case. The fine and full quantum control achieved using selected combinations of causal orders let us uncover new features: non monotonous behavior on the transmission of information with respect to the number of causal orders involved, and different values of the transmission of information depending on the specific combinations of causal orders considered. Our results are a stepping stone to assess efficiency of coherent quantum control and optimize resources in the implementation of new indefinite causal structures. Finally, we suggest an optical implementation using standard telecom technology to test our predictions.

quant-ph↗

arXiv2018

Entanglement of three-qubit random pure states

We study non-local properties of generic three-qubit pure states. First, we obtain the distributions of both the coefficients and the only phase in the five-term decomposition of Acín et al. for an ensemble of random pure states generated by the Haar measure on U(8). Furthermore, we analyze the probability distributions of two sets of polynomial invariants. One of these sets allows us to classify three-qubit pure states into four classes. Entanglement in each class is characterized using the minimal Rényi-Ingarden-Urbanik entropy. Besides, the fidelity of a three-qubit random state with the closest state in each entanglement class is investigated. We also present a characterization of these classes and the SLOCC classes in terms of the corresponding entanglement polytope.

quant-ph↗

arXiv2017

Exactly solvable one-qubit driving fields generated via non-linear equations

Using the Hubbard representation for $SU(2)$ we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of non-linear coupled equations. In order to find exact solutions, we use an inverse approach and find families of time-dependent Hamiltonians whose off-diagonal elements are connected with the Ermakov equation. The physical meaning of the so-obtained Hamiltonians is discussed in the context of the nuclear magnetic resonance phenomenon

quant-ph↗

arXiv2016

SU(1,1) and SU(2) Approaches to the Radial Oscillator: Generalized Coherent States and Squeezing of Variances

It is shown that each one of the Lie algebras su(1,1) and su(2) determine the spectrum of the radial oscillator. States that share the same orbital angular momentum are used to construct the representation spaces of the non-compact Lie group SU(1,1). In addition, three different forms of obtaining the representation spaces of the compact Lie group SU(2) are introduced, they are based on the accidental degeneracies associated with the spherical symmetry of the system as well as on the selection rules that govern the transitions between different energy levels. In all cases the corresponding generalized coherent states are constructed and the conditions to squeeze the involved quadratures are analyzed.

quant-ph↗

arXiv2015

Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states

We study the entanglement of a pure state of a composite quantum system consisting of several subsystems with $d$ levels each. It can be described by the Rényi-Ingarden-Urbanik entropy $S_q$ of a decomposition of the state in a product basis, minimized over all local unitary transformations. In the case $q=0$ this quantity becomes a function of the rank of the tensor representing the state, while in the limit $q \to \infty$ the entropy becomes related to the overlap with the closest separable state and the geometric measure of entanglement. For any bipartite system the entropy $S_1$ coincides with the standard entanglement entropy. We analyze the distribution of the minimal entropy for random states of three and four-qubit systems. In the former case the distributions of $3$-tangle is studied and some of its moments are evaluated, while in the latter case we analyze the distribution of the hyperdeterminant. The behavior of the maximum overlap of a three-qudit system with the closest separable state is also investigated in the asymptotic limit.

quant-ph↗

arXiv2013

Kronecker product in terms of Hubbard operators and the Clebsch-Gordan decomposition of SU(2)xSU(2)

We review the properties of the Kronecker (direct, or tensor) product of square matrices $A \otimes B \otimes C \cdots$ in terms of Hubbard operators. In its simplest form, a Hubbard operator $X_n^{i,j}$ can be expressed as the $n$-square matrix which has entry 1 in position $(i,j)$ and zero in all other entries. The algebra and group properties of the observables that define a multipartite quantum system are notably straightforward in such a framework. In particular, we use the Kronecker product in Hubbard notation to get the Clebsch-Gordan decomposition of the product group $SU(2) \times SU(2)$. Finally, the $n$-dimensional irreducible representations so obtained are used to derive closed forms of the Clebsch-Gordan coefficients that rule the addition of angular momenta. Our results can be further developed in many different directions.

math-ph↗