arXiv subjects

D. Goyeneche

Publications and source records attributed to D. Goyeneche.

15 recordsLinked to original sources

arXiv2026

Pulse-level control for quantum resource preparation

Minimizing the time required for quantum state preparation is crucial to mitigate decoherence and enable practical quantum algorithms on near-term hardware. In this work, we introduce a technique for quantum state preparation in transmon-qubit systems using optimized electromagnetic pulse sequences rather than discrete quantum gates. By directly targeting quantum correlations instead of specific target states, we identify minimal-time pulse protocols that optimize relevant entanglement resources, such as concurrence and the three-tangle for two and three qubit systems, respectively. For the figures of merit considered, this approach successfully achieves maximal entanglement in each case: Bell, GHZ and W like states. Beyond state preparation, the resource-oriented nature of the approach leads to a reduced effective expressivity of the control scheme, a feature that represents an advantage in algorithmic settings where excessive control freedom is known to hinder performance.

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arXiv2022

Mutually unbiased frames

In this work, the concept of mutually unbiased frames is introduced as the most general notion of unbiasedness for sets composed by linearly independent and normalized vectors. It encompasses the already existing notions of unbiasedness for orthonormal bases, regular simplices, equiangular tight frames, positive operator valued measure, and also includes symmetric informationally complete quantum measurements. After introducing the tool, its power is shown by finding the following results about the last mentioned class of constellations: (i) real fiducial states do not exist in any even dimension, and (ii) unknown $d$-dimensional fiducial states are parameterized, a priori, with roughly $3d/2$ real variables only, without loss of generality. Furthermore, multi-parametric families of pure quantum states having minimum uncertainty with regard to several choices of $d+1$ orthonormal bases are shown, in every dimension $d$. These last families contain all existing fiducial states in every finite dimension, and the bases include maximal sets of $d+1$ mutually unbiased bases, when $d$ is a prime number.

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arXiv2021

Optimal strategy to certify quantum nonlocality

Certification of quantum nonlocality plays a central role in practical applications like device-independent quantum cryptography and random number generation protocols. These applications entail the challenging problem of certifying quantum nonlocality, something that is hard to achieve when the target quantum state is weakly entangled, or when the source of errors is high, e.g. when photons propagate through the atmosphere or a long optical fiber. Here, we introduce a technique to find a Bell inequality with the largest possible gap between the quantum prediction and the classical local hidden variable limit for a given set of measurement frequencies. Our method represents an efficient strategy to certify quantum nonlocal correlations from experimental data without requiring extra measurements, in the sense that there is no Bell inequality with a larger gap than the one provided. Furthermore, we also reduce the photodetector efficiency required to close the detection loophole. We illustrate our technique by improving the detection of quantum nonlocality from experimental data obtained with weakly entangled photons.

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arXiv2017

Quantum measurements with prescribed symmetry

We introduce a method to determine whether a given generalised quantum measurement is isolated or it belongs to a family of measurements having the same prescribed symmetry. The technique proposed reduces to solving a linear system of equations in some relevant cases. As consequence, we provide a simple derivation of the maximal family of Symmetric Informationally Complete measurements (SIC)-POVM in dimension 3. Furthermore, we show that the following remarkable geometrical structures are isolated, so that free parameters cannot be introduced: (a) maximal sets of mutually unbiased bases in prime power dimensions from 4 to 16, (b) SIC-POVM in dimensions from 4 to 16 and (c) contextuality Kochen-Specker sets in dimension 3, 4 and 6, composed of 13, 18 and 21 vectors, respectively.

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arXiv2016

Multipartite entanglement in heterogeneous systems

Heterogeneous bipartite quantum pure states, composed of two subsystems with a different number of levels, cannot have both reductions maximally mixed. In this work, we demonstrate existence of a wide range of highly entangled states of heterogeneous multipartite systems consisting of $N>2$ parties such that every reduction to one and two parties is maximally mixed. Two constructions of generating genuinely multipartite maximally entangled states of heterogeneous systems for an arbitrary number of subsystems are presented. Such states are related to quantum error correction codes over mixed alphabets and mixed orthogonal arrays. Additionally, we show the advantages of considering heterogeneous systems in practical implementations of multipartite steering.

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arXiv2015

Five measurement bases determine pure quantum states on any dimension

A long standing problem in quantum mechanics is the minimum number of observables required for the characterisation of unknown pure quantum states. The solution to this problem is specially important for the developing field of high-dimensional quantum information processing. In this work we demonstrate that any pure d-dimensional state is unambiguously reconstructed by measuring 5 observables, that is, via projective measurements onto the states of 5 orthonormal bases. Thus, in our method the total number of different measurement outcomes (5d) scales linearly with d. The state reconstruction is robust against experimental errors and requires simple post-processing, regardless of d. We experimentally demonstrate the feasibility of our scheme through the reconstruction of 8-dimensional quantum states, encoded in the momentum of single photons.

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arXiv2014

Quantum tomography meets dynamical systems and bifurcations theory

A powerful tool for studying geometrical problems in Hilbert space is developed. In particular, we study the quantum pure state tomography problem in finite dimensions from the point of view of dynamical systems and bifurcations theory. First, we introduce a generalization of the Hellinger metric for probability distributions which allows us to find a geometrical interpretation of the quantum state tomography problem. Thereafter, we prove that every solution to the state tomography problem is an attractive fixed point of the so-called physical imposition operator. Additionally, we demonstrate that multiple states corresponding to the same experimental data are associated to bifurcations of this operator. Such a kind of bifurcations only occurs when informationally incomplete set of observables are considered. Finally, we prove that the physical imposition operator has a non-contractive Lipschitz constant 2 for the Bures metric. This value of the Lipschitz constant manifests the existence of the quantum tomography problem for pure states.

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arXiv2013

Quantum state reconstruction from dynamical systems theory

When an informationally incomplete set of observables is considered there are several solutions to the quantum state reconstruction problem using von Neumann measurements. The set of solutions are known as Pauli partners, which are not easy to find even numerically. We present, in a self-contained paper, a new way to find this solutions using the physical imposition operator. We show that every Pauli partner is an attractive fixed point of this operator, which means that we can find complete sets of Pauli partners very efficiently. As a particular case, we found numerically 24 mutually unbiased bases in dimension N=23 in less than 30 seconds in a standard PC. We hope that the algorithm presented can be adapted to construct MU Constellations, SIC-POVMs, Equiangular Tight Frames and Quantum t-Designs, which could open new possibilities to find numerical solutions to these open problems related with quantum information theory.

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arXiv2013

A new method to construct families of complex Hadamard matrices in even dimensions

We present a new method for constructing affine families of complex Hadamard matrices in every even dimension. This method has an intersection with the Diţă construction and it generalizes the Szöllősi's method. We reproduce well-known results, extend some families and present new families of complex Hadamard matrices in even dimensions. In particular, found more than 13 millon inequivalent affine families of complex Hadamard matrices in dimension 32. We also find analytical restrictions for any set of four mutually unbiased bases existing in dimension six.

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arXiv2013

Characterization of fiducial states in prime dimensions via mutually unbiased bases

In this work we present some new properties of fiducial states in prime dimensions. We parameterize fiducial operators on eigenvectors bases of displacement operators, which allows us to find a manifold $Ω$ of hermitian operators satisfying $\mathrm{Tr}(ρ)=\mathrm{Tr}(ρ^2)=1$ for any $ρ$ in $Ω$. This manifold contains the complete set of fiducial pure states in every prime dimension. Indeed, any quantum state $ρ\geq0$ belonging to $Ω$ is a fiducial pure state. Also, we present an upper bound for every probability associated to mutually unbiased decomposition of fiducial states. This bound allows us to prove that every fiducial state tends to be mutually unbiased to the maximal set of mutually unbiased bases in higher prime dimensions. Finally, we show that any $ρ$ in $Ω$ minimizes an entropic uncertainty principle related to the second order Rényi entropy.

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arXiv2013

Mutually unbiased triplets from non-affine families of complex Hadamard matrices in dimension six

We study the problem of constructing mutually unbiased bases in dimension six. This approach is based on an efficient numerical method designed to find solutions to the quantum state reconstruction problem in finite dimensions. Our technique suggests the existence of previously unknown symmetries in Karlsson's non-affine family $K_6^{(2)}$ which we confirm analytically. Also, we obtain strong evidence that no more than three mutually unbiased bases can be constructed from pairs which contain members of some non-affine families of complex Hadamard matrices.

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arXiv2010

Coherent states for free particles

The coherent states are reviewed with particular application to the free particle system. The didactic advantages of the formalism is emphasized. Several interesting features, like the relation of the coherent states with the Galilei group and with the Husimi distribution are presented. Keywords: quantum mechanics, coherent states, free particle.

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arXiv2010

Entanglement for all quantum states

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.

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arXiv2003

Quantum diffusion on a cyclic one dimensional lattice

The quantum diffusion of a particle in an initially localized state on a cyclic lattice with N sites is studied. Diffusion and reconstruction time are calculated. Strong differences are found for even or odd number of sites and the limit N->infinit is studied. The predictions of the model could be tested with micro - and nanotechnology devices.

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arXiv2002

Quantum mechanics in finite dimensional Hilbert space

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.

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