arXiv subjects

Jonas Maziero

Publications and source records attributed to Jonas Maziero.

At least 73 records · Page 4Linked to original sources

arXiv2020

Complete complementarity relations for multipartite pure states

Complementarity relations for wave-particle duality are saturated only for pure, single-quanton, quantum states. For a completely incoherent state, it is known that wave and particle quantifiers can reach zero, and hence no information about the wave and particle aspects of the system can be obtained. This means that the information is being shared with another systems, and quantum correlations can be seen as responsible for the loss of purity of the quanton, provided that the quanton is part of a multipartite pure quantum system. In this paper, by exploring the purity of bi- and tri-partite pure quantum states, we show that it is possible to obtain complete complementarity relations. This procedure allows us to create a general framework for obtaining complete complementarity relations for a subsystem that belongs to an arbitrary multi-partite quantum system in a pure state. Besides, by some simple examples, we show that if the predictability measure is changed then the correlation measure must also be changed in order to obtain complete complementarity relations for pure cases.

quant-ph↗

arXiv2020

Monogamy and trade-off relations for correlated quantum coherence

One of the fundamental differences between classical and quantum mechanics is in the ways correlations can be distributed among the many parties that compose a system. While classical correlations can be shared among many subsystems, in general quantum correlations cannot be freely shared. This unique property is known as monogamy of quantum correlations. In this work, we study the monogamy properties of the correlated coherence for the l 1 -norm and relative entropy measures of coherence. For the l 1 -norm the correlated coherence is monogamous for a particular class of quantum states. For the relative entropy of coherence, and using maximally mixed state as the reference incoherent state, we show that the correlated coherence is monogamous for tripartite pure quantum systems.

quant-ph↗

arXiv2020

Quantitative wave-particle duality relations from the density matrix properties

We derive upper bounds for Hilbert-Schmidt's quantum coherence of general states of a $d$-level quantum system, a qudit, in terms of its incoherent uncertainty, with the latter quantified using the linear and von Neumann's entropies of the corresponding closest incoherent state. Similar bounds are obtained for Wigner-Yanase's coherence. The reported inequalities are also given as coherence-populations trade-off relations. As an application example of these inequalities, we derive quantitative wave-particle duality relations for multi-slit interferometry. Our framework leads to the identification of predictability measures complementary to Hilbert-Schmidt's, Wigner-Yanase's, and $l_{1}$-norm quantum coherences. The quantifiers reported here for the wave and particle aspects of a quanton follow directly from the defining properties of the quantum density matrix (i.e., semi-positivity and unit trace), contrasting thus with most related results from the literature.

quant-ph↗

arXiv2019

Preparing tunable Bell-diagonal states on a quantum computer

The class of two-qubit Bell-diagonal states has been the workhorse for developing understanding about the geometry, dynamics, and applications of quantum resources. In this article, we present a quantum circuit for preparing Bell-diagonal states on a quantum computer in a tunable way. We implement this quantum circuit using the IBM Q 5 Yorktown quantum computer and, as an application example, we measure the non-local, steering, entanglement, and discord quantum correlations and non-local quantum coherence of Werner states.

quant-ph↗

arXiv2018

Gradient target propagation

We report a learning rule for neural networks that computes how much each neuron should contribute to minimize a giving cost function via the estimation of its target value. By theoretical analysis, we show that this learning rule contains backpropagation, Hebian learning, and additional terms. We also give a general technique for weights initialization. Our results are at least as good as those obtained with backpropagation. The neural networks are trained and tested in three problems: MNIST, MNIST-Fashion, and CIFAR-10 datasets. The associated code is available at https://github.com/tiago939/target.

cs.LG↗

arXiv2018

Entanglement production by the magnetic dipolar interaction dynamics

We consider two qubits prepared in a product state and evolved under the magnetic dipolar interaction (MDI). We describe the dependence of the entanglement generated by the MDI with time, with the interaction parameters, and with the system's initial state, identifying the symmetry and coherence aspects of those initial configurations that yield the maximal entanglement. We also show how one can obtain maximum entanglement from the MDI applied to some families of partially entangled initial states.

quant-ph↗

arXiv2017

Hilbert-Schmidt quantum coherence in multi-qudit systems

Using Bloch's parametrization for qudits ($d$-level quantum systems), we write the Hilbert-Schmidt distance (HSD) between two generic $n$-qudit states as an Euclidean distance between two vectors of observables mean values in $\mathbb{R}^{Π_{s=1}^{n}d_{s}^{2}-1}$, where $d_{s}$ is the dimension for qudit $s$. Then, applying the generalized Gell Mann's matrices to generate $SU(d_{s})$, we use that result to obtain the Hilbert-Schmidt quantum coherence (HSC) of $n$-qudit systems. As examples, we consider in details one-qubit, one-qutrit, two-qubit, and two copies of one-qubit states. In this last case, the possibility for controlling local and non-local coherences by tuning local populations is studied and the contrasting behaviors of HSC, $l_{1}$-norm coherence, and relative entropy of coherence in this regard are noticed. We also investigate the decoherent dynamics of these coherence functions under the action of qutrit dephasing and dissipation channels. At last, we analyze the non-monotonicity of HSD under tensor products and report the first instance of a consequence (for coherence quantification) of this kind of property of a quantum distance measure.

quant-ph↗

arXiv2017

The sudden change phenomenon of quantum discord

Even if the parameters determining a system's state are varied smoothly, the behavior of quantum correlations alike to quantum discord, and of its classical counterparts, can be very peculiar, with the appearance of non-analyticities in its rate of change. Here we review this sudden change phenomenon (SCP) discussing some important points related to it: Its uncovering, interpretations, and experimental verifications, its use in the context of the emergence of the pointer basis in a quantum measurement process, its appearance and universality under Markovian and non-Markovian dynamics, its theoretical and experimental investigation in some other physical scenarios, and the related phenomenon of double sudden change of trace distance discord. Several open questions are identified, and we envisage that in answering them we will gain significant further insight about the relation between the SCP and the symmetry-geometric aspects of the quantum state space.

quant-ph↗

arXiv2017

The Maccone-Pati uncertainty relation

The existence of incompatible observables constitutes one of the most prominent characteristics of quantum mechanics (QM) and can be revealed and formalized through uncertainty relations. The Heisenberg-Robertson-Schrödinger uncertainty relation (HRSUR) was proved at the dawn of quantum formalism and is ever-present in the teaching and research on QM. Notwithstanding, the HRSUR possess the so called triviality problem. That is to say, the HRSUR yields no information about the possible incompatibility between two observables if the system was prepared in a state which is an eigenvector of one of them. After about 85 years of existence of the HRSUR, this problem was solved recently by Lorenzo Maccone and Arun K. Pati. In this article, we start doing a brief discussion of general aspects of the uncertainty principle in QM and recapitulating the proof of HRSUR. Afterwards we present in simple terms the proof of the Maccone-Pati uncertainty relation, which can be obtained basically via the application of the parallelogram law and Cauchy-Schwarz inequality.

quant-ph↗

arXiv2017

Direct-dynamical entanglement-discord relations

In this article, by considering Bell-diagonal two-qubit initial states submitted to local dynamics generated by the phase damping, bit flip, phase flip, bit-phase flip, and depolarizing channels, we report some elegant direct-dynamical relations between geometric measures of entanglement and discord. The complex scenario appearing already in this simplified case study indicates that similarly simple relation shall hardly be found in more general situations.

quant-ph↗

arXiv2017

Environment-induced quantum coherence spreading of a qubit

We make a thorough study of the spreading of quantum coherence (QC), as quantified by the $l_{1}$-norm QC, when a qubit (a two-level quantum system) is subjected to noise quantum channels commonly appearing in quantum information science. We notice that QC is generally not conserved and that even incoherent initial states can lead to transitory system-environment QC. We show that for the amplitude damping channel the evolved total QC can be written as the sum of local and non-local parts, with the last one being equal to entanglement. On the other hand, for the phase damping channel (PDC) entanglement does not account for all non-local QC, with the gap between them depending on time and also on the qubit's initial state. Besides these issues, the possibility and conditions for time invariance of QC are regarded in the case of bit, phase, and bit-phase flip channels. Here we reveal the qualitative dynamical inequivalence between these channels and the PDC and show that the creation of system-environment entanglement does not necessarily imply in the destruction of the qubit's QC. We also investigate the resources needed for non-local QC creation, showing that while the PDC requires initial coherence of the qubit, for some other channels non-zero population of the excited state (i.e., energy) is sufficient. Related to that, considering the depolarizing channel we notice the qubit's ability to act as a catalyst for the creation of joint QC and entanglement, without need for nonzero initial QC or excited state population.

quant-ph↗

arXiv2016

Computing partial transposes and related entanglement functions

The partial transpose (PT) is an important function for entanglement testing and quantification and also for the study of geometrical aspects of the quantum state space. In this article, considering general bipartite and multipartite discrete systems, explicit formulas ready for the numerical implementation of the PT and of related entanglement functions are presented and the Fortran code produced for that purpose is described. What is more, we obtain an analytical expression for the Hilbert-Schmidt entanglement of two-qudit systems and for the associated closest separable state. In contrast to previous works on this matter, we only use the properties of the PT, not applying Lagrange multipliers.

quant-ph↗

arXiv2016

Computing partial traces and reduced density matrices

Taking partial traces for computing reduced density matrices, or related functions, is a ubiquitous procedure in the quantum mechanics of composite systems. In this article, we present a thorough description of this function and analyze the number of elementary operations (ops) needed, under some possible alternative implementations, to compute it on a classical computer. As we notice, it is worthwhile doing some analytical developments in order to avoid making null multiplications and sums, what can considerably reduce the ops. For instance, for a bipartite system $\mathcal{H}_{a}\otimes\mathcal{H}_{b}$ with dimensions $d_{a}=\dim\mathcal{H}_{a}$ and $d_{b}=\dim\mathcal{H}_{b}$ and for $d_{a},d_{b}\gg1$, while a direct use of partial trace definition applied to $\mathcal{H}_{b}$ requires $\mathcal{O}(d_{a}^{6}d_{b}^{6})$ ops, its optimized implementation entails $\mathcal{O}(d_{a}^{2}d_{b})$ ops. In the sequence, we regard the computation of partial traces for general multipartite systems and describe Fortran code provided to implement it numerically. We also consider the calculation of reduced density matrices via Bloch's parametrization with generalized Gell Mann's matrices.

quant-ph↗

arXiv2016

Computing coherence vectors and correlation matrices, with application to quantum discord quantification

Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a reasonable option. Notwithstanding, as we demonstrate in this article, some algebraic manipulations before programming can reduce considerably their computational complexity. Besides, we provide Fortran code to generate generalized Gell Mann matrices and to compute the optimized and unoptimized versions of the associated Bloch's vectors and correlation matrix, in the case of bipartite quantum systems. As a code test and application example, we consider the calculation of Hilbert-Schmidt quantum discords.

quant-ph↗

arXiv2016

Quantum correlated cluster mean-field theory applied to the transverse Ising model

Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there have been an urge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2016

The Kraus representation for the dynamics of open quantum systems

The necessity and utility of considering the interaction of a quantum system with its environment when describing its time evolution have been recognized in several branches of physics and of other sciences. The Kraus' representation is a general and succinct approach to describe such open system dynamics in a wide range of relevant physical scenarios. In this article, by abdicating from the generality of the formalism of quantum operations and with this avoiding its associated complications, we show in a simple manner how we can obtain the Kraus' representation using basically the closed system (system plus environment) unitary dynamics and the partial trace function. The example of a two-level atom interacting with the vacuum of the electromagnetic field is regarded for the sake of instantiating this formalism, which is then applied to study the time evolution of the atom's quantum coherence.

quant-ph↗

arXiv2016

Fortran code for generating random probability vectors, unitaries, and quantum states

The usefulness of generating random configurations is recognized in many areas of knowledge. Fortran was born for scientific computing and has been one of the main programming languages in this area since then. And several ongoing projects targeting towards its betterment indicate that it will keep this status in the decades to come. In this article, we describe Fortran codes produced, or organized, for the generation of the following random objects: numbers, probability vectors, unitary matrices, and quantum state vectors and density matrices. Some matrix functions are also included and may be of independent interest.

quant-ph↗

arXiv2015

Random Sampling of Quantum States: A Survey of Methods

The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here we review some methods that may be used for performing that task. We start by presenting a simple procedure for generating random state vectors, for which the main tool is the random sampling of unbiased discrete probability distributions (DPD). Afterwards the creation of random density matrices is addressed. In this context we first present the standard method, which consists in using the spectral decomposition of a quantum state for getting RQS from random DPDs and random unitary matrices. In the sequence the Bloch vector parametrization method is described. This approach, despite being useful in several instances, is not in general convenient for RQS generation. In the last part of the article we regard the overparametrized method (OPM) and the related Ginibre and Bures techniques. The OPM can be used to create random positive semidefinite matrices with unit trace from randomly produced general complex matrices in a simple way that is friendly for numerical implementations. We consider a physically relevant issue related to the possible domains that may be used for the real and imaginary parts of the elements of such general complex matrices. Subsequently a too fast concentration of measure in the quantum state space that appears in this parametrization is noticed.

quant-ph↗