Using the relative entropy of total correlation, we derive an expression relating the mutual info... more Using the relative entropy of total correlation, we derive an expression relating the mutual information of n-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications. Besides, by utilizing the extended strong subadditivity of von Neumann entropy, we obtain generalized monogamy relations for the total correlation in three-partite mixed states. These inequalities lead to a tight lower bound for this correlation in terms of the sum of the bipartite mutual informations. We use this bound to propose a measure for residual three-partite total correlation and discuss the non-applicability of this kind of quantifier to measure genuine multiparty correlations.
We investigate pairwise quantum correlation as measured by the quantum discord as well as its cla... more We investigate pairwise quantum correlation as measured by the quantum discord as well as its classical counterpart in the thermodynamic limit of anisotropic XY spin-1/2 chains in a transverse magnetic field for both zero and finite temperatures. Analytical expressions for both classical and quantum correlations are obtained for spin pairs at any distance. In the case of zero temperature, it is shown that the quantum discord for spin pairs farther than second-neighbors is able to characterize a quantum phase transition, even though pairwise entanglement is absent for such distances. For finite temperatures, we show that quantum correlations can be increased with temperature in the presence of a magnetic field. Moreover, in the XX limit, the thermal quantum discord is found to be dominant over classical correlation while the opposite scenario takes place for the transverse field Ising model limit.
We consider two qubits prepared in a product state and evolved under the magnetic dipolar interac... more 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.
In Ref. [Phys. Rev. A 100, 062317 (2019)], the authors reported an algorithm to implement, in a c... more In Ref. [Phys. Rev. A 100, 062317 (2019)], the authors reported an algorithm to implement, in a circuit-based quantum computer, a general quantum measurement (GQM) of a two-level quantum system, a qubit. Even though their algorithm seems right, its application involves the solution of an intricate non-linear system of equations in order to obtain the angles determining the quantum circuit to be implemented for the simulation. In this article, we identify and discuss a simple way to circumvent this issue and implement GQMs on any d-level quantum system through quantum state preparation algorithms. Using some examples for one qubit, one qutrit and two qubits, we illustrate the easy of application of our protocol. Besides, we show how one can utilize our protocol for simulating quantum instruments, for which we also give an example. All our examples are demonstrated using IBM's quantum processors.
With the rapid development of quantum computers, several applications are being proposed for them... more With the rapid development of quantum computers, several applications are being proposed for them. Quantum simulations, simulation of chemical reactions, solution of optimization problems and quantum neural networks (QNNs) are some examples. However, problems such as noise, limited number of qubits and circuit depth, and gradient vanishing must be resolved before we can use them to their full potential. In the field of quantum machine learning, several models have been proposed. In general, in order to train these different models, we use the gradient of a cost function with respect to the model parameters. In order to obtain this gradient, we must compute the derivative of this function with respect to the model parameters. One of the most used methods in the literature to perform this task is the parameter-shift rule method. This method consists of evaluating the cost function twice for each parameter of the QNN. A problem with this method is that the number of evaluations grows linearly with the number of parameters. In this work we study an alternative method, called Evolution Strategies (ES), which are a family of black box optimization algorithms which iteratively update the parameters using a search gradient. An advantage of the ES method is that in using it one can control the number of times the cost function will be evaluated. We apply the ES method to the binary classification task, showing that this method is a viable alternative for training QNNs. However, we observe that its performance will be strongly dependent on the hyperparameters used. Furthermore, we also observe that this method, alike the parameter shift rule method, suffers from the problem of gradient vanishing.
Revista Brasileira de Ensino de Física, Jun 1, 2016
A representação de Kraus para a dinâmica de sistemas quânticos abertos (The Kraus representation ... more A representação de Kraus para a dinâmica de sistemas quânticos abertos (The Kraus representation for the dynamics of open quantum systems)
Coherence vectors and correlation matrices are important functions frequently used in physics. Th... more 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 paper, 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 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.
The trace distance (TD) possesses several of the good properties required for a faithful distance... more The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable features, its possible non-monotonicity under taking tensor products of its arguments (NMuTP), has been hitherto unexplored. In this article we advance analytical and numerical investigations of this issue considering different classes of states living in a discrete and finite dimensional Hilbert space. Our results reveal that although this property of TD does not shows up for pure states and for some particular classes of mixed states, it is present in a non-negligible fraction of the regarded density operators. Hence, even though the percentage of quartets of states leading to the NMuTP drawback of TD and its strength decrease as the system's dimension grows, this property of TD must be taken into account before using it as a figure of merit for distinguishing mixed quantum states.
The generation of pseudo-random discrete probability distributions is of paramount importance for... more The generation of pseudo-random discrete probability distributions is of paramount importance for a wide range of stochastic simulations spanning from Monte Carlo methods to the random sampling of quantum states for investigations in quantum information science. In spite of its significance, a thorough exposition of such a procedure is lacking in the literature. In this article we present relevant details concerning the numerical implementation and applicability of what we call the iid, normalization, and trigonometric methods for generating an unbiased probability vector p = (p 1 , • • • , p d). An immediate application of these results regarding the generation of pseudo-random pure quantum states is also described.
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed i... more 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.
We make a thorough study of the spreading of quantum coherence (QC), as quantified by the l1-norm... more We make a thorough study of the spreading of quantum coherence (QC), as quantified by the l1-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 bitphase 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.
In 1935, Einstein, Podolsky, and Rosen claimed the incompleteness of quantum mechanics by assumin... more In 1935, Einstein, Podolsky, and Rosen claimed the incompleteness of quantum mechanics by assuming that local actions cannot influence the elements of reality in a distant location. In this Letter, we show that Alice's local quantum operations can be correlated with the quantum reality of observables in the causally disconnected laboratory of Bob. We propose a modified optical quantum eraser experiment that can be implemented using current technology for verifying our theoretical predictions, without any need for retrodiction. We simulate such an experiment using IBM quantum computers.
We utilize IBM's quantum computers to perform a full quantum simulation of the optical quantum er... more We utilize IBM's quantum computers to perform a full quantum simulation of the optical quantum eraser (QE) utilizing a Mach-Zehnder interferometer with a variable partially-polarizing beam splitter (VPPBS) at the input. The use of the VPPBS motivates us to introduce the entangled quantum eraser, for which the path information is erased using a Bell-basis measurement. We also investigate the behavior of the wave aspect, i.e., the quantum coherence, as well as the particle character, represented by the predictability and entanglement, as delineated in complete complementarity relations (CCRs). As we show in this article, the utilization of the VPPBS uncover interesting aspects of the QE and CCRs. For instance, we can recover the full wave-behavior by the erasure procedure even when we have only partial knowledge about the path through entanglement.
Quantum discord (QD) reveals the nonclassical nature of correlations in bipartite quantum states,... more Quantum discord (QD) reveals the nonclassical nature of correlations in bipartite quantum states, going beyond the entanglement-separability paradigm. In this article we discuss the suitability of QD in what concern its possible asymmetry with relation to the bipartition we choose to compute it. We obtain an analytical formula for a symmetrized version of QD (SQD) in Bell-diagonal states. We observe that if correlation is regarded as a shared property, then the SQD could be a convenient quantifier for asymmetric states.
In Refs. [Phys. Rev. A 96, 062303 (2017)] and [Sci. China Phys. Mech. Astron. 61, 70311 (2018)], ... more In Refs. [Phys. Rev. A 96, 062303 (2017)] and [Sci. China Phys. Mech. Astron. 61, 70311 (2018)], the authors reported an algorithm to simulate, in a circuit-based quantum computer, a general quantum channel (QC). However, the application of their algorithm is limited because it entails the solution of intricate non-linear systems of equations in order to obtain the quantum circuit to be implemented for the simulation. Motivated by this issue, in this article we identify and discuss a simple way to implement the simulation of QCs on any d-level quantum system through quantum state preparation algorithms, that have received much attention in the quantum information science literature lately. We exemplify the versatility of our protocol applying it to most well known qubit QCs, to some qudit QCs, and to simulate the effect of Lorentz transformations on spin states. We also regard the application of our protocol for initial mixed states. Most of the given application examples are demonstrated using IBM's quantum computers.
The class of two-qubit Bell-diagonal states has been the workhorse for developing understanding a... more 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.
Using the relative entropy of total correlation, we derive an expression relating the mutual info... more Using the relative entropy of total correlation, we derive an expression relating the mutual information of n-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications. Besides, by utilizing the extended strong subadditivity of von Neumann entropy, we obtain generalized monogamy relations for the total correlation in three-partite mixed states. These inequalities lead to a tight lower bound for this correlation in terms of the sum of the bipartite mutual informations. We use this bound to propose a measure for residual three-partite total correlation and discuss the non-applicability of this kind of quantifier to measure genuine multiparty correlations.
We investigate pairwise quantum correlation as measured by the quantum discord as well as its cla... more We investigate pairwise quantum correlation as measured by the quantum discord as well as its classical counterpart in the thermodynamic limit of anisotropic XY spin-1/2 chains in a transverse magnetic field for both zero and finite temperatures. Analytical expressions for both classical and quantum correlations are obtained for spin pairs at any distance. In the case of zero temperature, it is shown that the quantum discord for spin pairs farther than second-neighbors is able to characterize a quantum phase transition, even though pairwise entanglement is absent for such distances. For finite temperatures, we show that quantum correlations can be increased with temperature in the presence of a magnetic field. Moreover, in the XX limit, the thermal quantum discord is found to be dominant over classical correlation while the opposite scenario takes place for the transverse field Ising model limit.
We consider two qubits prepared in a product state and evolved under the magnetic dipolar interac... more 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.
In Ref. [Phys. Rev. A 100, 062317 (2019)], the authors reported an algorithm to implement, in a c... more In Ref. [Phys. Rev. A 100, 062317 (2019)], the authors reported an algorithm to implement, in a circuit-based quantum computer, a general quantum measurement (GQM) of a two-level quantum system, a qubit. Even though their algorithm seems right, its application involves the solution of an intricate non-linear system of equations in order to obtain the angles determining the quantum circuit to be implemented for the simulation. In this article, we identify and discuss a simple way to circumvent this issue and implement GQMs on any d-level quantum system through quantum state preparation algorithms. Using some examples for one qubit, one qutrit and two qubits, we illustrate the easy of application of our protocol. Besides, we show how one can utilize our protocol for simulating quantum instruments, for which we also give an example. All our examples are demonstrated using IBM's quantum processors.
With the rapid development of quantum computers, several applications are being proposed for them... more With the rapid development of quantum computers, several applications are being proposed for them. Quantum simulations, simulation of chemical reactions, solution of optimization problems and quantum neural networks (QNNs) are some examples. However, problems such as noise, limited number of qubits and circuit depth, and gradient vanishing must be resolved before we can use them to their full potential. In the field of quantum machine learning, several models have been proposed. In general, in order to train these different models, we use the gradient of a cost function with respect to the model parameters. In order to obtain this gradient, we must compute the derivative of this function with respect to the model parameters. One of the most used methods in the literature to perform this task is the parameter-shift rule method. This method consists of evaluating the cost function twice for each parameter of the QNN. A problem with this method is that the number of evaluations grows linearly with the number of parameters. In this work we study an alternative method, called Evolution Strategies (ES), which are a family of black box optimization algorithms which iteratively update the parameters using a search gradient. An advantage of the ES method is that in using it one can control the number of times the cost function will be evaluated. We apply the ES method to the binary classification task, showing that this method is a viable alternative for training QNNs. However, we observe that its performance will be strongly dependent on the hyperparameters used. Furthermore, we also observe that this method, alike the parameter shift rule method, suffers from the problem of gradient vanishing.
Revista Brasileira de Ensino de Física, Jun 1, 2016
A representação de Kraus para a dinâmica de sistemas quânticos abertos (The Kraus representation ... more A representação de Kraus para a dinâmica de sistemas quânticos abertos (The Kraus representation for the dynamics of open quantum systems)
Coherence vectors and correlation matrices are important functions frequently used in physics. Th... more 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 paper, 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 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.
The trace distance (TD) possesses several of the good properties required for a faithful distance... more The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable features, its possible non-monotonicity under taking tensor products of its arguments (NMuTP), has been hitherto unexplored. In this article we advance analytical and numerical investigations of this issue considering different classes of states living in a discrete and finite dimensional Hilbert space. Our results reveal that although this property of TD does not shows up for pure states and for some particular classes of mixed states, it is present in a non-negligible fraction of the regarded density operators. Hence, even though the percentage of quartets of states leading to the NMuTP drawback of TD and its strength decrease as the system's dimension grows, this property of TD must be taken into account before using it as a figure of merit for distinguishing mixed quantum states.
The generation of pseudo-random discrete probability distributions is of paramount importance for... more The generation of pseudo-random discrete probability distributions is of paramount importance for a wide range of stochastic simulations spanning from Monte Carlo methods to the random sampling of quantum states for investigations in quantum information science. In spite of its significance, a thorough exposition of such a procedure is lacking in the literature. In this article we present relevant details concerning the numerical implementation and applicability of what we call the iid, normalization, and trigonometric methods for generating an unbiased probability vector p = (p 1 , • • • , p d). An immediate application of these results regarding the generation of pseudo-random pure quantum states is also described.
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed i... more 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.
We make a thorough study of the spreading of quantum coherence (QC), as quantified by the l1-norm... more We make a thorough study of the spreading of quantum coherence (QC), as quantified by the l1-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 bitphase 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.
In 1935, Einstein, Podolsky, and Rosen claimed the incompleteness of quantum mechanics by assumin... more In 1935, Einstein, Podolsky, and Rosen claimed the incompleteness of quantum mechanics by assuming that local actions cannot influence the elements of reality in a distant location. In this Letter, we show that Alice's local quantum operations can be correlated with the quantum reality of observables in the causally disconnected laboratory of Bob. We propose a modified optical quantum eraser experiment that can be implemented using current technology for verifying our theoretical predictions, without any need for retrodiction. We simulate such an experiment using IBM quantum computers.
We utilize IBM's quantum computers to perform a full quantum simulation of the optical quantum er... more We utilize IBM's quantum computers to perform a full quantum simulation of the optical quantum eraser (QE) utilizing a Mach-Zehnder interferometer with a variable partially-polarizing beam splitter (VPPBS) at the input. The use of the VPPBS motivates us to introduce the entangled quantum eraser, for which the path information is erased using a Bell-basis measurement. We also investigate the behavior of the wave aspect, i.e., the quantum coherence, as well as the particle character, represented by the predictability and entanglement, as delineated in complete complementarity relations (CCRs). As we show in this article, the utilization of the VPPBS uncover interesting aspects of the QE and CCRs. For instance, we can recover the full wave-behavior by the erasure procedure even when we have only partial knowledge about the path through entanglement.
Quantum discord (QD) reveals the nonclassical nature of correlations in bipartite quantum states,... more Quantum discord (QD) reveals the nonclassical nature of correlations in bipartite quantum states, going beyond the entanglement-separability paradigm. In this article we discuss the suitability of QD in what concern its possible asymmetry with relation to the bipartition we choose to compute it. We obtain an analytical formula for a symmetrized version of QD (SQD) in Bell-diagonal states. We observe that if correlation is regarded as a shared property, then the SQD could be a convenient quantifier for asymmetric states.
In Refs. [Phys. Rev. A 96, 062303 (2017)] and [Sci. China Phys. Mech. Astron. 61, 70311 (2018)], ... more In Refs. [Phys. Rev. A 96, 062303 (2017)] and [Sci. China Phys. Mech. Astron. 61, 70311 (2018)], the authors reported an algorithm to simulate, in a circuit-based quantum computer, a general quantum channel (QC). However, the application of their algorithm is limited because it entails the solution of intricate non-linear systems of equations in order to obtain the quantum circuit to be implemented for the simulation. Motivated by this issue, in this article we identify and discuss a simple way to implement the simulation of QCs on any d-level quantum system through quantum state preparation algorithms, that have received much attention in the quantum information science literature lately. We exemplify the versatility of our protocol applying it to most well known qubit QCs, to some qudit QCs, and to simulate the effect of Lorentz transformations on spin states. We also regard the application of our protocol for initial mixed states. Most of the given application examples are demonstrated using IBM's quantum computers.
The class of two-qubit Bell-diagonal states has been the workhorse for developing understanding a... more 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.
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Papers by Jonas Maziero