arXiv subjects

Marcos L. W. Basso

Publications and source records attributed to Marcos L. W. Basso.

36 records · Page 2Linked to original sources

arXiv2023

Quantum simulation of the generalized-entangled quantum eraser and the related complete complementarity relations

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.

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arXiv2022

Local predictability and coherence versus distributed entanglement in entanglement swapping from partially entangled pure states

Complete complementarity relations, as e.g. $P(ρ_{A})^{2} + C(ρ_{A})^{2} + E(|Ψ\rangle_{AB})^{2}=1$, constrain the local predictability, $P$, and local coherence, $C$, and the entanglement, $E$, of bipartite pure states. For pairs of qubits prepared initially in a particular class of partially entangled pure states with null local coherence, these relations were used in Ref. [Phys. Lett. A, 451, 128414 (2022)] to provide an operational connection between local predictability of the pre-measurement states with the probability of the maximally entangled components of the states after the Bell-basis measurement of the entanglement swapping protocol (ESP). In this article, we extend this result for general pure initial states establishing the relation between $P$, $C$ and the distributed entanglement in the ESP. We use IBM's quantum computers to verify experimentally some instances of these general theoretical results.

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arXiv2022

Operational connection between predictability and entanglement in entanglement swapping from partially entangled pure states

Complementarity and entanglement are fundamental features of Quantum Mechanics that were recently related in triality equalities that involve quantum coherence, the wave aspect of a qubit, and quantum predictability and quantum entanglement, the particle aspect of a qubit. In this article, we give an operational connection between redictability and entanglement in entanglement swapping from initially partially entangled states. For this, we show that the predictability of the pre-measurement one-qubit density matrix is directly related to the probability of the partially entangled component of the post-measurement state. Going even further, we analyze the entanglement swapping for partially entangled states in the light of complementarity relations and show that, in the cases where the entanglement increases after a Bell-basis measurement, the predictability is consumed when compared to the initially prepared state.

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arXiv2022

Entanglement Monotones from Complementarity Relations

Bohr's complementarity and Schrödinger's entanglement are two prominent physical characters of quantum systems. In this letter, we formally connect them. It is known that complementarity relations for wave-particle duality are saturated only for pure, single-quanton, quantum states. For mixed states, the wave-particle quantifiers never saturate a complementarity relation and can even reach zero for a maximally mixed state. To fully characterize a quanton, it is not enough to consider its wave-particle aspect; we have also to regard its quantum correlations with other systems. Here we prove that for any complete complementarity relation involving predictability and visibility measures that satisfy the criteria established in the literature, these corresponding quantum correlations are entanglement monotones.

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arXiv2022

Reality variation under monitoring with weak measurements

Recently, inspired by Einstein-Podolsky-Rosen's notion of elements of reality, Bilobran and Angelo gave a formal and operational characterization of (ir)reality [EPL 112, 40005 (2015)]. From this approach, the authors were able to define a measure of (ir)realism, or (in)definiteness, of an observable given a preparation of a quantum system. As well, in [Phys. Rev. A 97, 022107 (2018)], Dieguez and Angelo studied the variation of reality of observables by introducing a map, called monitoring, through weak projective non-revealed measurements. The authors showed that an arbitrary-intensity unrevealed measurement of a given observable $X$ generally increases its reality, also increasing the reality of its incompatible observables $X'$. However, from these results, natural questions arise: under the monitoring map of $X$, how much does the reality of $X'$ increase in comparison to that of $X$? Does it always increase? This is the kind of question we address in this article. Surprisingly, we show that it is possible that the variation of the reality of $X'$ is bigger than the variation of the reality of $X$. As well, the monitoring map of $X$ does not affect the already established reality of $X'$, even when they are maximally incompatible. On the other hand, there are circumstances where the variation of reality of both observables is the same, even when they are maximally incompatible. Besides, we give a quantum circuit to implement the monitoring map and use it to experimentally verify the variation of reality of observables using IBM's quantum computers.

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arXiv2022

Predictability as a quantum resource

Just recently, complementarity relations (CRs) have been derived from the basic rules of Quantum Mechanics. The complete CRs are equalities involving quantum coherence, $C$, quantum entanglement, and predictability, $P$. While the first two are already quantified in the resource theory framework, such a characterization lacks for the last. In this article, we start showing that, for a system prepared in a state $ρ$, $P$ of $ρ$, with reference to an observable $X$, is equal to $C$, with reference to observables mutually unbiased (MU) to $X$, of the state $Φ_{X}(ρ)$, which is obtained from a non-revealing von Neumann measurement (NRvNM) of $X$. We also show that $P^X(ρ)>C^{Y}(Φ_{X}(ρ))$ for observables not MU. Afterwards, we provide quantum circuits for implementing NRvNMs and use these circuits to experimentally test these (in)equalities using the IBM's quantum computers. Furthermore, we give a resource theory for predictability, identifying its free quantum states and free quantum operations and discussing some predictability monotones. Besides, after applying one of these predictability monotones to study bipartite systems, we discuss the relation among the resource theories of quantum coherence, predictability, and purity.

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arXiv2022

The Sagnac effect for spin-$1/2$ particles through local Wigner rotations

In this article, we study the Sagnac effect for spin-$1/2$ particles through local Wigner rotations according to the framework developed by [H. Terashima and M. Ueda, Phys. Rev. A 69, 032113 (2004)]. Since the spin of the particle plays the role of a quantum `clock', as the quanton moves in a superposed path it gets entangled with the momentum (or the path), and this will cause the interferometric visibility to drop, since there is a difference in proper time elapsed along the two trajectories, which is known as the Sagnac time delay.

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arXiv2021

Entanglement monotones connect distinguishability and predictability

Distinguishability and predictability are part of complementarity relations which apply to two different kinds of interference experiments, with and without a path-detector, respectively. In [Opt. Comm. 179, 337 (2000)], Englert and Bergou pointed out the possible connection between distinguishability, predictability, and entanglement. They even conjectured that an entanglement measure was hidden between the measures of distinguishability and predictability. Here, we push forward this conjecture. We start defining a new entropic distinguishability measure and suggesting an entanglement measure as the difference between this entropic distinguishability and an entropic predictability measure already defined in the literature. Besides, we prove that it is possible to define an entanglement monotone from the largest value of the distinguishability and the corresponding predictability, provided that the predictability satisfy the criteria already established in the literature. Thus, this result formally connects an entanglement monotone with distinguishability and the corresponding predictability, without appealing to specific measures.

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arXiv2021

Complete complementarity relations: Connections with EPR realism and decoherence and extension to mixed quantum states

Wave-particle duality is an essential character of quantum systems. In the last few years, much progress has being made towards formally quantifying these quantum features. The properties of the quantum density matrix were shown to lead to duality inequalities for single-quanton mixed states and to triality identities, also known as complete complementarity relations (CCRs), for two-quanton pure states. In this article, we establish connections between CCRs and EPR (ir)realism, as formalized by Bilobran and Angelo in [Europhys. Lett. 112, 40005 (2015)]. Besides, we show that, for tripartite pure states $|ψ_{ABE}\rangle$, CCRs can be applied to obtain the system-environment entanglement of formation, $E_{f}(ρ_{AE})$, through the local information of a system $A$ and its classical correlation with an auxiliary system $B$. Moreover, we discuss CCRs in the context of the emergence of the pointer basis in the decoherence process identified via the constancy of system-apparatus classical correlations. We also obtain CCRs for purified mixed bipartite quantum-classical states. In addition, we derive CCR for mixed-bipartite two-qudit quantum states and discuss its interpretations.

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arXiv2021

The Effect of Stationary Axisymmetric Spacetimes in Interferometric Visibility

In this manuscript, we consider a scenario in which a spin-1/2 quanton goes through a superposition of co-rotating and counter-rotating geodetic circular paths, which play the role of the paths of a Mach-Zehnder interferometer in a stationary and axisymmetric spacetime. Since the spin of the particle plays the role of a quantum clock, as the quanton moves in a superposed path it gets entangled with the momentum (or the path), and this will cause the interferometric visibility (or the internal quantum coherence) to drop, since, in stationary axisymmetric spacetimes there is a difference in proper time elapsed along the two trajectories. However, as we show here, the proper time of each path will couple to the corresponding local Wigner rotation, and the effect in the spin of the superposed particle will be a combination of both. Besides, we discuss a general framework to study the local Wigner rotations of spin-1/2 particles in general stationary axisymmetric spacetimes for circular orbits.

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arXiv2021

An uncertainty view on complementarity and a complementarity view on uncertainty

Since the uncertainty about an observable of a system prepared in a quantum state is usually described by its variance, when the state is mixed, the variance is a hybrid of quantum and classical uncertainties. Besides that, complementarity relations are saturated only for pure, single-quanton, quantum states. For mixed states, the wave-particle quantifiers never saturate the complementarity relation and can even reach zero for a maximally mixed state. So, to fully characterize a quanton it is not sufficient to consider its wave-particle aspect; one has also to regard its correlations with other systems. In this paper, we discuss the relation between quantum correlations and local classical uncertainty measures, as well as the relation between quantum coherence and quantum uncertainty quantifiers. We obtain a complete complementarity relation for quantum uncertainty, classical uncertainty, and predictability. The total quantum uncertainty of a d-paths interferometer is shown to be equivalent to the Wigner-Yanase coherence and the corresponding classical uncertainty is shown to be a quantum correlation quantifier. The duality between complementarity and uncertainty is used to derive quantum correlations measures that complete the complementarity relations for $l_1$-norm and $l_2$-norm coherences. Besides, we show that Brukner-Zeilinger's invariant information quantifies both the wave and particle characters of a quanton and we obtain a sum uncertainty relation for the generalized Gell Mann's matrices.

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arXiv2021

Complete complementarity relations in system-environment decoherent dynamics

We investigate the system-environment information flow from the point of view ofcomplete complementarity relations. We consider some commonly used noisy quantum channels:Amplitude damping, phase damping, bit flip, bit-phase flip, phase flip, depolarizing, and correlatedamplitude damping. By starting with an entangled bipartite pure quantum state, with the linearentropy being the quantifier of entanglement, we study how entanglement is redistributed and turnedinto general correlations between the degrees of freedom of the whole system. For instance, it ispossible to express the entanglement entropy in terms of the multipartite quantum coherence or interms of the correlated quantum coherence of the different partitions of the system. In addition,we notice that for the depolarizing and bit-phase flip channels the wave and particle aspects candecrease or increase together. Besides, by considering the environment as part of a pure quantumsystem, the linear entropy is shown to be not just a measure of mixedness of a particular subsystem,but a correlation measure of the subsystem with rest of the world.

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arXiv2021

Interferometric Visibility in Curved Spacetimes

In [M. Zych et al., Nat. Commun. 2, 505 (2011)], the authors predicted that the interferometric visibility is affected by a gravitational field in way that cannot be explained without the general relativistic notion of proper time. In this work, we take a different route and start deriving the same effect using the unitary representation of the local Lorentz transformation in the Newtonian Limit. In addition, we show that the effect on the interferometric visibility due to gravity persists in different spacetime geometries. However, the influence is not necessarily due to the notion of proper time. For instance, by constructing a `astronomical' Mach-Zehnder interferometer in the Schwarzschild spacetime, the influence on the interferometric visibility can be due to another general relativistic effect, the geodetic precession. Besides, by using the unitary representation of the local Lorentz transformation, we show that this behavior of the interferometric visibility is general for an arbitrary spacetime, provided that we restrict the motion of the quanton to a two-dimensional spacial plane.

gr-qc↗

arXiv2021

Complete complementarity relations in curved spacetimes

We extend complete complementarity relations to curved spacetimes by considering a succession of infinitesimal local Lorentz transformations, which implies that complementarity remains valid as the quanton travels through its world line and the complementarity aspects in different points of spacetime are connected. This result allows the study of these different complementary aspects of a quantum system as it travels through spacetime. In particular, we study the behavior of these different complementary properties of massive spin-$1/2$ particles in the Schwarzschild spacetime. For geodetic circular orbits, we find that the spin state of one particle oscillates between a separable and an entangled state. For non-geodetic circular orbits, we notice that the frequency of these oscillations gets bigger as the orbit gets nearer to the Schwarzschild radius $r_s$.

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arXiv2021

Experimental tests of density matrix's properties-based complementarity relations

Bohr's complementarity principle is of fundamental historic and conceptual importance for Quantum Mechanics (QM), and states that, with a given experimental apparatus configuration, one can observe either the wave-like or the particle-like character of a quantum system, but not both. However, it was eventually realized that these dual behaviors can both manifest partially in the same experimental setup, and, using ad hoc proposed measures for the wave and particle aspects of the quanton, complementarity relations were proposed limiting how strong these manifestations can be. Recently, a formalism was developed and quantifiers for the particleness and waveness of a quantum system were derived from the mathematical structure of QM entailed in the density matrix's basic properties ($ρ\ge 0$, $\mathrm{Tr}ρ=1$). In this article, using IBM Quantum Experience quantum computers, we perform experimental tests of these complementarity relations applied to a particular class of one-qubit quantum states and also for random quantum states of one, two, and three qubits.

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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.

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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.

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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.

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