A study of the dynamics of quantum correlations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Symmetry restoration and quantumness reestablishment

A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.

Nonclassicality Criteria from Phase-Space Representations and Information-Theoretical Constraints Are Maximally Inequivalent

We consider two celebrated criteria for defining the nonclassicality of bipartite bosonic quantum systems, the first stemming from information theoretic concepts and the second from physical constraints on the quantum phase space. Consequently, two sets of allegedly classical states are singled out: (i) the set C composed of the so-called classical-classical (CC) states—separable states that are locally distinguishable and do not possess quantum discord; (ii) the set P of states endowed with a positive P representation (P-classical states)—mixtures of Glauber coherent states that, e.g., fail to show negativity of their Wigner function. By showing that C and P are almost disjoint, we prove that the two defining criteria are maximally inequivalent. Thus, the notions of classicality that they put forward are radically different. In particular, generic CC states show quantumness in their P representation, and vice versa, almost all P-classical states have positive quantum discord and, hence, are not CC. This inequivalence is further elucidated considering different applications of P-classical and CC states. Our results suggest that there are other quantum correlations in nature than those revealed by entanglement and quantum discord.

Transferring entanglement to the steady state of flying qubits

The transfer of entanglement from optical fields to qubits provides a viable approach to entangling remote qubits in a quantum network. In cavity quantum electrodynamics, the scheme relies on the interaction between a photonic resource and two stationary intracavity atomic qubits. However, it might be hard in practice to trap two atoms simultaneously and synchronize their coupling to the cavities. To address this point, we propose and study entanglement transfer from cavities driven by an entangled external field to controlled flying qubits. We consider two exemplary non-Gaussian driving fields: NOON and entangled coherent states. We show that in the limit of long coherence time of the cavity fields, when the dynamics is approximately unitary, entanglement is transferred from the driving field to two atomic qubits that cross the cavities. On the other hand, a dissipation-dominated dynamics leads to very weakly quantum-correlated atomic systems, as witnessed by vanishing quantum discord.

Experimental Distribution of Entanglement with Separable Carriers

The key requirement for quantum networking is the distribution of entanglement between nodes. Surprisingly, entanglement can be generated across a network without direct transfer - or communication - of entanglement. In contrast to information gain, which cannot exceed the communicated information, the entanglement gain is bounded by the communicated quantum discord, a more general measure of quantum correlation that includes but is not limited to entanglement. Here, we experimentally entangle two communicating parties sharing three initially separable photonic qubits by exchange of a carrier photon that is unentangled with either party at all times. We show that distributing entanglement with separable carriers is resilient to noise and in some cases becomes the only way of distributing entanglement through noisy environments.

Criticality, factorization, and long-range correlations in the anisotropic XY model

We study the long-range quantum correlations in the anisotropic XY model. By first examining the thermodynamic limit, we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Furthermore, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite-size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.

Single- and two-mode quantumness at a beam splitter

In the context of bipartite bosonic systems, two notions of classicality of correlations can be defined: P-classicality, based on the properties of the Glauber-Sudarshan P-function; and C-classicality, based on the entropic quantum discord. It has been shown that these two notions are maximally inequivalent in a static (metric) sense -- as they coincide only on a set of states of zero measure. We extend and reinforce quantitatively this inequivalence by addressing the dynamical relation between these types of non-classicality in a paradigmatic quantum-optical setting: the linear mixing at a beam splitter of a single-mode Gaussian state with a thermal reference state. Specifically, we show that almost all P-classical input states generate outputs that are not C-classical. Indeed, for the case of zero thermal reference photons, the more P-classical resources at the input the less C-classicality at the output. In addition, we show that the P-classicality at the input -- as quantified by the non-classical depth -- does instead determine quantitatively the potential of generating output entanglement. This endows the non-classical depth with a new operational interpretation: it gives the maximum number of thermal reference photons that can be mixed at a beam splitter without destroying the output entanglement.

Nonclassicality and criticality in symmetry protected magnetic phases

Quantum and global discord in a spin-1 Heisenberg chain subject to single-ion anisotropy (uniaxial field) are studied using exact diagonalisation and the density matrix renormalisation group (DMRG). We find that these measures of quantum non-classicality are able to detect the quantum phase transitions confining the symmetry protected Haldane phase and show critical scaling with universal exponents. Moreover, in the case of thermal states, we find that quantum discord can increase with increasing temperature.

On the quantumness of correlations in nuclear magnetic resonance

Nuclear magnetic resonance (NMR) was successfully employed to test several protocols and ideas in quantum information science. In most of these implementations, the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this paper, we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement-separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogue of the single-photon Mach-Zehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrates how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present.

Dissonance as a resource for probing the qubit depolarizing channel

Quantum channel identification, a standard problem in quantum metrology, is the task of estimating parameter(s) of a quantum channel. We investigate dissonance (quantum discord in the absence of entanglement) as an aid to quantum channel identification and find evidence for dissonance as a resource for quantum information processing. We consider the specific case of dissonant Bell-diagonal probes of the qubit depolarizing channel, using quantum Fisher information as a measure of statistical information extracted by the probe. In this setting dissonant quantum probes yield more statistical information about the depolarizing probability than do corresponding probes without dissonance and greater dissonance yields greater information. This effect only operates consistently when we control for classical correlation between the probe and its ancilla and the joint and marginal purities of the ancilla and probe.

The case for quantum key distribution

Quantum key distribution (QKD) promises secure key agreement by using quantum mechanical systems. We argue that QKD will be an important part of future cryptographic infrastructures. It can provide long-term confidentiality for encrypted information without reliance on computational assumptions. Although QKD still requires authentication to prevent man-in-the-middle attacks, it can make use of either information-theoretically secure symmetric key authentication or computationally secure public key authentication: even when using public key authentication, we argue that QKD still offers stronger security than classical key agreement.

Is there something quantum-like about the human mental lexicon?

Following an early claim by Nelson & McEvoy suggesting that word associations can display `spooky action at a distance behaviour', a serious investigation of the potentially quantum nature of such associations is currently underway. In this paper quantum theory is proposed as a framework suitable for modelling the mental lexicon, specifically the results obtained from both intralist and extralist word association experiments. Some initial models exploring this hypothesis are discussed, and they appear to be capable of substantial agreement with pre-existing experimental data. The paper concludes with a discussion of some experiments that will be performed in order to test these models.

Quantum memory

New models of human cognition inspired by quantum theory could underpin information technologies that are better aligned with howwe recall information.

Is there something quantum-like about the human mental lexicon?

This talk proceeds from the premise that IR should engage in a more substantial dialogue with cognitive science. After all, how users decide relevance, or how they chose terms to modify a query are processes rooted in human cognition. Recently, there has been a growing literature applying quantum theory (QT) to model cognitive phenomena. This talk will survey recent research, in particular, modelling interference effects in human decision making. One aspect of QT will be illustrated - how quantum entanglement can be used to model word associations in human memory. The implications of this will be briefly discussed in terms of a new approach for modelling concept combinations. Tentative links to human adductive reasoning will also be drawn. The basic theme behind this talk is QT can potentially provide a new genre of information processing models (including search) more aligned with human cognition.

Idealistic quantum psychopathology : a way forward?

Quantum psychopathology holds the so called “quantum mind” hypothesis, which is controversial. In addition, this hypothesis focuses attention onto quantum processes in the brain, and how this may relate to psychopathological issues. This is very “low level”. As a consequence, it is challenging to form bridges to “higher level” problems related to psychopathology. By adopting the stance used in the quantum interaction community or researchers, this reply puts forward the idea that an idealistic approach may circumvent the controversy and opens the way for addressing challenges at higher levels of psychopathology.