Narrow Results

Message Sequence Charts (MSCs) and High-level Message Sequence Charts (HMSCs) are formalisms used to describe scenarios of message passing protocols. We propose using Allen's logic to represent the temporal order of the messages. We introduce the concept of discord to quantify the discrepancies between the intuition and the semantics of the ordering between messages in different nodes of an HMSC. We study the algorithmic properties of this concept: we show that while the discord of a pair of messages is hard to compute in general, the problem becomes polynomial-time computable if the number of nodes of the HMSC or the number of processes is constant. Moreover, for a given HMSC, it is always computationally easy to identify a pair of messages that exhibits the worst-case discord and compute the discord of this pair.

We review the basic idea behind resource theories, where we quantify quantum resources by specifying a restricted class of operations. This divides the state space into various sets, including states which are free (because they can be created under the class of operations), and those which are a resource (because they cannot be). One can quantify the worth of the resource by the relative entropy distance to the set of free states, and under certain conditions, this is a unique measure which quantifies the rate of state to state transitions. The framework includes entanglement, asymmetry and purity theory. It also includes thermodynamics, which is a hybrid resource theory combining purity theory and asymmetry. Another hybrid resource theory which merges purity theory and entanglement can be used to study quantumness of correlations and discord, and we present quantumness in this more general framework of resource theories.

We review recent studies on the measures of zero temperature quantum correlations namely, the quantum entanglement (concurrence) and discord present in the final state of a transverse XY spin chain following a quench through quantum critical points; the aim of these studies is to explore the scaling of the above quantities as a function of the quench rate. A comparative study between the concurrence and the quantum discord shows that their behavior is qualitatively the same though there are quantitative differences. For the present model, the scaling of both the quantities are given by the scaling of the density of the defect present in the final state though one cannot find a closed form expression for the discord. We also extend our study of quantum discord to a transverse Ising chain in the presence of a three spin interaction. Finally, we present a study of the dynamical evolution of quantum discord and concurrence when two central qubits, initially prepared in a Werner state, are coupled to the environmental XY spin chain which is driven through quantum critical points. The qualitative behavior of quantum discord and concurrence are found to be similar as that of the decoherence factor.

Quantum information protocols are often designed in the ideal situation with no decoherence. However, in real setup, these protocols are subject to the decoherence and thus reducing fidelity of the measurement outcome. In this work, we analyze the effect of state-dependent bath on the quantum correlations and the fidelity of a single qubit teleportation. We model our system-bath interaction as qubits interacting with a common bath of bosons, and the state dependence of the bath is generated through a projective measurement on the joint state in thermal equilibrium. The analytic expressions for the time evolution of entanglement, discord and average fidelity of quantum teleportation are calculated. It is shown that due to the presence of initial system-bath correlations, the system maintains quantum correlations for long times. Furthermore, due to the presence of finite long-time entanglement of the quantum channel, the average fidelity is shown to be higher than its classical value.

We investigate the dynamics of quantum and classical correlations in a system of two qubits under local colored-noise dephasing channels. The time evolution of a single qubit interacting with its own environment is described by a memory kernel non-Markovian master equation. The memory effects of the non-Markovian reservoirs introduce new features in the dynamics of quantum and classical correlations compared to the white noise Markovian case. Depending on the geometry of the initial state, the system can exhibit frozen discord and multiple sudden transitions between classical and quantum decoherence [L. Mazzola, J. Piilo and S. Maniscalco, Phys. Rev. Lett. 104 (2010) 200401]. We provide a geometric interpretation of those phenomena in terms of the distance of the state under investigation to its closest classical state in the Hilbert space of the system.

A framework for categorizing entropic measures of non-classical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum entropic quantity and the corresponding classical quantity obtained from measurements on the two systems. Three types of entropic quantities are used, and three different measurement strategies are applied to these quantities. Many of the resulting measures of non-classical correlations have been proposed previously. Properties of the various measures are explored, and results of evaluating the measures for two-qubit quantum states are presented.

We study the effect of external electric bias on the quantum correlations in the array of optically excited three coupled semiconductor quantum dots. The correlations are characterized by the quantum discord and concurrence and are observed using excitonic qubits. We employ the lower bound of concurrence for thermal density matrix at different temperatures. The effect of the Förster interaction on correlations will be studied. Our theoretical model detects nonvanishing quantum discord when the electric field is on while concurrence dies, ensuring the existence of nonclassical correlations as measured by the quantum discord.

In this work we introduce the randomness which is truly quantum mechanical in nature arising as an act of measurement. For a composite classical system, we have the joint entropy to quantify the randomness present in the total system and that happens to be equal to the sum of the entropy of one subsystem and the conditional entropy of the other subsystem, given we know the first system. The same analogy carries over to the quantum setting by replacing the Shannon entropy by the von Neumann entropy. However, if we replace the conditional von Neumann entropy by the average conditional entropy due to measurement, we find that it is different from the joint entropy of the system. We call this difference Measurement Induced Randomness (MIR) and argue that this is unique of quantum mechanical systems and there is no classical counterpart to this. In other words, the joint von Neumann entropy gives only the total randomness that arises because of the heterogeneity of the mixture and we show that it is not the total randomness that can be generated in the composite system. We generalize this quantity for N-qubit systems and show that it reduces to quantum discord for two-qubit systems. Further, we show that it is exactly equal to the change in the cost quantum state merging that arises because of the measurement. We argue that for quantum information processing tasks like state merging, the change in the cost as a result of discarding prior information can also be viewed as a rise of randomness due to measurement.

In this paper, we investigate, in the framework of the theory of open quantum systems, based on completely positive dynamical semigroups, the Markovian dynamics of Gaussian Rényi-2 correlations — quantum entanglement, quantum discord, mutual information and classical correlations in a system composed of two bosonic modes, interacting with a squeezed thermal bath. We show that the time evolution of the Rényi-2 correlations strongly depends on the parameters of the initial Gaussian squeezed thermal state of the considered system and on the parameters characterizing the squeezed thermal bath. It is shown that while Gaussian Rényi-2 entanglement is suppressed in a finite time, due to the interaction with the squeezed thermal bath, the correlations beyond entanglement — Gaussian Rényi-2 discord, classical correlations and mutual information undergo a freezing-like behavior, namely they decay only asymptotically, in the limit of large times. We also illustrate a fundamental hierarchy for bipartite Gaussian correlations.