Fernando Galve

Genuine Quantum and Classical Correlations in Multipartite Systems

Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify the distance between two density matrices. Moreover, we show that, for pure states of three qubits, both quantum and classical bipartite correlations obey a ladder ordering law fixed by two-body mutual informations, or, equivalently, by one-qubit entropies.

Unified view of correlations using the square-norm distance

The distance between a quantum state and its closest state not having a certain property has been used to quantify the amount of correlations corresponding to that property. This approach allows a unified view of the various kinds of correlations present in a quantum system. In particular, using relative entropy as a distance measure, total correlations can be meaningfully separated into a quantum part and a classical part thanks to an additive relation involving only the distances between states. Here we investigate a unified view of correlations using as a distance measure the square norm, which has already been used to define the so-called geometric quantum discord. We thus also consider geometric quantifiers for total and classical correlations, finding, for a quite general class of bipartite states, their explicit expressions. We analyze the relationship among geometric total, quantum, and classical correlations, and we find that they no longer satisfy a closed additivity relation.

Maximally discordant mixed states of two qubits

We study the relative strength of classical and quantum correlations, as measured by discord, for two-qubit states. Quantum correlations appear only in the presence of classical correlations, while the reverse is not always true. We identify the family of states that maximize the discord for a given value of the classical correlations and show that the largest attainable discord for mixed states is greater than for pure states. The difference between discord and entanglement is emphasized by the remarkable fact that these states do not maximize entanglement and are, in some cases, even separable. Finally, by random generation of density matrices uniformly distributed over the whole Hilbert space, we quantify the frequency of the appearance of quantum and classical correlations for different ranks.

Orthogonal measurements are almost sufficient for quantum discord of two qubits

The common use in the literature of orthogonal measurements in obtaining quantum discord for two-qubit states is discussed and compared with more general measurements. We prove the optimality of orthogonal measurements for rank-2 states. While for rank-3 and -4 mixed states they are not optimal, we present strong numerical evidence showing that they give the correct quantum discord up to minimal corrections. Based on the connection, through purification with an ancilla, between discord and entanglement of formation (EoF), we give a tight upper bound for the EoF of a 2⊗N mixed state of rank 2, given by an optimal decomposition of 2 elements. We also provide an alternative way to compute the quantum discord for two qubits based on the Bloch vectors of the state.

Synchronization, quantum correlations and entanglement in oscillator networks

Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although several mechanisms and conditions for synchronous behavior in spatially extended systems and networks have been identified, the emergence of this phenomenon has been largely unexplored in quantum systems until very recently. Here we discuss synchronization in quantum networks of different harmonic oscillators relaxing towards a stationary state, being essential the form of dissipation. By local tuning of one of the oscillators, we establish the conditions for synchronous dynamics, in the whole network or in a motif. Beyond the classical regime we show that synchronization between (even unlinked) nodes witnesses the presence of quantum correlations and entanglement. Furthermore, synchronization and entanglement can be induced between two different oscillators if properly linked to a random network.

Entropy production and thermodynamic power of the squeezed thermal reservoir.

We analyze the entropy production and the maximal extractable work from a squeezed thermal reservoir. The nonequilibrium quantum nature of the reservoir induces an entropy transfer with a coherent contribution while modifying its thermal part, allowing work extraction from a single reservoir, as well as great improvements in power and efficiency for quantum heat engines. Introducing a modified quantum Otto cycle, our approach fully characterizes operational regimes forbidden in the standard case, such as refrigeration and work extraction at the same time, accompanied by efficiencies equal to unity.

Quantum correlations and mutual synchronization

We acknowledge financial support from the MICINN (Spain) and FEDER (EU) through project FIS2007- 60327 (FISICOS), from CSIC through project CoQuSys (200450E566) and from the Govern Balear through project AAEE0113/09. GLG is supported by Juan de la Cierva program.

Irreversible Work and Inner Friction in Quantum Thermodynamic Processes

We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can be treated on an equal footing, as both can be linked with the heat exchanged in thermalization processes and both can be expressed as relative entropies. Furthermore, we show that a specific fluctuation relation for the entropy production associated with the inner friction exists, which allows the inner friction to be written in terms of its cumulants.

Entanglement dynamics of nonidentical oscillators under decohering environments

We acknowledge funding from FISICOS (FIS2007-60327) and CoQuSys (200450E566). G.L.G. is supported by the Spanish Ministry of Science and Innovation through the program Juan de la Cierva.

Energy cost and optimal entanglement production in harmonic chains

We investigate nonequilibrium entanglement generation in a chain of harmonic oscillators with time–dependent linear coupling. We use optimal control theory to determine the coupling modulation that leads to maximum logarithmic negativity for a pair of opposite oscillators and show that it corresponds to a synchronization of the eigenmodes of the chain. We further analytically relate the maximum attainable entanglement to the irreversible work done to produce it, thus bridging nonequilibrium entanglement production and nonequilibrium thermodynamics.