arXiv subjects

Fernando Nicacio

Publications and source records attributed to Fernando Nicacio.

9 recordsLinked to original sources

arXiv2024

Physical consequences of Lindbladian invariance transformations

On its own, the invariance properties of Markovian master equations have mostly played a mathematical or computational role in the evaluation of quantum open system dynamics. Because all forms of the equation lead to the same time evolution for the state of the system, the fixation of a particular form has only gained physical meaning when correlated with additional information such as in the evolution of quantum trajectories or the study of decoherence-free subspaces. Here, we show that these symmetry transformations can be exploited, on their own, to optimize practical physical tasks. In particular, we present a general formulation showing how they can be used to change the measurable values of physical quantities regarding the exchange of energy and/or information with the environment. We also analyze examples of optimization in quantum thermodynamics and, finally, discuss practical implementations in terms of quantum trajectories.

quant-ph↗

arXiv2022

Thermal equilibrium in Gaussian dynamical semigroups

We characterize all Gaussian dynamical semigroups in continuous variables quantum systems of n-bosonic modes which have a thermal Gibbs state as a stationary solution. This is performed through an explicit relation between the diffusion and dissipation matrices, which characterize the semigroup dynamic, and the covariance matrix of the thermal equilibrium state. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices, and the identification of different Gaussian dynamical semigroups which shares the same thermal equilibrium state.

quant-ph↗

arXiv2022

Gauge Quantum Thermodynamics of Time-local non-Markovian Evolutions

Dealing with a generic time-local non-Markovian master equation, we define current and power to be process-dependent as in classical thermodynamics. Each process is characterized by a symmetry transformation, a gauge of the master equation, and is associated with different amounts of heat and/or work. Once the symmetry requirement fixes the thermodynamical quantities, a consistent gauge interpretation of the laws of thermodynamics emerges. We also provide the necessary and sufficient conditions for a system to have a gauge-independent thermodynamical behavior and show that systems satisfying Quantum Detailed Balance conditions are gauge-independent. Applying the theory to quantum thermal engines, we show that gauge transformations can change the machine efficiency, however, yet constrained by the classical Carnot bound.

quant-ph↗

arXiv2018

Relative Phase Shifts for Metaplectic Isotopies Acting on Mixed Gaussian States

We address in this paper the notion of relative phase shift for mixed quantum systems. We study the Pancharatnam-Sjoeqvist phase shift for metaplectic isotopies acting on Gaussian mixed states. We complete and generalize previous results obtained by one of us while giving rigorous proofs. This gives us the opportunity to review and complement the theory of the Conley-Zehnder index which plays an essential role in the determination of phase shifts.

math-ph↗

arXiv2017

Unified framework to determine Gaussian states in continuous variable systems

Gaussian states are the backbone of quantum information protocols with continuous variable systems, whose power relies fundamentally on the entanglement between the different modes. In the case of global pure states, knowledge of the reduced states in a given bipartition of a multipartite quantum system bears information on the entanglement in such bipartition. For Gaussian states, the reduced states are also Gaussian, so there determination requires essentially the experimental determination of their covariance matrix. Here, we develop strategies to determine the covariance matrix of an arbitrary n-mode bosonic Gaussian state through measurement of the total phase acquired when appropriate metaplectic evolutions, associated with quadratic Hamiltonians, are applied. Simply one-mode metaplectic evolutions, such rotations, squeezing and shear transformations, in addition to a single two-mode rotation, allows to determine all the covariance matrix elements of a n-mode bosonic system. All the single-mode metaplectic evolutions are applied conditionally to a state in which an ancilla qubit is entangled with the n-mode system. The ancillary system provides, after measurement, the value of the total phase of each evolution. The proposed method is experimentally friendly to be implemented in the most currently used continuous variable systems.

quant-ph↗

arXiv2014

Tight Bounds for the Entanglement of Formation of Gaussian States

We establish tight upper and lower bounds for the Entanglement of Formation of an arbitrary two-mode Gaussian state employing necessary properties of Gaussian channels. Both bounds are strictly given by the Entanglement of Formation of symmetric Gaussian states, which are simply constructed from the reduced states obtained by partial trace of the original one.

quant-ph↗

arXiv2013

Minkowski structure for purity and entanglement of Gaussian bipartite states

The relation between the symplectic and Lorentz groups is explored to investigate entanglement features in a two-mode bipartite Gaussian state. We verify that the correlation matrix of arbitrary Gaussian states can be associated to a hyperbolic space with a Minkowski metric, which is divided in two regions - separablelike and entangledlike, in equivalence to timelike and spacelike in special relativity. This correspondence naturally allows the definition of two insightful invariant squared distances measures - one related to the purity and another related to amount of entanglement. The second distance allows us to define a measure for entanglement in terms of the invariant interval between the given state and its closest separable state, given in a natural manner without the requirement of a minimization procedure.

quant-ph↗

arXiv2010

Phase Space Structure of Generalized Gaussian Cat States

We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states, e.g., a coherent state and a squeezed state. The Wigner functions of such states exhibit the typical pair of Gaussian hills plus an interference term which presents a novel structure, as compared with the standard superposition of coherent states (degenerate case). We prove that, in any dimensions, the structure of the interference term is characterized by a particular quadratic form; in one degree of freedom the phase is hyperbolic. This phase-space structure survives the action of a thermal reservoir. We also discuss certain superpositions of {\em mixed} Gaussian states generated by conditional Gaussian operations or Kerr-type dynamics on thermal states.

quant-ph↗

arXiv2008

WKB Propagation of Gaussian Wavepackets

We analyze the semiclassical evolution of Gaussian wavepackets in chaotic systems. We prove that after some short time a Gaussian wavepacket becomes a primitive WKB state. From then on, the state can be propagated using the standard TDWKB scheme. Complex trajectories are not necessary to account for the long-time propagation. The Wigner function of the evolving state develops the structure of a classical filament plus quantum oscillations, with phase and amplitude being determined by geometric properties of a classical manifold.

nlin.CD↗