Renan Cabrera

Wigner phase-space distribution as a wave function

We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman-von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner functions negativity.

Operational Dynamic Modeling Transcending Quantum and Classical Mechanics

We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.

The canonical coset decomposition of unitary matrices through Householder transformations

This paper reveals the relation between the canonical coset decomposition of unitary matrices and the corresponding decomposition via Householder reflections. These results can be used to parametrize unitary matrices via Householder reflections.

Time-resolved quantum process tomography using Hamiltonian-encoding and observable-decoding

The Hamiltonian encoding observable decoding (HE-OD) technique is experimentally demonstrated for process tomography of laser-induced dynamics in atomic Rb vapor. With the assistance of a laser pulse truncation method, a time dependent reconstruction of the quantum evolution is achieved. HE-OD can perform full as well as partial process tomography with appropriate measurements to characterize the system. The latter feature makes HE-OD tomography suitable for analyzing quantum processes in complex systems.

Fidelity between unitary operators and the generation of robust gates against off-resonance perturbations

We perform a functional expansion of the fidelity between two unitary matrices in order to find necessary conditions for the robust implementation of a target gate. Comparison of these conditions with those obtained from the the Magnus expansion and Dyson series shows that they are equivalent in the first order. By exploiting techniques from robust design optimization, we account for issues of experimental feasibility by introducing an additional criterion to the search for control pulses. This search is accomplished by exploring the competition between the multiple objectives in the implementation of the NOT gate by means of evolutionary multi-objective optimization.

Wigner–Lindblad Equations for Quantum Friction

Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena.

Dirac open-quantum-system dynamics: Formulations and simulations

We present an open-system interaction formalism for the Dirac equation. Overcoming a complexity bottleneck of alternative formulations, our framework enables efficient numerical simulations (utilizing a typical desktop) of relativistic dynamics within the von Neumann density matrix and Wigner phase-space descriptions. Employing these instruments, we gain important insights into the effect of quantum dephasing for relativistic systems in many branches of physics. In particular, the conditions for robustness of Majorana spinors against dephasing are established. Using the Klein paradox and tunneling as examples, we show that quantum dephasing does not suppress negative energy particle generation. Hence, the Klein dynamics is also robust to dephasing.

Average fidelity in n-qubit systems

This Letter generalizes the expression for the average fidelity of single qubits, as found by Bowdrey et al. [M.D. Bowdrey, D.K.L. Oi, A.J. Short, K. Banaszek, J.A. Jones, Phys. Lett. A 294 (2002) 258], to the case of n qubits. We use a simple algebraic approach with basis elements for the density-matrix expansion expressed as Kronecker products of n Pauli spin matrices. An explicit integration over initial states is avoided by invoking the invariance of the state average under unitary transformations of the initial density matrix. The results have applications to measurements of quantum information, for example in ion-trap and NMR experiments.

Conceptual inconsistencies in finite-dimensional quantum and classical mechanics

Utilizing operational dynamic modeling [Phys. Rev. Lett. 109, 190403 (2012); arXiv:1105.4014], we demonstrate that any finite-dimensional representation of quantum and classical dynamics violates the Ehrenfest theorems. Other peculiarities are also revealed, including the nonexistence of the free particle and ambiguity in defining potential forces. Non-Hermitian mechanics is shown to have the same problems. This work compromises a popular belief that finite-dimensional mechanics is a straightforward discretization of the corresponding infinite-dimensional formulation.

How to Make Distinct Dynamical Systems Appear Spectrally Identical

We show that a laser pulse can always be found that induces a desired optical response from an arbitrary dynamical system. As illustrations, driving fields are computed to induce the same optical response from a variety of distinct systems (open and closed, quantum and classical). As a result, the observed induced dipolar spectra without detailed information on the driving field are not sufficient to characterize atomic and molecular systems. The formulation may also be applied to design materials with specified optical characteristics. These findings reveal unexplored flexibilities of nonlinear optics.