Practical implementation of mutually unbiased bases using quantum circuits

The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work out a simple and efficient method based on cyclic generation of mutually unbiased bases. The basic generator requires only Hadamard and controlled-phase gates, which are available in most practical realizations of these systems. We show how complete sets of mutually unbiased bases with different entanglement structures can be realized for three and four qubits. We also analyze the quantum circuits implementing the various entanglement classes.Comment: 5 pages, 2 color figures. Comments welcome

A sum rule for charged elementary particles

There may be a link between the quantum properties of the vacuum and the parameters describing the properties of light propagation, culminating in a sum over all types of elementary particles existing in Nature weighted only by their squared charges and independent of their masses. The estimate for that sum is of the order of 100.Comment: Accepted for publication in European Physical Journal

Variations on the adiabatic invariance: the Lorentz pendulum

We analyze a very simple variant of the Lorentz pendulum, in which the length is varied exponentially, instead of uniformly, as it is assumed in the standard case. We establish quantitative criteria for the condition of adiabatic changes in both pendula and put in evidence their substantially different physical behavior with regard to adiabatic invariance.Comment: To appear in American Journal of Physic

Simple quantum model for light depolarization

Depolarization of quantum fields is handled through a master equation of the Lindblad type. The specific feature of the proposed model is that it couples dispersively the field modes to a randomly distributed atomic reservoir, much in the classical spirit of dealing with this problem. The depolarizing dynamics resulting from this model is analyzed for relevant states.Comment: Improved version. Accepted for publication in the Journal of the Optical Society of America

Invisibility and PT Symmetry: A Simple Geometrical Viewpoint

We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via M\"{o}bius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.Comment: 13 pages. No figure. Accepted for publication in Symmetr

Efficient tomography with unknown detectors

We compare the two main techniques used for estimating the state of a physical system from unknown measurements: standard detector tomography and data-pattern tomography. Adopting linear inversion as a fair benchmark, we show that the difference between these two protocols can be traced back to the nonexistence of the reverse-order law for pseudoinverses. We capitalize on this fact to identify regimes where the data-pattern approach outperforms the standard one and vice versa. We corroborate these conclusions with numerical simulations of relevant examples of quantum state tomography.Comment: 13 pages, 6 figures. Submitted for publication. Comments most welcome

Discrete phase-space structure of nn-qubit mutually unbiased bases

We work out the phase-space structure for a system of $n$ qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field \Gal{2^n} and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for $n$ qubits.Comment: Title changed. Improved version. Accepted for publication in Annals of Physic