arXiv subjects

M. Rivera-Tapia

Publications and source records attributed to M. Rivera-Tapia.

5 recordsLinked to original sources

arXiv2026

The role of Wigner rotation in estimating the specific angular momentum of a Kerr spacetime

We study the rotation of the polarization due to the gravitational field in the Kerr spacetime and the possibility of estimating the specific angular momentum that parameterizes this metric. Our approach is based on a geodesic interferometer, that is, a Mach-Zehnder interferometer whose arms are defined by null geodesics, and a single photon propagating within it. We show that the detection probability at the output ports of the interferometer is a function of two phase differences, one arising from the gravitational time delay and the other from the polarization rotation, both computed under the slow rotation and weak field approximations. Thereby, the interferometric visibility is a signature of two relativistic effects. Using the detection probability, we obtain an estimate for the specific angular momentum and characterize its uncertainty.

gr-qc↗

arXiv2026

Discrimination of metric theories

We study the possibility of discriminating between metric theories within the Parametrized Post-Newtonian formalism. In this approach, the two-dimensional quantum state of a massive quantum clock becomes, after propagating at low speed and in a weak gravitational field, a function of the post-Newtonian parameters and thus a signature of a metric theory. To discriminate among metric theories, we resort to quantum-state discrimination strategies such as minimum-error and unambiguous discrimination. In particular, we show that it is possible to refute the hypothesis that a particular metric theory describes spacetime with a single detection event and that it is possible to discriminate with certainty between two different metrics, also with a single detection event. In general, the success probability of the discrimination strategy is a harmonic function of the product of the difference of the proper time corresponding to each quantum clock state, the energy difference between the energy eigenstates of the quantum clock, the propagation length, and speed. It is thus possible to find suitable length and speed scales such that the success probability is close to one by selecting a quantum system with the highest energy difference and the longest natural lifetime. According to this, atomic nuclei such as thorium are considered the most suitable quantum clocks. We also show that the use of a ensemble of quantum clocks leads to a significant increase in the probability of success in discriminating between post-Newtonian parameters that differ by $10^{-5}$. This facilitates achieving a probability of success approaching unity with distances on the scale of several kilometers and velocities approximating one-thousandth of the speed of light for a ensemble of only 10 quantum clocks.

gr-qc↗

arXiv2024

Estimation of high-dimensional unitary transformations saturating the Quantum Cramér-Rao bound

We propose an estimation procedure for $d$-dimensional unitary transformations. For $d>2$, the unitary transformations close to the identity are estimated saturating the quantum Cramér-Rao bound. For $d=2$, the estimation of all unitary transformations is also optimal with some prior information. We show through numerical simulations that, even in the absence of prior information, two-dimensional unitary transformations can be estimated with greater precision than by means of standard quantum process tomography.

quant-ph↗

arXiv2020

Weak Gravitational Field Effects On Large-Scale Optical Interferometric Bell Tests

The technological refinement of experimental techniques has recently allowed the generation of two-photon polarization-entangled states at low Earth orbit, which has been subsequently applied to quantum communications. This achievement paves the way to study the interplay between General Relativity and Quantum Mechanics in new setups. Here, we study the generation of two-photon energy-time entangled states via large scale Franson and Hugged interferometric arrays in the presence of a weak gravitational field. We show that for certain configurations of the arrays, an entangled state emerges as a consequence of the gravitational time delay. We also show that the aforementioned arrays generate entanglement and violate the Clauser-Horne-Shymony-Holt inequality under suitable conditions even in the presence of frequency dispersion.

quant-ph↗

arXiv2015

A Clifford Bundle Approach to the Wave Equation of a Spin 1/2 Fermion in the de Sitter Manifold

In this paper we give a Clifford bundle motivated approach to the wave equation of a free spin $1/2$ fermion in the de Sitter manifold, a brane with topology $M=\mathrm{S0}(4,1)/\mathrm{S0}(3,1)$ living in the bulk spacetime $\mathbb{R}^{4,1}=(\mathring{M}=\mathbb{R}^{5},\boldsymbol{\mathring{g}})$ and equipped with a metric field $\boldsymbol{g:=-i}^{\ast}\boldsymbol{\mathring{g}%}$ with $\boldsymbol{i}:M\rightarrow\mathring{M}$ being the inclusion map. To obtain the analog of Dirac equation in Minkowski spacetime in the structure $\mathring{M}$ we appropriately factorize the two Casimir invariants $C_{1}$ and $C_{2}$ of the Lie algebra of the de Sitter group using the constraint given in the linearization of $C_{2}$ as input to linearize $C_{1}$. In this way we obtain an equation that we called \textbf{DHESS1,}which in previous studies by other authors was simply postulated.$.$Next we derive a wave equation (called \textbf{DHESS2}) for a free spin $1/2$ fermion in the de Sitter manifold using a heuristic argument which is an obvious generalization of a heuristic argument (described in detail in Appendix D) permitting a derivation of the Dirac equation in Minkowski spacetime and which shows that such famous equation express nothing more than the fact that the momentum of a free particle is a constant vector field over timelike \ integral curves of a given velocity field. It is a remarkable fact that \textbf{DHESS1}and \textbf{DHESS2}\ coincide. One of the main ingredients in our paper is the use of the concept of Dirac-Hestenes spinor fields. Appendices B and C recall this concept and its relation with covariant Dirac spinor fields usualy used by physicists.

math-ph↗