We present a new quantum algebraic description of an electron localized in space-time. Positions in space and time, mass and Clifford generators are defined as quantum operators. Commutation relations and relativistic shifts under frame transformations are determined within a unique algebraic framework. Redshifts, i.e. shifts under transformations to uniformly accelerated frames, are evaluated and found to differ from the expressions of classical relativity.
We have studied entanglement between two Dirac modes respectively observed by two independently accelerated observers. Due to Unruh effect, the entanglement degrades, but residual nonzero entanglement remains even when the accelerations of both observers are infinite. We have also investigated quantum teleportation using entangled Dirac modes, and calculated the fidelities in various cases. In general, the fidelity depends on the single-qubit state $γ|0\rangle +δ|1\rangle$ to be teleported, as well as which Bell state to use. In the limit that both accelerations are infinite, the average fidel…
In this paper we study the Dirac equation in the Rindler spacetime. The solution of the wave equation in an accelerated reference frame is obtained. The differential equation associated to this wave equation is mapped into a Sturm-Liouville problem of a Schrödinger-like equation. We derive a compact expression for the energy spectrum associated with the Dirac equation in an accelerated reference. It is shown that the noninertial effect of the accelerated reference frame mimics an external potential in the Dirac equation and, moreover, allows the formation of bound states.
Entanglement of Dirac fields has been studied and it is known to decrease with increasing acceleration when a quantum state is shared between users in non-inertial frames. A new form of an entangled vacuum state observed by the accelerated observer is postulated in which it is assumed that entanglement is present between the modes of the quantum field with sharp and opposite momenta defined in two causally disconnected regions of space-time. We find that this assumption does not affect the entanglement of the system.
We describe a method of construction of gauge-invariant operators (Dirac observables or ``evolving constants of motion'') from the knowledge of the eigenstates of the gauge generator in time-reparametrization invariant mechanical systems. These invariant operators evolve unitarily with respect to an arbitrarily chosen time variable. We emphasize that the dynamics is relational, both in the classical and quantum theories. In this framework, we show how the ``emergent Wentzel-Kramers-Brillouin time'' often employed in quantum cosmology arises from a weak-coupling expansion of invariant transitio…
Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to properly account for non-classical features in the context of condensed matter physics (scrambling, dynamical phase transitions) metrology (standard and post-selected), thermodynamics (power output and fluctuation theorems), foundations (contextuality, anomalous weak values) and more. Given the growing relevance of the KDQ across the quantum sciences, our aim is two-fold: First, we highlight the role played by quasiprobabilities in characterizing the statistics of quantum observables and …
We present a mathematical formalism of non-Hermitian quantum mechanics, following the Dirac-von Neumann formalism of quantum mechanics. In this formalism, the state postulate is the same as in the Dirac-von Neumann formalism, but the observable postulate should be changed to include para-Hermitian operators (spectral operators of scalar type with real spectrum) representing observable, as such both the measurement postulate and the evolution postulate must be modified accordingly. This is based on a Stone type theorem as proved here that the dynamics of non-Hermitian quantum systems is governe…
In this paper, we study a proposal put forward recently by Bodendorfer, Mele and Münch and Garc\'ıa-Quismondo and Marugán, in which the two polymerization parameters of spherically symmetric black hole spacetimes are the Dirac observables of the four-dimensional Ashtekar's variables. In this model, black and white hole horizons in general exist and naturally divide the spacetime into the external and internal regions. In the external region, the spacetime can be made asymptotically flat by properly choosing the dependence of the two polymerization parameters on the Ashtekar variables. Then, we…
We present a scheme to describe the dynamics of accelerating discrete-time quantum walk for one- and two-particle in position space. We show the effect of acceleration in enhancing the entanglement between the particle and position space in one-particle quantum walk and in generation of entanglement between the two unentangled particle in two-particle quantum walk. By introducing the disorder in the form of phase operator we study the transition from localization to delocalization as a function of acceleration. These inter-winding connection between acceleration, entanglement generation and lo…
