Related papers: Lindblad evolutions, Born rule, Heralding and clon…
The aim of the famous Born and Jordan 1925 paper was to put Heisenberg's matrix mechanics on a firm mathematical basis. Born and Jordan showed that if one wants to ensure energy conservation in Heisenberg's theory it is necessary and…
In previous work of the authors, we investigated the Born and inverse Born series for a scalar wave equation with linear and nonlinear terms, the nonlinearity being cubic of Kerr type [8]. We reported conditions which guarantee convergence…
We deduce the Born rule. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics--a linear, not Hilbert', vector space--and empirical notion of the statistical length of a state. Its statistical nature…
We suggest and describe how to analyze new types of experiments that would test a proposed model of the quantum measurement process. That model produces the Born Rule as a corollary, and so agrees with conventional quantum predictions. The…
In this paper, we consider the evolution of an (infinitely large) population under recombination and additional evolutionary forces, modelled by a measure-valued ordinary differential equation. We provide a stochastic representation for the…
A model of correlated particles described by a generalized probability theory is suggested whose dynamics is subject to a non-linear version of Schr\"odinger equation. Such equations arise in many different contexts, most notably in the…
Recenty Abrams and Lloyd have proposed a fast algorithm that is based on a nonlinear evolution of a state of a quantum computer. They have explicitly used the fact that nonlinear evolutions in Hilbert spaces do not conserve scalar products…
We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-hermitian Hamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an additional…
We compare different quantum Master equations for the time evolution of the reduced density matrix. The widely applied secular approximation (rotating wave approximation) applied in combination with the Born-Markov approximation generates a…
The non-linear second order Born-Infeld equation is reduced to a simpler first order complex equation, which can be trivially solved for the coordinates as functions of the field. Each solution is determined by the choice of a holomorphic…
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As…
The Lindblad equation is a widely used quantum master equation to model the dynamical evolution of open quantum systems whose states are described by density matrices. These solution matrices are characterized by semi-positiveness and trace…
The problem of black-body radiation is considered in the Born-Infeld theory of electrodynamics. In particular, at 2-loop order the deviation from the Planck expression due to the self-interaction of photons is calculated. It is seen that…
Distributing entangled states over potentially long distances provides a key resource for many protocols in quantum communication and quantum cryptography. Ideally, this should be implemented in a heralded manner. By starting with four…
We propose a protocol to realize atomic nonadiabatic holonomic quantum computation (NHQC) with two computational atoms and an auxiliary atom. Dynamics of the system is analyzed in the regime of Rydberg blockade, and robust laser pulses are…
The apparent discrepancy between the Rosenbluth and the polarization transfer method for the ratio of the electric to magnetic proton form factors can be explained by a two-photon exchange correction which does not destroy the linearity of…
We propose and study a toy model for the quantum measurements that yield the Born's rule of quantum probability. In this model, the electrons interact with local photon modes and the photon modes are dissipatively coupled with local photon…
We present a derivation of the Lindblad equation - an important tool for the treatment of non-unitary evolutions - that is accessible to undergraduate students in physics or mathematics with a basic background on quantum mechanics. We…
Entanglement is the basic building block of linear optical quantum computation, and as such understanding how to generate it in detail is of great importance for optical architectures. We prove that Bell states cannot be generated using…
We show that optimal universal cloning of the polarization state of photons can be achieved via stimulated emission in three-level systems, both of the Lambda and the V type. We establish the equivalence of our systems with coupled harmonic…