Related papers: Quantum Mechanics of Stochastic Systems
We show that for a particular model, the quantum mechanical bootstrap is capable of finding exact results. We consider a solvable system with Hamiltonian $H=SZ(1-Z)S$, where $Z$ and $S$ satisfy canonical commutation relations. While this…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…
Random numbers are a valuable commodity in gaming and gambling, simulation, conventional and quantum cryptography, and in non-conventional computing schemes such as stochastic computing. We propose to generate a random bit using a position…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
This paper is concerned with the generation of Gaussian invariant states in cascades of open quantum harmonic oscillators governed by linear quantum stochastic differential equations. We carry out infinitesimal perturbation analysis of the…
Stochastic realization of the wave function in quantum mechanics, with the inclusion of soliton representation of extended particles, is discussed. The concept of Stochastic Qubits is used for quantum computing modeling.
In classical physics the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, unidirectional transfer of population between the densely and sparsely populated…
Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…
We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos…
The ability to distill quantum coherence is pivotal for optimizing the performance of quantum technologies; however, such a task cannot always be accomplished with certainty. Here we develop a general framework of probabilistic distillation…
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…
We present an analysis of quantum mechanics and its problems and paradoxes taking into account the results that have been obtained during the last two decades by investigations in the field of `quantum structures research'. We concentrate…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
Randomness is a fundamental aspect of quantum mechanics, arising from the measurement process that collapses superpositions into definite outcomes according to Born's rule. Generating large-scale random quantum states is crucial for quantum…
The reconstruction of quantum states from experimental measurements, often achieved using quantum state tomography (QST), is crucial for the verification and benchmarking of quantum devices. However, performing QST for a generic…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…