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The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…
Parametrically driven oscillators can emerge as a basis for the next generation of qubits. Classically, these systems exhibit two stable oscillatory states with opposite phases. Upon quantization, these states turn into a pair of closely…
Quantum cascade lasers are recognized as propitious candidates for future terahertz optoelectronics. Here we demonstrate several definite advantages of quantum dot cascade structures over quantum well devices, which suffer fundamental…
We introduce action quantum speed limits (QSLs) as a family of bounds on the minimal time to connect two states that, unlike the usual geometric approach, crucially depend on how the path is traversed, i.e. on the instantaneous speed. The…
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
We consider quantum trajectories of composite systems as generated by the stochastic unraveling of the respective Lindblad-master-equation. Their classical limit is taken to correspond to local jumps between orthogonal states. Based on…
We present a proposal for quantum information processing with neutral atoms trapped in optical lattices as qubits. Initialization and coherent control of single qubits can be achieved with standard laser cooling and spectroscopic…
We describe a nonstandard version of the quantum plane, the one in the basis of divided powers at an even root of unity $q=e^{i\pi/p}$. It can be regarded as an extension of the "nearly commutative" algebra $C[X,Y]$ with $X Y =(-1)^p Y X$…
In a recent paper [9], R. E. Curto, S. H. Lee and J. Yoon asked the following question: Let $T$ be a subnormal operator, and assume that $T^2$ is quasinormal. Does it follow that $T$ is quasinormal?. In [36] we answered this question in the…
The primary purpose of this paper is to show the existence of normal square and nth roots of some classes of bounded operators on Hilbert spaces. Two interesting simple results hold. Namely, under simple conditions we show that if any…
Quantum gravity remains an elusive theory, in spite of our thorough understanding of the quantum theory and the general theory of relativity separately, presumably due to the lack of any observational clues. We argue that the theory of…
In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum…
We consider the question of asymptotic stability of quantum trajectories undergoing quantum non-demolition imperfect measurement, that is to say the convergence of the estimated trajectory towards the true trajectory whose parameters and…
We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension.…
Transition operator method is proposed for description of the dynamics of spectroscopic transitions. Quantum-mechanical analogue of Landau-Lifshitz equation has been derived for the system representing itself the periodical…
We consider the definition of quantum walks on directed graphs. Call a directed graph reversible if, for each pair of vertices (i, j), if i is connected to j then there is a path from j to i. We show that reversibility is a necessary and…
This paper presents a scheme for linear-optical implementation of a programmable quantum router. Polarization encoded photon qubit is coherently routed to various spatial modes according to the state of several control qubits. In our…
The proposal that the one-parameter solutions of the real part of the Schrodinger equation (quantum Hamilton-Jacobi equation) can be regarded as `quantum particle trajectories' has received considerable attention recently. Opinions as to…
In the foreseeable future, toolchains for quantum computing should offer automatic means of transforming a high level problem formulation down to a hardware executable form. Thereby, it is crucial to find (multiple) transformation paths…