Related papers: Universal Procedure for Enforcing Quantum Constrai…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
We explicitly construct an Archimedean order unit space whose state space is affinely isomorphic to the set of quantum commuting correlations. Our construction only requires fundamental techniques from the theory of order unit spaces and…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
We describe an approach for characterizing the process of quantum gates using quantum process tomography, by first modeling them in an extended Hilbert space, which includes non-qubit degrees of freedom. To prevent unphysical processes from…
We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous…
A full quantum mechanical treatment of open quantum systems via a Master equation is often limited by the size of the underlying Hilbert space. As an alternative, the dynamics can also be formulated in terms of systems of coupled…
An effective, accessible abstraction hierarchy has made using and programming computers possible for people across all disciplines. Establishing such a hierarchy for quantum programming is an outstanding challenge, especially due to a…
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a…
For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises…
We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a…
A complete perturbative expansion for the Hamiltonian describing the motion of a quantomechanical system constrained to move on an arbitrary submanifold of its configuration space $R^n$ is obtained.
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…
In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of "physical experiment" and assuming "experimental accessibility and simplicity" as specified by…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
We introduce a master constraint operator on the kinematical Hilbert space of loop quantum gravity representing a set of gauge conditions which classically fix the densitized triad to be diagonal. We argue that the master constraint…
We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…