Related papers: Quantum stochastic integrals as operators
Schwinger's quantization scheme is extended in order to solve the problem of the formulation of quantum mechanics on a space with a group structure. The importance of Killing vectors in a quantization scheme is showed. Usage of these…
We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the…
We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. As usual, we define these local observables by their form factors; but rather than exhibiting their $n$-point functions…
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
We start with a discussion of the use of mathematics to model the real world then justify the role of Hilbert space formalism for such modelling in the general context of quantum logic. Following this, the incompleteness of the…
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to…
A natural counterpart to the Lie-Trotter product formula for norm-continuous one-parameter semigroups is proved, for the class of quasicontractive quantum stochastic operator cocycles whose expectation semigroup is norm continuous. Compared…
A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…
We present a method for constructing a quantum Markov partition. Its elements are obtained by quantizing the characteristic function of the classical rectangles. The result is a set of quantum operators which behave asymptotically as…
We express the probabilistic character associated to the wave function by treating it as a stochastic variable. This is accomplished by means of a stochastic equation for the wave function whose noise changes the phase of the wave function…
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private…
A new model of quantum computing has recently been proposed which, in analogy with a classical lambda-calculus, exploits quantum processes which operate on other quantum processes. One such quantum meta-operator takes N unitary…
In this paper the quantum integrals of the Hamiltonian of the quantum many-body problem with the interaction potential K/sinh^2(x) (Sutherland operator) are constructed as images of higher Casimirs of the Lie algebra gl(N) under a certain…
We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, the fractional integration operator is a martingale transform, however, it may vanish if the filtration is excessively…
Integrable quantum computation is defined as quantum computing via the integrable condition, in which two-qubit gates are either nontrivial unitary solutions of the Yang--Baxter equation or the Swap gate (permutation). To make the…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Canonical coordinates for the Schr\"odinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schr\"odinger equation, considered as a classical field theory, shares with Liouville completely…