相关论文: Towards a skew lattice approach to quantum (comput…

In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…

The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatable groupoids are proved. Necessary and sufficient…

A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…

In this paper we study the quantum generalisation of the skew divergence, which is a dissimilarity measure between distributions introduced by L. Lee in the context of natural language processing. We provide an in-depth study of the quantum…

We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…

It is shown that two observers have mutually commuting observables if they are able to prepare in each subsector of their common state space some state exhibiting no mutual correlations. This result establishes a heretofore missing link…

As has already been pointed out by Birkhoff and von Neumann, quantum logic can be formulated in terms of projective geometry. In three-dimensional Hilbert space, elementary logical propositions are associated with one-dimensional subspaces,…

Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…

We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The…

Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct…

The perturbation theory is developed based on small parameters which naturally appear in solid state quantum computation. We report the simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A…

Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…

Quantum mechanics, devoid of any additional assumption, does not give any theoretical constraint on the projection basis to be used for the measurement process. It is shown in this paper that it does neither allow any physical means for an…

Considering the simultaneous measurement of non-commuting observables, we define a geometric measure for the degree of non-commuting behavior of quantum measurements coming from the initial and final states of the measurements. The…

Joint, or simultaneous, measurements of non-commuting observables are possible within quantum mechanics, if one accepts an increase in the variances of the jointly measured observables. In this paper, we discuss joint measurements of a spin…

A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial…

Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…

Everett's interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves…

Non-commutative quantum physics at the atom scale can arise from coarse graining of a classical statistical ensemble at the Planck scale. Position and momentum of an isolated particle are classical observables which remain computable in…

It is shown that quantum logic is a logic in the very same way in which classical logic is a logic. Soundness and completeness of both quantum and classical logics have been proved for novel lattice models that are not orthomodular and…