There are infinite frames of reference at once while taking into account the motion of an object and all of them can be superposed to one another forming a dynamical net frame bundle. This results in a non-Hilbert space which represents a kind of state space of the object at hand. It will be shown that a particular type of this non-Hilbertian structure can be used to represent all elementary systems as the quantum counterpart of the net frame bundle. In order to achieve such a result, it is mandatory to adopt a nonstandard quantum field theoretical approach in which the mass distribution and the gauge conditions of a physical system are intrinsically connected.There are infinite frames of reference at once while taking into account the motion of an object and all of them can be superposed to one another forming a dynamical net frame bundle. This results in a non-Hilbert space which represents a kind of state space of the object at hand. It will be shown that a particular type of this non-Hilbertian structure can be used to represent all elementary systems as the quantum counterpart of the net frame bundle. In order to achieve such a result, it is mandatory to adopt a nonstandard quantum field theoretical approach in which the mass distribution and the gauge conditions of a physical system are intrinsically connected.

Jun 14, 20223 citations

QUANTUM THEORY WITHOUT THE SUPERPOSITION PRINCIPLE.

И.С. Шапиро

Jan 1, 19720 citations

The Hilbertian Tensor Norm and its Connection to Quantum Information Theory

Dejan D. Dukaric

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.

arXiv:1008.1948Aug 11, 20104 citations

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm

\gamma_2

and its dual

\gamma_2^*

that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.