Despite advances in artificial intelligence models, neural networks still cannot achieve human performance, partly due to differences how information is encoded and processed compared brain. Information an network (ANN) represented using a statistical method as fitting function, enabling handling of structural patterns image, text, speech processing. However, substantial changes the characteris...

A combination of a finite number linear independent states forms superposition in way that cannot be conceived classically. Here, using the tools resource theory superposition, we give conditions for class state transformations. These strictly depend on scalar products basis and reduce to well-known majorization condition quantum coherence limit orthonormal basis. To further superposition-free ...

Abstract We characterize all pairs of entire functions $$(u,\psi )$$ ( u , ψ ) for which the induced weighted superposition operator $$S_{(u,\psi )}$$ S transforms one Fock space ...

Attacks on cryptographic protocols are usually modeled by allowing an adversary to ask queries to an oracle. Security is then defined by requiring that as long as the queries satisfy some constraint, there is some problem the adversary cannot solve, such as compute a certain piece of information. Even if the protocol is quantum, the queries are typically classical. In this paper, we introduce a...

Attention is focused on continuous-space shift-invariant systems with continuous system maps and inputs and outputs that are elements of L∞(IR ). It is shown that infinite superposition can fail in this important setting. It is also shown that continuous shift-invariant linear mappings need not commute with the operation of integration (even when the two composite operations are well defined). ...