Physics – Quantum Physics
Scientific paper
2005-06-16
Physics
Quantum Physics
Essential simplification of the definitions of orthostructure and ortho-Bornian structure: the key new insights is captured by
Scientific paper
Elaborating on our joint work with Abramsky in quant-ph/0402130 we further unravel the linear structure of Hilbert spaces into several constituents. Some prove to be very crucial for particular features of quantum theory while others obstruct the passage to a formalism which is not saturated with physically insignificant global phases. First we show that the bulk of the required linear structure is purely multiplicative, and arises from the strongly compact closed tensor which, besides providing a variety of notions such as scalars, trace, unitarity, self-adjointness and bipartite projectors, also provides Hilbert-Schmidt norm, Hilbert-Schmidt inner-product, and in particular, the preparation-state agreement axiom which enables the passage from a formalism of the vector space kind to a rather projective one, as it was intended in the (in)famous Birkhoff & von Neumann paper. Next we consider additive types which distribute over the tensor, from which measurements can be build, and the correctness proofs of the protocols discussed in quant-ph/0402130 carry over to the resulting weaker setting. A full probabilistic calculus is obtained when the trace is moreover linear and satisfies the \em diagonal axiom, which brings us to a second main result, characterization of the necessary and sufficient additive structure of a both qualitatively and quantitatively effective categorical quantum formalism without redundant global phases. Along the way we show that if in a category a (additive) monoidal tensor distributes over a strongly compact closed tensor, then this category is always enriched in commutative monoids.
No associations
LandOfFree
De-linearizing Linearity: Projective Quantum Axiomatics from Strong Compact Closure does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with De-linearizing Linearity: Projective Quantum Axiomatics from Strong Compact Closure, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and De-linearizing Linearity: Projective Quantum Axiomatics from Strong Compact Closure will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-5396