• Corpus ID: 248495990

Gleason's theorem for composite systems

@inproceedings{Frembs2022GleasonsTF,
  title={Gleason's theorem for composite systems},
  author={Markus Frembs and Andreas Doring},
  year={2022}
}
Gleason’s theorem [25] is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it presents a key insight into the projective geometry of Hilbert spaces, showing that finitely additive measures on the projection lattice P(H) extend to positive linear functionals on the algebra of bounded operators B(H) . Over many years, and by the effort of various authors, the theorem has been broadened in… 

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References

SHOWING 1-10 OF 51 REFERENCES

Getting to the Bottom of Noether's Theorem

We examine the assumptions behind Noether's theorem connecting symmetries and conservation laws. To compare classical and quantum versions of this theorem, we take an algebraic approach. In both

Bohrification of operator algebras and quantum logic

It is proved that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski–Mulvey) of the “Bohrification” of A, which is a commutative Rickart C*-algebra in the topos of functors from A to the category of sets.

Kochen–Specker Theorem for von Neumann Algebras

The Kochen–Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind

Contextuality and the fundamental theorems of quantum mechanics

Contextuality is a key feature of quantum mechanics, as was first brought to light by Bohr [ Albert Einstein: Philosopher-Scientist, Library of Living Philosophers Vol. VII, edited by P. A. Schilpp

Quantum measures and states on Jordan algebras

A problem of Mackey for von Neumann algebras has been settled by the conjunction of the early work of Gleason and the recent advances of Christensen and Yeadon. We show that Mackey's conjecture holds

A Topos for Algebraic Quantum Theory

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr’s idea that the empirical

The Mackey-Gleason Problem

Let A be a von Neumann algebra with no direct summand of Type I 2 , and let P(A) be its lattice of projections. Let X be a Banach space. Let m:P(A)→X be a bounded function such that m(p+q)=m(p)+m(q)

The Representation of Physical Quantities With Arrows δ̆ o ( A ) : Σ →

This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to

A topos foundation for theories of physics: II. Daseinisation and the liberation of quantum theory

This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise

A Topos Perspective on the Kochen-Specker Theorem II. Conceptual Aspects and Classical Analogues

In a previous paper, we proposed assigning asthe value of a physical quantity in quantum theory acertain kind of set (a sieve) of quantities that arefunctions of the given quantity. The motivation
...