On quasiequivalence of locally normal states

R. L. Hudson, G. R. Moody

Alexander Semenovich Holevo

Jacqueline Caminiti, Federico Capeccia, Jonathan Sorce

In quantum field theory, it is not always possible to excite one state out of another using only local operators. This paper establishes abstract algebraic criteria for (local) excitability in general quantum theories, and computes these criteria explicitly for zero-mean Gaussian states in (generalized) free field theories. We find that in this context, due to the special nature of Gaussian states, one-way excitability always implies two-way excitability, and our results generalize the "quasiequivalence theorems" of Powers, Stormer, van Daele, Araki, and Yamagami. A key role in our proof is played by the information-theoretic tool of canonical purification. In appendices, we provide a pedagogical introduction to the algebraic formulation of (generalized) free field theory.

Maarten Van den Nest, Jeroen Dehaene, Bart De Moor

Etang Chen

A facial version of superposition principle is introduced in algebraic quantum theory; similar to the quantum logic approach it exhibits characteristic features of quantum theory. It is shown that any pair of primary states satisfy the superposition principle if and only if they are quasiequivalent. A coherent sector is then defined as a quasi-equivalent class of primary states, which holds for both pure states in quantum theory and pure thermodynamic phases in quantum statistical mechanics.

É. É. Shnol