Phase entanglement negativity for bipartite fermionic systems

B Xu, X Qi, J Hou - Physical Review A, 2024 - APS
We discuss the behavior of positive linear maps in fermionic systems and then propose the
phase partial transpose and the phase entanglement negativity. We show that every …

X-arability of mixed quantum states

H Derksen, N Johnston, B Lovitz… - arXiv preprint arXiv …, 2024 - arxiv.org
The problem of determining when entanglement is present in a quantum system is one of
the most active areas of research in quantum physics. Depending on the setting at hand …

Ergodic theorems in quantum probability: an application to the monotone stochastic processes

V Crismale, F Fidaleo, YG Lu - arXiv preprint arXiv:1505.04688, 2015 - arxiv.org
We give sufficient conditions ensuring the strong ergodic property of unique mixing for $ C^*
$-dynamical systems arising from Yang-Baxter-Hecke quantisation. We discuss whether …

Tail algebras for monotone and q-deformed exchangeable stochastic processes

V Crismale, S Rossi - Annali di Matematica Pura ed Applicata (1923-), 2023 - Springer
We compute the tail algebras of exchangeable monotone stochastic processes. This allows
us to prove the analogue of de Finetti's theorem for this type of processes. In addition, since …

Exchangeable stochastic processes and symmetric states in quantum probability

V Crismale, F Fidaleo - Annali di Matematica Pura ed Applicata (1923-), 2015 - Springer
We analyze general aspects of exchangeable quantum stochastic processes, as well as
some concrete cases relevant for several applications to Quantum Physics and Probability …

De Finetti-type theorems on quasi-local algebras and infinite Fermi tensor products

V Crismale, S Rossi, P Zurlo - Infinite Dimensional Analysis …, 2023 - World Scientific
Local actions of ℙ ℕ, the group of finite permutations on ℕ, on quasi-local algebras are
defined and proved to be ℙ ℕ-abelian. It turns out that invariant states under local actions …

Wick order, spreadability and exchangeability for monotone commutation relations

V Crismale, F Fidaleo, ME Griseta - Annales Henri Poincaré, 2018 - Springer
We exhibit a Hamel basis for the concrete*∗-algebra M _o M o associated to monotone
commutation relations realised on the monotone Fock space, mainly composed by Wick …

-fermi systems and detailed balance

V Crismale, R Duvenhage, F Fidaleo - Analysis and Mathematical Physics, 2021 - Springer
A systematic theory of product and diagonal states is developed for tensor products of Z _2 Z
2-graded*∗-algebras, as well as Z _2 Z 2-graded C^* C∗-algebras. As a preliminary step to …

Failure of the Ryll-Nardzewski theorem on the CAR algebra

V Crismale, S Rossi - Journal of Functional Analysis, 2022 - Elsevier
Spreadability of a sequence of random variables is a distributional symmetry that is
implemented by suitable actions of JZ, the unital semigroup of strictly increasing maps on Z …

Symmetries and ergodic properties in quantum probability

V Crismale, F Fidaleo - arXiv preprint arXiv:1609.09856, 2016 - arxiv.org
We deal with the general structure of (noncommutative) stochastic processes by using the
standard techniques of Operator Algebras. Any stochastic process is associated to a state on …