The simplex of tracial quantum symmetric states
نویسندگان
چکیده
منابع مشابه
Symmetric States in Quantum Geometry
Symmetric states are defined in the kinematical sector of loop quantum gravity and applied to spherical symmetry and homogeneity. Consequences for the physics of black holes and cosmology are discussed.
متن کاملFree Fisher Information for Non-tracial States
We extend Voiculescu’s microstates-free definitions of free Fisher information and free entropy to the non-tracial framework. We explain the connection between these quantities and free entropy with respect to certain completely positive maps acting on the core of the non-tracial non-commutative probability space. We give a condition on free Fisher information of an infinite family of variables...
متن کاملExtremal Marginal Tracial States in Coupled Systems
Let Γ be the convex set consisting of all states φ on the tensor product B ⊗ B of the algebra B = Mn(C) of all n × n matrices over the complex numbers C with the property that the restrictions φ B⊗I and φ I⊗B are the unique tracial states on B ⊗ I and I ⊗ B . We find necessary and sufficient conditions for such a state, called a marginal tracial state, to be extremal in Γ . We also give a chara...
متن کاملA Tracial Quantum Central Limit Theorem
We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples converges to a classical limit. The proof is based on a central limit theorem for ordered joint distributions together with a commutator estimate related to the Baker-Campbell-Hausdorff expansion. The result can be cons...
متن کاملComputational Distinguishability between Quantum States: Random Coset States vs. Maximally Mixed States over the Symmetric Groups
We introduce a new underlying problem for computational cryptographic schemes secure against quantum adversaries. The problem is a distinction problem between quantum states which is a natural generalization of distinction problems between probability distributions, which are commonly used in computational cryptography. Specifically speaking, our problem QSCDff is defined as a quantum state com...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2014
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm225-3-2