A von Neumann Algebra Approach to Quantum Metrics Quantum Relations is popular PDF and ePub book, written by Greg Kuperberg in 2012, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, A von Neumann Algebra Approach to Quantum Metrics Quantum Relations can be Read Online from any device for your convenience.
A von Neumann Algebra Approach to Quantum Metrics Quantum Relations Book PDF Summary
In A von Neumann Algebra Approach to Quantum Metrics, Kuperberg and Weaver propose a new definition of quantum metric spaces, or W*-metric spaces, in the setting of von Neumann algebras. Their definition effectively reduces to the classical notion in the atomic abelian case, has both concrete and intrinsic characterizations, and admits a wide variety of tractable examples. A natural application and motivation of their theory is a mutual generalization of the standard models of classical and quantum error correction. In Quantum Relations Weaver defines a ``quantum relation'' on a von Neumann algebra $\mathcal{M}\subseteq\mathcal{B}(H)$ to be a weak* closed operator bimodule over its commutant $\mathcal{M}'$. Although this definition is framed in terms of a particular representation of $\mathcal{M}$, it is effectively representation independent. Quantum relations on $l^\infty(X)$ exactly correspond to subsets of $X^2$, i.e., relations on $X$. There is also a good definition of a ``measurable relation'' on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, Weaver can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and he can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. He is also able to intrinsically characterize the quantum relations on $\mathcal{M}$ in terms of families of projections in $\mathcal{M}{\overline{\otimes}} \mathcal{B}(l^2)$.
Detail Book of A von Neumann Algebra Approach to Quantum Metrics Quantum Relations PDF
- Author : Greg Kuperberg
- Release : 29 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821853412
- Genre : Mathematics
- Total Page : 153 pages
- Language : English
- PDF File Size : 9,7 Mb
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