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Graduate Seminar Series

Tue., Oct. 24, 2023 11:30 a.m.

Location: ED 438

Speaker: Shane Crerar

Title: Probability of Entanglement (91 kB)

Abstract:

For Hilbert spaces H and K, with 2 ≤ dim H ≤ dim K < ∞, the set of isometries from H to the direct sum of r copies of K, denoted V^r(H;K), can be associated with the set of extensions of a faithful state ω of B(H) to states of B(K ⊗ H) that have rank at most r, denoted E ^r(ω). More precisely, there is a natural left action of scalar r × r matrices on V^r(H;K) such that the quotient V^r(H;K)/U(r) is in bijection with E ^r(ω). This allows probability measures on E ^r(ω) to be constructed from measures on V^r(H;K). The construction and properties of V^r(H;K) will be discussed, with particular attention given to the efficacy of using geometric methods to measure the probability that a given extension is entangled.