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 Vr(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 Vr(H;K) such that the quotient Vr(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 Vr(H;K). The construction and properties of Vr(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.