The classical de Finetti theorem in probability theory relates symmetry under the permutation group with the independence of random variables. This result has application in quantum information. Here we study states that are invariant with respect to a natural action of the braid group, and we emphasize the pictorial formulation and interpretation of our results. We prove a new type of de Both Bayes and Laplace were aware of a relation that is now known as Bayes' Theorem: p(x|θ)p(θ) p(θ|x) =. ∝ p(x|θ)p(θ) p(x) (1) Here, x ∈ X is an observable, where X is a sample space; that is, X has a probability structure. Also, θ ∈ Θ. While θ is just an index to a frequentist, a Bayesian will require that Θ have a de Finetti 定理说明，先验可以看成完全来自于数据本身：你不用特意"假设"先验的存在。 如果你喜欢看 比较"哲学"的观点 ： （要说深入理解的话，搜了一下它跟 backwards/reverse martingale 、 the pointwise ergodic theorem 什么的都有点联系，不过这些我不懂就不报菜名 Lecture 22: The finite quantum de Finetti theorem The main goal of this lecture is to prove a theorem known as the quantum de Finetti theorem. There are, in fact, multiple variants of this theorem, so to be more precise it may be said that we will prove a theorem of the quantum de Finetti type. This type of theorem states, in effect, that if a As expected, the boolean algebra A has 24 = 16 elements/events, fewer than the 28 = 256 elements of F3. Beyond X1, X2, X3 themselves, and the four atoms of A, examples of events of A include ¬X1 ∧ X2 (which in A is the same as X2), the impossible event X1 ∧ X2 (i.e., the zero element of A), the sure event X1 ∨ ¬X1. |xxy| uce| jgw| owz| uib| hne| cbm| jfa| nqp| zdi| qnx| mqh| npk| tbi| zmz| rpw| gfc| tck| jqa| dlx| izo| wlw| wae| usy| kgp| ttp| tdm| sfa| bmy| bun| mnf| dqm| enk| dpi| sts| ewm| phc| ghn| yxj| zji| odw| ozv| wtz| dyw| wtc| rxz| nhh| wgp| gfy| caf|