Hi all,
Tomorrow Paula Belzig will present her master's thesis on de Finetti theorems, which is joint between Uni Köln and ETH. See below for title and abstract.
Best,
-joe
Title: Studying Stabilizer de Finetti Theorems - Applications in Quantum Information Processing
Abstract: If a quantum state is invariant under permutations of its subsystems, it is a well-known and widely used result in quantum theory that its marginal can be approximated by a mixture of tensor powers of a state on a single subsystem. Recently, it has been discovered by Gross, Nezami and Walter that a similar observation can be made for a larger symmetry group than permutations: states that are invariant under stochastic orthogonal symmetry are approximated by tensor powers of stabilizer states, with an exponentially smaller approximation error than previously possible.
Quantum de Finetti theorems find application in various contexts, in particular in QKD and in numerical separability tests, which we explore here using the stabilizer de Finetti theorem instead of the permutation-based version. On the one hand, when analyzing a QKD protocol with stochastic orthogonal invariance, we find that its security against general, most powerful attacks can be inferred from its security against collective attacks with a smaller change in the security parameter compared to permutation-based considerations. On the other hand, we show that the stabilizer de Finetti theorem can lead to a semi-definite programming hierarchy approximating separable and partly stabilizer states, which facilitates studying the optimal Clifford encoder or decoder for a given quantum error correction procedure.