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.