Related papers: Quantum de Finetti Theorems under Local Measuremen…
We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a…
According to the quantum de Finetti theorem, if the state of an N-partite system is invariant under permutations of the subsystems then it can be approximated by a state where almost all subsystems are identical copies of each other,…
We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multi-fold product states. The approximation is measured by distinguishability under fully…
When analysing quantum information processing protocols one has to deal with large entangled systems, each consisting of many subsystems. To make this analysis feasible, it is often necessary to identify some additional structure. de…
We show that $\varepsilon$-additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $\mathrm{poly}(1/\varepsilon)$. This stands in contrast to…
The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires…
De Finetti theorems show how sufficiently exchangeable states are well-approximated by convex combinations of i.i.d. states. Recently, it was shown that in many quantum information applications a more relaxed de Finetti reduction (i.e. only…
Symmetries are of fundamental interest in many areas of science. In quantum information theory, if a quantum state is invariant under permutations of its subsystems, it is a well-known and widely used result that its marginal can be…
We provide quantitative bounds on the characterisation of multiparticle separable states by states that have locally symmetric extensions. The bounds are derived from two-particle bounds and relate to recent studies on quantum versions of…
We work in a general framework where the state of a physical system is defined by its behaviour under measurement and the global state is constrained by no-signalling conditions. We show that the marginals of symmetric states in such…
The de Finetti theorem and its extensions concern the structure of multipartite probability distributions with certain symmetry properties, the paradigmatic original example being permutation symmetry. These theorems assert that such…
We present a quasipolynomial-time algorithm for solving the weak membership problem for the convex set of separable, i.e. non-entangled, bipartite density matrices. The algorithm decides whether a density matrix is separable or whether it…
We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm…
We introduce and study a new model of interactive proofs: AM(k), or Arthur-Merlin with k non-communicating Merlins. Unlike with the better-known MIP, here the assumption is that each Merlin receives an independent random challenge from…
Predicting the outcomes of quantum measurements is a cornerstone of quantum information theory and a key resource for quantum technologies. Here, we introduce a comprehensive framework for quantifying the predictability of measurements on a…
The aim of device-independent quantum key distribution (DIQKD) is to study protocols that allow the generation of a secret shared key between two parties under minimal assumptions on the devices that produce the key. These devices are…
In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…
We show how to bound the accuracy of a family of semi-definite programming relaxations for the problem of polynomial optimization on the hypersphere. Our method is inspired by a set of results from quantum information known as quantum de…