Related papers: A de Finetti representation for finite symmetric q…

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…

The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, towards probabilistic mixtures of independent and…

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…

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 formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a…

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…

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…

Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other.…

Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing to bound the error made by mean-field approaches. Such…

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…

Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…

Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…

The quantum de Finetti theorem says that, given a symmetric state, the state obtained by tracing out some of its subsystems approximates a convex sum of power states. The more subsystems are traced out, the better this approximation…

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…

Permutation symmetries of multipartite quantum states are defined only when the constituent subsystems are of equal dimensions. In this work we extend this notion of permutation symmetry to heterogeneous systems, that is, systems composed…

We prove a new kind of quantum de Finetti theorem for representations of the unitary group U(d). Consider a pure state that lies in the irreducible representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained in the tensor…

De Finetti theorems tell us that if we expect the likelihood of outcomes to be independent of their order, then these sequences of outcomes could be equivalently generated by drawing an experiment at random from a distribution, and…

We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti's classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z.…

Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally…

We prove a generalization of the quantum de Finetti theorem when the local space is an infinite-dimensional Fock space. In particular, instead of considering the action of the permutation group on $n$ copies of that space, we consider the…