Related papers: The quantum de Finetti representation for the Baye…
In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for…
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.…
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…
Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. The classical de Finetti's theorem provides a representation of infinitely…
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…
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…
Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number…
In Everettian quantum mechanics, justifications for the Born rule appeal to self-locating uncertainty or decision theory. Such justifications have focused exclusively on a pure-state Everettian multiverse, represented by a wave function.…
The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In…
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…
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…
For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist,…
What does it mean for a causal structure to be `unknown'? Can we even talk about `repetitions' of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary,…
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…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
Quantum theory has evolved from a set of provisional rules to an indispensable framework that underlies much of modern technology and infrastructure. Yet, after a century, Born's probability postulate remains at odds with the theory's…
The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum…
Probabilities in quantum theory are traditionally given by Born's rule as the expectation values of projection operators. Here it is shown that Born's rule is insufficient in universes so large that they contain identical multiple copies of…