Related papers: A de Finetti theorem for quantum causal structures
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
We define syntax and semantics of quantum circuits, allowing measurement gates and classical channels. We define circuit-based quantum algorithms and prove that, semantically, any such algorithm is equivalent to a single measurement that…
Quantum teleportation is a very helpful information-theoretic protocol that allows to transfer an unknown arbitrary quantum state from one location to another without having to transmit the quantum system through the intermediate region.…
One of the essential building blocks of classical computer programs is the "if" clause, which executes a subroutine depending on the value of a control variable. Similarly, several quantum algorithms rely on applying a unitary operation…
If a unitary transformation has a decomposition into a quantum circuit with no directed path from input $a$ to output $b$, then $a$ does not influence $b$ through the overall unitary. Conversely, it is known that if $a$ does not influence…
For the quantum stochastic processes generated by the Boolean Commutation Relations, we prove the following version of De Finetti Theorem: each of such Boolean process is exchangeable if and only if it is independent and identically…
A quantum process encodes the causal structure that relates quantum operations performed in local laboratories. The process matrix formalism includes as special cases quantum mechanics on a fixed background space-time, but also allows for…
Quantum coherence plays a fundamental and operational role in different areas of physics. A resource theory has been developed to characterize the coherence of distinguishable particles systems. Here we show that indistinguishability of…
Reconstructions of quantum theory usually implicitly assume that experimental events are ordered within a global causal structure. The process matrix framework accommodates quantum correlations that violate an inequality verified by all…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable…
Understanding quantum theory's causal structure stands out as a major matter, since it radically departs from classical notions of causality. We present advances in the research program of causal decompositions, which investigates the…
A crucial question is how objective and classical behavior arises from a fundamental physical theory. Here we provide a natural definition of a decoherence process valid in all causal theories, and show how its behavior can be extremely…
Causality has been often confused with the notion of determinism. It is mandatory to separate the two notions in view of the debate about quantum foundations. Quantum theory provides an example of causal not-deterministic theory. Here we…
Finding a causal model for a set of classical variables is now a well-established task---but what about the quantum equivalent? Even the notion of a quantum causal model is controversial. Here, we present a causal discovery algorithm for…
More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case…
We study sequences of noncommutative random variables which are invariant under "quantum transformations" coming from an orthogonal quantum group satisfying the "easiness" condition axiomatized in our previous paper. For 10 easy quantum…
A central question for causal inference is to decide whether a set of correlations fit a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for…
A number of phenomena generally believed characteristic of quantum mechanics and seen as interpretively problematic--the incompatibility and value-indeterminacy of variables, the non-existence of dispersion-free states, the failure of the…
We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical…