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Entangling dynamics beyond quantum theory

P. David, Remigiusz Augusiak

Published Nov 17, 2011• 2 citations
OpenAlex

Abstract

We explore the existence of entangling dynamics in a large family of theories which contains quantum theory as a special case. We classify all continuouslyreversible and locally-tomographic theories for bipartite systems where each subsystem has a state space with the geometry of a Euclidean ball (like the Bloch ball of a qubit but with dimension not necessarily equal to three). We show that the only theory in this family which has interacting dynamics is quantum theory, and all the other theories do not allow for entanglement nor violation of Bell inequalities. This suggests that, once dynamics is taken into account, entanglement and violation of Bell inequalities are very singular phenomena.

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We explore the existence of entangling dynamics in a large family of theories which contains quantum theory as a special case. We classify all continuouslyreversible and locally-tomographic theories for bipartite systems where each subsystem has a state space with the geometry of a Euclidean ball (like the Bloch ball of a qubit but with dimension not necessarily equal to three). We show that the only theory in this family which has interacting dynamics is quantum theory, and all the other theories do not allow for entanglement nor violation of Bell inequalities. This suggests that, once dynamics is taken into account, entanglement and violation of Bell inequalities are very singular phenomena.
We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state space. In addition to this we impose two very natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories interacting dynamics is impossible. This result reveals that "existence of entanglement" is the requirement with minimal logical content which singles out quantum theory from our family of theories.
We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state space. In addition to this, we impose two very natural assumptions: the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories, interacting dynamics is impossible. This result reveals that “existence of entanglement” is the requirement with minimal logical content which singles out quantum theory from our family of theories.
We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of generalized Bell inequalities are summarized. We investigate maximal violations of Bell inequalities as well as states not violating (certain) Bell inequalities. Finally, we discuss the relation between Bell inequality violations and entanglement properties currently discussed in quantum information theory.
We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of generalized Bell inequalities are summarized. We investigate maximal violations of Bell inequalities as well as states not violating (certain) Bell inequalities. Finally, we discuss the relation between Bell inequality violations and entanglement properties currently discussed in quantum information theory.
We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of generalized Bell inequalities are summarized. We investigate maximal violations of Bell inequalities as well as states not violating (certain) Bell inequalities. Finally, we discuss the relation between Bell inequality violations and entanglement properties currently discussed in quantum information theory.
Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite systems. We provide a general construction of genuinely multipartite entangled states that do not display genuinely multipartite nonlocality, thus proving that entanglement and nonlocality are inequivalent for any number of parties.