Quantum Foundations

The principle of information causality, proposed as a generalization of no signaling principle, has efficiently been applied to outcast beyond quantum correlations as unphysical. In this talk, we show that this principle, when utilized properly, can provide physical rationale toward structural derivation of multipartite quantum systems. In accordance with the no signaling condition, the state and effect spaces of a composite system can allow different possible mathematical descriptions, even when descriptions for the individual systems are assumed to be quantum. While in one extreme, namely, the maximal tensor product composition, the state space becomes quite exotic and permits composite states that are not allowed in quantum theory, the other extreme - minimal tensor product composition - contains only separable states, and the resulting theory allows only Bell local correlation. As we show, none of these compositions is commensurate with information causality, and hence cannot be the bona-fide description of nature. Information causality therefore promises an information-theoretical derivation of self duality of the state and effect cones for composite quantum systems.

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The field of indefinite order in quantum theory was born from an attempt to construct a theory of quantum gravity, where the first step is to construct a generalized quantum theory in which events could have an indefinite order [1]. It is expected that such a theory would lead us more naturally to the construction of a quantum gravity theory. One way to explore this topic operationally is to consider that two agents Alice and Bob apply operations A and B on a given target system and that quantum mechanics holds locally for each agent [2].  The quantum switch is the simplest example of a task with indefinite order, where the order of operations applied by two agents on a target system is entangled with the state of a quantum control system. In particular, in the gravitational quantum switch, the order of these operations is entangled with the state of a quantum spacetime [3].

In this talk, I will present a recent result, where we propose a distinct protocol for performing a gravitational quantum switch [4]. One of the agents crosses the interior region of massive spherical shells in a superposition of different radii and becomes entangled with their geometry. This entanglement is used as a resource to control the order of operation in the implementation of the quantum switch. Novel features of the protocol include: i) the superposition of nonisometric geometries; ii) the existence of a region with a definite geometry; iii) the fact that the agent that experiences the superposition of geometries is in free fall, preventing information on the global geometry to be obtained by this agent.

[1] Hardy, J. Phys. A: Math. Theor. 40, 3081 (2007);
[2] Chiribella, D’Ariano, Perinotti, Valiron, PRA 88, 022318 (2013); Oreshkov, Costa, Brukner, Nat. Commun. 3, 1092 (2012).
[3] Zych, Costa, Pikovski, Brukner, Nat. Commun. 10, 3772 (2019).
[4] Móller, Sahdo, Yokomizo, arXiv:2306.10984 (2023).

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