Composition of Multipartite Quantum Systems: Perspective from Timelike Paradigm

Figuring out the physical rationale behind natural selection of quantum theory is one of the most acclaimed quests in quantum foundational research. This pursuit has inspired several axiomatic initiatives to derive a mathematical formulation of the theory by identifying the general structure of state and effect space of individual systems as well as specifying their composition rules. This generic framework can allow several consistent composition rules for a multipartite system even when state and effect cones of individual subsystems are assumed to be quantum. Nevertheless, for any bipartite system, none of these compositions allows beyond quantum spacelike correlations. In this Letter, we show that such bipartite compositions can admit stronger-than-quantum correlations in the timelike domain and, hence, indicates pragmatically distinct roles carried out by state and effect cones. We discuss consequences of such correlations in a communication task, which accordingly opens up a possibility of testing the actual composition between elementary quanta.

Figure 1

Intuitive representation of the state and effect cones for different compositions of two individual quantum systems. (a) SEP theory: Only separable states are allowed, whereas effects are more exotic than the effects allowed in quantum theory. (b) Quantum theory: The state cone and effect cone exactly overlap (self-dual). (c) $\overline{\mathrm{SEP}}$ theory: The effect cone is constrained in comparison to quantum theory but allows states that are more exotic than quantum states. The state cone of $\mathrm{SEP}+{\delta }_{NP}$ lies strictly in between SEP and $\mathcal{Q}$, whereas for $\overline{\mathrm{SEP}}-{\xi }_{NP}$ theory it lies strictly in between $\mathcal{Q}$ and $\overline{\mathrm{SEP}}$. Examples of such compositions are shown in (a) and (b) with light shaded cones.

Figure 2

Timelike and spacelike correlations. (a) The preparation (blue) and measurement (green) devices receive inputs $x$ and $y$, respectively, and finally an outcome $a$ is obtained. The blue device prepares two elementary systems which are individually described as quantum bits, but the global description of the preparation is unknown. This setting can generate stronger-than-quantum correlation as shown in Theorem 1. In (b), correlations generated by spacelike separated measurement devices acting on two qubits always imply a quantum description of the joint preparation [18].