The state-space structure for a composite quantum system is postulated among several mathematically consistent possibilities that are compatible with a local quantum description. For instance, the unentangled Gleason's theorem allows a state space that includes density operators as a proper subset among all possible composite states. However, bipartite correlations obtained in Bell-type experiments from this broader state space are, in fact, quantum simulable [Barnum et al., Phys. Rev. Lett. 104, 140401 (2010)], and hence, such spacelike correlations are no good for making a distinction among different compositions. In this work we analyze the communication utilities of these different composite models and show that they can lead to distinct utilities in a simple communication game involving two players. Our analysis thus establishes that a beyond quantum composite structure can lead to beyond quantum correlations in the timelike scenario and hence welcomes new principles to isolate the quantum correlations from the beyond quantum ones. We also prove a no-go theorem that the classical information carrying capacity of different such compositions cannot be greater than that of the corresponding quantum composite systems.
The state-space structure for a composite quantum system is postulated among several mathematically consistent possibilities that are compatible with a local quantum description. For instance, the unentangled Gleason's theorem allows a state space that includes density operators as a proper subset among all possible composite states. However, bipartite correlations obtained in Bell-type experiments from this broader state space are, in fact, quantum simulable [Barnum et al., Phys. Rev. Lett. 104, 140401 (2010)], and hence, such spacelike correlations are no good for making a distinction among different compositions. In this work we analyze the communication utilities of these different composite models and show that they can lead to distinct utilities in a simple communication game involving two players. Our analysis thus establishes that a beyond quantum composite structure can lead to beyond quantum correlations in the timelike scenario and hence welcomes new principles to isolate the quantum correlations from the beyond quantum ones. We also prove a no-go theorem that the classical information carrying capacity of different such compositions cannot be greater than that of the corresponding quantum composite systems.
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.
Quantum correlations often defy an explanation in terms of fundamental notions of classical physics, such as causality, locality, and realism. While the mathematical theory underpinning quantum correlations between spacelike separated systems has been well-established since the 1930s, the mathematical theory for correlations between non-spacelike separated systems is much less developed. In this work, we develop the theory of what we refer to as "local-density operators", which we view as joint states for possibly non-spacelike separated quantum systems. Local-density operators are unit trace operators whose marginals are genuine density operators, which we show not only subsumes the notion of density operator, but also several extensions of the notion of density operator into the spatiotemporal domain, such as pseudo-density operators and quantum states over time. More importantly, we prove a result which establishes a one-to-one correspondence between local-density operators and what we refer to as "Dirac measures", which are complex-valued measures on the space of separable projectors associated with two quantum systems. In the case that one of the systems is the trivial quantum system with a one-dimensional Hilbert space, our result recovers the fundamental result known as Gleason's Theorem, which implies that the Born rule from quantum theory is the only way in which one may assign probabilities to the outcomes of measurements performed on quantum systems in a non-contextual manner. As such, our results establish a direct generalization of Gleason's Theorem to measurements performed on possibly non-spacelike separated systems, thus extending the mathematical theory of quantum correlations across space to quantum correlations across space and time.
Physical theories with local structure similar to quantum theory can allow beyond-quantum global states that are in agreement with unentangled Gleason's theorem. In a standard Bell experiment any such bipartite state produces correlations that are always quantum simulable. In this limited classical-input-classical-output Bell scenario, we show that there exist bipartite beyond-quantum states that produce correlations all of which are in-fact classically simulable. However, if the type of Bell scenario is generalized to consider quantum states as inputs, we then show that any such bipartite beyond-quantum state yields beyond-quantum input-output correlations. We also analyze the implication of this quantum input scenario while studying generic multipartite correlations obtained from local quantum theory but potentially allowing different global structure. Our study suggests the requirement of type sensitive information principles for isolating the quantum correlations from the beyond-quantum ones.
Bell non-locality is a powerful framework to distinguish classical, quantum and post-quantum resources, which relies on non-communicating players. Under which restriction can we have the same separations, if we allow for communication? Non-signalling state assemblages, and the fact that they can always be simultaneously purified, turned out to be the key element to restrict the simplest bipartite communication scenario, the prepare-and-measure, to the standard bipartite Bell scenario. Yet, many distinctive features of quantum theory are genuinely multipartite and cannot be reduced to two-party behaviour. In this work we are interested in extending this simultaneous purification inspired result to all multipartite communication schemes. As a first step, we unify and extend the simultaneous purification result from states to instruments and super-instruments, which are composable structures, and open up the possibility to explore more complex communication scenarios. Our main contribution is to establish that arbitrary compositions of non-signalling assemblages cannot escape the standard spatial quantum Bell correlations set. As a consequence, any interactive quantum realization of correlations outside of this set must involve at least one signalling assemblage of quantum operations, even when the resulting correlations are non-signalling.
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 Letter, 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.
Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A striking consequence of this facet is the violation of Bell inequalities, which has been experimentally demonstrated via Bell tests. The prediction of this phenomenon originates as quantum systems are prescribed to combine according to the composition postulate, i.e. the tensor-product rule. This rule has also an operationally salient formulation given in terms of discriminability of composite states via local measurements. However, both the theoretical and the empirical status of such a postulate have been repeatedly challenged, questioning its independence from other physical principles -- most notably from quantum postulates pertaining solely to single systems. Is the composition postulate the only viable way to combine quantum systems into a consistent physical theory? Here, this long-standing problem is resolved by answering in the negative. This is achieved by adopting an operational approach to physical theories and exhibiting a family of theories that differ from standard quantum theory in their system-composition rule. These theories have the same predictions as standard quantum theory as far as Bell-like correlation scenarios are concerned. Quantum theory is thus established to embody genuinely more than quantum correlations. As a result, foundational programmes based on single-system principles only, or on mere Bell-like correlations, are operationally incomplete. On the experimental side, ascertaining the independence of postulates is a fundamental step to adjudicate between quantum theory and alternative physical theories: hence, the composition postulate calls for experimental scrutiny independently of the other features of quantum theory.