The Causal Structure of Quantum Information

Dirk Bouwmeester, ARTUR K. EKERT, Anton Zeilinger

David Gutierrez Ule

Quantum Informational Geometrodynamics (QI-G) treats spacetime, matter, and interactions as emergent structures of a discrete causal network carrying quantum information. This paper investigates whether a multiplicity of effectively autonomous realities can arise within QI-G without postulating a fundamental multiverse. We formulate a kinematic space permitting superpositions of causal-network configurations, introduce coarse-grained causal histories and their decoherence functional, and define an informational causal branch through three jointly necessary conditions: suppressed interference, stable causal records, and approximate dynamical autonomy. Each branch may admit its own coarse-grained Lorentzian geometry and intrinsic causal time, so that no external simultaneity relation between branches is required. An exact sector-decomposition result is established for block-diagonal dynamics. A redundant-record model further yields the suppression law η_N = ∏_{j=1}^{N}|r_j| and the threshold ∑_j[-ln|r_j|] ≥ ln(ε^{-1}) for effective branching at tolerance ε. We also propose, as a testable but presently unproved QI-G-specific ansatz, that the decoherence rate is controlled by an informational separation functional combining quantum Jensen–Shannon divergence, causal-structure mismatch, and emergent-curvature mismatch. The resulting framework supports emergent effective multiversality but does not establish a literal or empirically distinct multiverse. Such a conclusion would require a derivation of branch-selection scales, probabilities, and residual recoherence directly from the QI-G action.

Etera R. Livine, Daniel R. Terno

We use techniques of quantum information theory to analyze the quantum causal histories approach to quantum gravity. While it is consistent to introduce closed timelike curves (CTCs), they cannot generically carry independent degrees of freedom. Moreover, if the effective dynamics of the chronology-respecting part of the system is linear, it should be completely decoupled from the CTCs. In the absence of a CTC, not all causal structures admit the introduction of quantum mechanics. It is possible for those and only those causal structures that can be represented as quantum computational networks. Dynamics of the subsystems should not be unitary or even completely positive. However, we show that other commonly made assumptions ensure the complete positivity of the reduced dynamics.

Antoine Browaeys

Matthias Salzger, V. Vilasini

Abstract Formalisms for higher order quantum processes provide a theoretical formalisation of quantum processes where the order of agents’ operations need not be definite and acyclic, but may be subject to quantum superpositions. This has led to the concept of indefinite causal structures (ICS) which have garnered much interest. However, the interface between these information-theoretic approaches and spatiotemporal notions of causality is less understood, and questions relating to the physical realisability of ICS in a spatiotemporal context persist despite progress in their information-theoretic characterisation. Further, previous work suggests that composition of processes is not so straightforward in ICS frameworks, which raises the question of how this connects with the observed composability of physical experiments in spacetime. To address these points, we compare the formalism of quantum circuits with quantum control of causal order (QC-QC), which models an interesting class of ICS processes, with that of causal boxes, which models composable quantum information protocols in spacetime. We incorporate the set-up assumptions of the QC-QC framework into the spatiotemporal perspective and show that every QC-QC can be mapped to a causal box that satisfies these set up assumptions and acts on a Fock space while reproducing the QC-QC’s behaviour in a relevant subspace defined by the assumptions. Using a recently introduced concept of fine-graining, we show that the causal box corresponds to a fine-graining of the QC-QC, which unravels the original ICS of the QC-QC into a set of quantum operations with a well-defined and acyclic causal order, compatible with the spacetime structure. Our results also clarify how the composability of physical experiments is recovered, while highlighting the essential role of relativistic causality and the Fock space structure.

Vasil Dinev Penchev