Embedding cyclic causal structures in acyclic space-times: no-go results for indefinite causality

• URL: http://arxiv.org/abs/2203.11245v3
• Date: Wed, 27 Dec 2023 21:06:01 GMT
• Title: Embedding cyclic causal structures in acyclic space-times: no-go results for indefinite causality
• Authors: V. Vilasini and Renato Renner
• Abstract summary: Causality can be defined in terms of space-time or based on information-theoretic structures, which correspond to very different notions of causation. We develop a framework that disentangles the two causality notions and formalises their relations. Our work offers concrete insights on the operational meaning of indefinite causality, both within and beyond the context of a fixed space-time.
• Score: 2.1030878979833467
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Causality can be defined in terms of space-time or based on information-theoretic structures, which correspond to very different notions of causation. Yet, in physical experiments, these notions play together in a compatible manner. The process matrix framework is useful for modelling indefinite causal structures (ICS) in an information-theoretic sense, but there remain important open questions regarding the physicality of such processes. In particular, there are several experiments that claim to implement ICS processes in Minkowski space-time, which presents an apparent theoretical paradox: how can an indefinite information-theoretic causal structure be compatible with a definite space-time structure? To address this, we develop a general framework that disentangles the two causality notions and formalises their relations. The framework describes a composition of quantum operations through feedback loops, and the embedding of the resulting (possibly cyclic) information-theoretic structure in an acyclic space-time structure. Relativistic causality is formalised as an operational compatibility condition between the two structures. Reformulating the process matrix framework here, we establish no-go results which imply that it is impossible to physically realise ICS in a fixed space-time with space-time localised quantum systems. Further, we prove that physical realisations of any ICS process, even those involving space-time non-localised systems, will ultimately admit an explanation in terms of a definite (and acyclic) causal order process, at a more fine-grained level. These results fully resolve the apparent paradox and we discuss their implications for the interpretation of the above-mentioned experiments. Moreover, our work offers concrete insights on the operational meaning of indefinite causality, both within and beyond the context of a fixed space-time.

Related papers

• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes. We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram. We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Entanglement cones and horizons in analogue cosmological production of Dirac fermions [49.1574468325115]
  We study the appearance of fermion condensates for self-interacting Dirac fermions. We show that the combined breakdown of time-reversal symmetry due to the expanding spacetime, and parity due to a pseudo-scalar condensate, manifest through the structure of the light-cone-like propagation of entanglement in this analogue cQFT.
  arXiv  Detail & Related papers  (2025-03-24T22:20:16Z)
• Fundamental limits for realising quantum processes in spacetime [1.7802147489386633]
  We derive no-go theorems for quantum experiments realisable in classical background spacetimes. Our first theorem implies that realisations of ICO processes that do not violate relativistic causality must involve the non-localization of systems in spacetime. The second theorem shows that for any such realisation of an ICO process, there exists a more fine-grained description in terms of a definite and acyclic causal order process.
  arXiv  Detail & Related papers  (2024-08-23T21:41:49Z)
• A Measure-Theoretic Axiomatisation of Causality [55.6970314129444]
  We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
  arXiv  Detail & Related papers  (2023-05-19T13:15:48Z)
• Compatibility of Cyclic Causal Structures with Spacetime in General Theories with Free Interventions [0.0]
  We show the possibility of operationally detectable causal loops embedded in (1+1)-Minkowski spacetime without superluminal signalling. We establish new properties of HO affects relations and apply them to infer causal structures. We study the embedding of information-theoretic causal structures into partially ordered spacetimes.
  arXiv  Detail & Related papers  (2022-11-07T14:30:03Z)
• Is the relativistic Structure of Spacetime Ontic or Epistemic? [0.0]
  We argue that Bell's nonlocal correlations cannot readily be explained within the standard relativistic framework. This suggests that we should re-examine our understanding of spacetime.
  arXiv  Detail & Related papers  (2022-02-16T19:14:36Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Non-standard entanglement structure of local unitary self-dual models as a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
  We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry. We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
  arXiv  Detail & Related papers  (2021-11-29T23:37:58Z)
• Time and Evolution in Quantum and Classical Cosmology [68.8204255655161]
  We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory.
  arXiv  Detail & Related papers  (2021-07-02T09:17:55Z)
• Background Independence and Quantum Causal Structure [0.0]
  One of the key ways in which quantum mechanics differs from relativity is that it requires a fixed background reference frame for spacetime. A combination of the two theories is expected to yield non-classical, or "indefinite", causal structures. We present a background-independent formulation of the process matrix formalism.
  arXiv  Detail & Related papers  (2021-06-02T09:13:13Z)
• Wavefunctions and Minkowski Space-Time: On the Reconciliation of Quantum Theory with Special Relativity [0.0]
  The implications of the relativistic space-time structure for a physical description by quantum mechanical wave-functions are investigated. An analysis of the wave-function alone does not suffice to answer the question of relativistic compatibility of the theory. The actual events in space time, which are predicted and described by the theory, are crucial.
  arXiv  Detail & Related papers  (2020-08-29T17:59:28Z)
• Projection evolution and quantum spacetime [68.8204255655161]
  We discuss the problem of time in quantum mechanics. An idea of construction of a quantum spacetime as a special set of the allowed states is presented. An example of a structureless quantum Minkowski-like spacetime is also considered.
  arXiv  Detail & Related papers  (2019-10-24T14:54:11Z)
• Interference of Clocks: A Quantum Twin Paradox [39.645665748998816]
  Phase of matter waves depends on proper time and is susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. It is conceivable that atom interferometers measure general-relativistic time-dilation effects. We show that closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential.
  arXiv  Detail & Related papers  (2019-05-22T12:30:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.