Noncausal Page-Wootters circuits

• URL: http://arxiv.org/abs/2105.02304v2
• Date: Fri, 11 Mar 2022 14:01:59 GMT
• Title: Noncausal Page-Wootters circuits
• Authors: Veronika Baumann, Marius Krumm, Philippe Allard Gu\'erin, \v{C}aslav Brukner
• Abstract summary: Page-Wootters formalism associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. We describe how to extract process matrices from scenarios involving such agents with quantum clocks, and analyze their properties.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal structure present in general relativity displays quantum uncertainty. This may lead to a phenomenon known as indefinite or quantum causal structure, as captured by the process matrix formalism. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. In this paper we combine the process matrix framework with a generalization of the Page-Wootters formalism in which one considers several agents, each with their own discrete quantum clock. We describe how to extract process matrices from scenarios involving such agents with quantum clocks, and analyze their properties. The description via a history state with multiple clocks imposes constraints on the implementation of process matrices and on the perspectives of the agents as described via causal reference frames. While it allows for scenarios where different definite causal orders are coherently controlled, we explain why certain noncausal processes might not be implementable within this setting.

Related papers

• A decompositional framework for process theories in spacetime [0.0]
  We show how to extend the formalism of process theories to incorporate a background causal structure arising from a fixed spacetime. Future directions include extending the framework to indefinite causal structures and studying exotic causal influence.
  arXiv  Detail & Related papers  (2024-11-13T00:37:55Z)
• Quantum Time: a novel resource for quantum information [0.0]
  Time in relativity theory has a status different from that adopted by standard quantum mechanics. Time is considered as a parameter measured with reference to an external absolute Newtonian frame.
  arXiv  Detail & Related papers  (2023-10-25T13:13:59Z)
• Indefinite order in the interface of quantum mechanics and gravity [0.0]
  We discuss the notion of indefinite order, which first appears in an abstract generalization of Quantum Theory. We present how scenarios involving gravity in low energies could lead to indefinite order.
  arXiv  Detail & Related papers  (2023-10-03T01:16:27Z)
• Quantum operations with the time axis in a superposed direction [0.0]
  We introduce an expanded concept of matrix transposition, that takes into account general bipartite unitary transformations of a quantum operation's future and past Hilbert spaces. This framework may have applications in approaches that treat time and space equally like quantum gravity.
  arXiv  Detail & Related papers  (2023-06-05T10:20:59Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• No-signalling constrains quantum computation with indefinite causal structure [45.279573215172285]
  We develop a formalism for quantum computation with indefinite causal structures. We characterize the computational structure of higher order quantum maps. We prove that these rules, which have a computational and information-theoretic nature, are determined by the more physical notion of the signalling relations between the quantum systems.
  arXiv  Detail & Related papers  (2022-02-21T13:43:50Z)
• 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)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• There is only one time [110.83289076967895]
  We draw a picture of physical systems that allows us to recognize what is this thing called "time" We derive the Schr"odinger equation in the first case, and the Hamilton equations of motion in the second one.
  arXiv  Detail & Related papers  (2020-06-22T09:54:46Z)
• 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)

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.