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Principle of Information Causality Rationalizes Quantum Composition.

Ram Krishna Patra1, Sahil Gopalkrishna Naik1, Edwin Peter Lobo2

  • 1Department of Physics of Complex Systems, S.N. Bose National Center for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India.

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Information causality, a generalization of the no signaling principle, helps derive multipartite quantum systems. It rules out exotic states and Bell local correlations, showing neither extreme composition is nature's bona fide description.

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Area of Science:

  • Quantum Information Theory
  • Foundations of Quantum Mechanics
  • Multipartite Quantum Systems

Background:

  • The no signaling principle is a fundamental constraint in quantum mechanics, ensuring that information cannot be transmitted instantaneously between separated systems.
  • Information causality, a stronger principle, generalizes no signaling and has been used to exclude unphysical correlations beyond quantum mechanics.
  • The structure of composite quantum systems, particularly their state and effect spaces, is crucial for understanding quantum correlations.

Purpose of the Study:

  • To demonstrate how information causality can provide a physical rationale for the structural derivation of multipartite quantum systems.
  • To analyze different mathematical descriptions of composite systems under the no signaling condition and their compatibility with information causality.
  • To explore the implications of information causality for the self-duality of state and effect cones in composite quantum systems.

Main Methods:

  • Investigated the implications of the no signaling condition on the state and effect spaces of composite quantum systems.
  • Analyzed two extreme compositions: maximal tensor product (exotic states) and minimal tensor product (Bell local correlations).
  • Assessed the compatibility of these compositions with the principle of information causality.

Main Results:

  • Neither the maximal nor the minimal tensor product composition of quantum systems is compatible with information causality.
  • The maximal tensor product allows for states not permitted by quantum theory, while the minimal tensor product restricts correlations to be Bell local.
  • These findings indicate that neither extreme composition represents a bona fide description of nature according to information causality.

Conclusions:

  • Information causality serves as a powerful tool for deriving the structure of multipartite quantum systems.
  • The principle excludes unphysical descriptions of composite systems that arise from extreme tensor product compositions.
  • Information causality offers a pathway towards an information-theoretical derivation of the self-duality of state and effect cones for composite quantum systems.