Discord and Decoherence

Abstract

In quantum information theory, quantum discord has been proposed as a tool to characterise the presence of "quantum correlations" between the subparts of a given system. Whether a system behaves quantum-mechanically or classically is believed to be impacted by the phenomenon of decoherence, which originates from the unavoidable interaction between this system and an environment. Generically, decoherence is associated with a decrease of the state purity, i.e. a transition from a pure to a mixed state. In this paper, we investigate how quantum discord is modified by this quantum-to-classical transition. This study is carried out on systems described by quadratic Hamiltonians and Gaussian states, with generalised squeezing parameters. A generic parametrisation is also introduced to describe the way the system is partitioned into two subsystems. We find that the evolution of quantum discord in presence of an environment is a competition between the growth of the squeezing amplitude and the decrease of the state purity. In phase space, this corresponds to whether the semi-minor axis of the Wigner ellipse increases or decreases, which has a clear geometrical interpretation. Finally, these considerations are applied to primordial cosmological perturbations, thus allowing us to investigate how large-scale structures in our universe, which are believed to arise from quantum fluctuations, can exhibit classical properties.

35 pages without appendices (total 57 pages), 10 figures, typo corrected in the labels of figure 3

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• Decoherence out of fire: Purity loss in expanding and contracting universes
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• Enhanced power on small scales and evolution of quantum state of perturbations in single and two field inflationary models
• Real-space Bell inequalities in de Sitter
• The Early Universe as an Open Quantum System: Complexity and Decoherence
• Quantum entanglement in cosmology
• In-in formalism for the entropy of quantum fields in curved spacetimes
• Real-space quantum-to-classical transition of time dependent background fluctuations
• Quantum diffusion and large primordial perturbations from inflation
• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields
• Cosmological particle production in a quantum field simulator as a quantum mechanical scattering problem
• Distinguishing cosmological models through quantum signatures of primordial perturbations
• Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum
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• Entanglement and correlations between local observables in de Sitter spacetime
• Amplifying quantum discord during inflationary magnetogenesis through violation of parity
• Violation of Bell inequalities from Cosmic Microwave Background data
• Probing the self-coherence of primordial quantum fluctuations with complexity
• Violation of the Leggett-Garg inequality in photon-graviton conversion
• Anharmonic Effects on the Squeezing of Axion Perturbations