The information in a wave

Abstract

We provide the notion of entropy for a classical Klein-Gordon real wave, that we derive as particular case of a notion entropy for a vector in a Hilbert space with respect to a real linear subspace. We then consider a localised automorphism on the Rindler spacetime, in the context of a free neutral Quantum Field Theory, that is associated with a second quantised wave, and we explicitly compute its entropy $S$, that turns out to be given by the entropy of the associated classical wave. Here $S$ is defined as the relative entropy between the Rindler vacuum state and the corresponding sector state (coherent state). By $\lambda$-translating the Rindler spacetime into itself along the upper null horizon, we study the behaviour of the corresponding entropy $S(\lambda )$. In particular, we show that the QNEC inequality in the form $\frac{d^2}{d{\lambda }^2}S(\lambda )\ge 0$ holds true for coherent states, because $\frac{d^2}{d{\lambda }^2}S(\lambda )$ is the integral along the space horizon of a manifestly non-negative quantity, the component of the stress-energy tensor in the null upper horizon direction.

23 pages. Minor corrections; references have been updated

References in corpus (9)

• Notes on Some Entanglement Properties of Quantum Field Theory
• Entropy distribution of localised states
• Modular Flow of Excited States
• Relative entropy for coherent states from Araki formula
• Comment on the Bekenstein bound
• Entropy of Coherent Excitations
• On Landauer's principle and bound for infinite systems
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• Relative entropy of coherent states on general CCR algebras
• Entropy for spherically symmetric, dynamical black holes from the relative entropy between coherent states of a scalar quantum field
• On the mass dependence of the modular operator for a double cone
• Relative Entropy in de Sitter is a Noether Charge
• Relative entropy of an interval for a massless boson at finite temperature
• Loop Groups and QNEC
• Modular Hamiltonian for fermions of small mass
• On the Thermodynamics of the q-Particles
• A numerical analysis of Araki-Uhlmann relative entropy in Quantum Field Theory
• Petz-Rényi relative entropy in QFT from modular theory
• The fermionic massless modular Hamiltonian
• Signal communication and modular theory
• Entanglement Entropy in CFT and Modular Nuclearity
• Relative entropy of single-mode squeezed states in Quantum Field Theory
• Modular Nuclearity and Entanglement measures