The $\hslash \to 0$ Limit of the Entanglement Entropy

Abstract

Entangled quantum states share properties that do not have classical analogs, in particular, they show correlations that can violate Bell inequalities. It is therefore an interesting question to see what happens to entanglement measures -- such as the entanglement entropy for a pure state -- taking the semi-classical limit, where the naive expectation is that they may become singular or zero. This conclusion is however incorrect. In this paper, we determine the $\hslash \to 0$ limit of the bipartite entanglement entropy for a one-dimensional system of $N$ quantum particles in an external potential and we explicitly show that this limit is finite. Moreover, if the particles are fermionic, we show that the $\hslash \to 0$ limit of the bipartite entanglement entropy coincides with the Shannon entropy of $N$ bits.

11 pages, 1 figure. Published version: some references added, discussion slightly improved

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Cited by in corpus (9)

• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory I: Free Theories, Twist Fields and Qubits
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory II: Numerics, Interacting Theories and Higher Dimensions
• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory III: Bosonic and Fermionic Negativity
• Subsystem distances between quasiparticle excited states
• Path Integrals from Spacetime Quantum Actions
• Semiclassical Limit of Measurement-Induced Transition in Many-Body Chaos in Integrable and Nonintegrable Oscillator Chains
• Shannon entropy in quasiparticle states of quantum chains
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density