Holographic spacetime emerges as the 1-Wasserstein space of quantum state distributions under optimal transport, matching AdS2 black hole geometry in the SYK model and identified with generalized Krylov complexity.
Villani et al.,Optimal transport: old and new, vol
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Effective dimension of Wasserstein space for quantum energy eigenstates reduces with increasing chaos, capturing Lyapunov exponents and indicating scar states via optimal transport geometry.
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Holography and Optimal Transport: Emergent Wasserstein Spacetime in Harmonic Oscillator, SYK and Krylov Complexity
Holographic spacetime emerges as the 1-Wasserstein space of quantum state distributions under optimal transport, matching AdS2 black hole geometry in the SYK model and identified with generalized Krylov complexity.
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Wasserstein Space of Quantum Chaos
Effective dimension of Wasserstein space for quantum energy eigenstates reduces with increasing chaos, capturing Lyapunov exponents and indicating scar states via optimal transport geometry.