Relative entropy and holography

By David Blanco, H. Casini, Ling-Yan Hung, R. Myers. 2013

417 citations recorded by the source corpus.

A bstractRelative entropy between two states in the same Hilbert space is a fundamental statistical measure of the distance between these states. Relative entropy is always positive and increasing with the system size. Interestingly, for two states which are infinitesimally different to each other, vanishing of relative entropy gives a powerful equation ΔS = ΔH for the first order variation of the entanglement entropy ΔS and the expectation value of the modular Hamiltonian ΔH. We evaluate relative entropy between the vacuum and other states for spherical regions in the AdS/CFT framework. We check that the relevant equations and inequalities hold for a large class of states, giving a strong support to the holographic entropy formula. We elaborate on potential uses of the equation ΔS = ΔH for vacuum state tomography and obtain modified versions of the Bekenstein bound.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/86ab10a002f9b3fdb7e223957150987e150f3fdb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. R. Myers
2. Aitor Lewkowycz
3. Mark Van Raamsdonk
4. T. Faulkner
5. Xi Dong
6. M. Huerta
7. H. Casini
8. E. Witten

In Atomic and Molecular Physics, and Optics

1. R. Myers
2. D. Harlow
3. Thomas Hartman
4. T. Faulkner
5. Aitor Lewkowycz
6. J. Maldacena
7. E. Witten
8. Xi Dong

In Nuclear and High Energy Physics

1. R. Myers
2. D. Harlow
3. T. Takayanagi
4. Thomas Hartman
5. T. Faulkner
6. Aitor Lewkowycz
7. J. Maldacena
8. S. Raju

Citations in the corpus

• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement (2016, background): “Hence, for infinitesimal perturbations σ 1⁄4 ρþ δρ, we have Dðσ∥ρÞ 1⁄4 0 to linear order, and we arrive at the EFL [3],”
• On volumes of subregions in holography and complexity (2016, background): “It would be interesting to understand if there is a relation to bulk relative entropy [16, 63, 64].”
• Bulk locality and quantum error correction in AdS/CFT (2014, background): “fixed boundary region A to recede towards the boundary, giving it less access to bulk operators defined at fixed renormalized geodesic distance (for some related discussion see [10, 25, 26, 34, 35]).”
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• Quantum corrections to holographic entanglement entropy (2013, background): “) This was discussed extensively in [41] where this saturation was named the Entanglement Plateaux (see also [1, 23, 42].”
• Entropy, extremality, euclidean variations, and the equations of motion (2017, methodology): “This gives an expression for δK from which we can read 〈KTμν〉 in holographic theories (similar comments were made in [14, 38]).”
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• Holographic Complexity (2015, background): “Since the explicit form of the modular Hamiltonian is known for the subsystem we are considering[14], it would be interesting to find the fidelity susceptibility directly from the modular Hamiltonian.”
• Black hole chemistry: thermodynamics with Lambda (2016, background): “showing that entanglement entropy in CFTs satisfy a first law [239, 240].”