Bound Entanglement in Thermalized States and Black Hole Radiation
We study the mixed-state entanglement structure of chaotic quantum many-body systems at late times using the recently developed equilibrium approximation. A rich entanglement phase diagram emerges when we generalize this technique to evaluate the logarithmic negativity for various universality classes of macroscopically thermalized states. Unlike in the infinite-temperature case, when we impose energy constraints at finite temperature, the phase diagrams for the logarithmic negativity and the mutual information become distinct. In particular, we identify a regime where the negativity is extensive but the mutual information is subextensive, indicating a large amount of bound entanglement. When applied to evaporating black holes, these results imply that there is quantum entanglement within the Hawking radiation long before the Page time, although this entanglement may not be distillable into Einstein-Podolsky-Rosen pairs. We claim that at this earlier time, rather than the Page time, information about diaries thrown into the black hole first starts to leak out.
- Research Organization:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- Grant/Contract Number:
- SC0012567; SC0019127
- OSTI ID:
- 1879768
- Alternate ID(s):
- OSTI ID: 1907982
- Journal Information:
- Physical Review Letters, Journal Name: Physical Review Letters Vol. 129 Journal Issue: 6; ISSN 0031-9007
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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