Round 8: Tossup 11

This quantity characteristically scales logarithmically with evolution time in systems displaying many-body localization. This quantity evolves over time to form an inverted V shape on the Page curve. For a tripartite quantum (10[1])system, this quantity obeys strong subadditivity. For pure states, the distillable and squashed entanglements reduce to this quantity. For a system with density matrix rho, this quantity equals the negative trace of rho times (10[1])log rho. (10[2])By the Bekenstein–Hawking formula, (10[1])the area of a black hole is proportional (10[1])to its value of this quantity. (10[1]-5[1])In classical information theory, this (10[1])quantity expresses the absence of information about a system (10[1])and is (10[1])measured in shannons. For 10 points, (10[1])name this quantity that increases in accordance with the second law of thermodynamics. (0[1])■END■

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