Strong subadditivity of quantum entropy information
In quantum information theory, strong subadditivity of quantum entropy (SSA) is the relation among the von Neumann entropies of various quantum subsystems of a larger quantum system consisting of three subsystems (or of one quantum system with three degrees of freedom). It is a basic theorem in modern quantum information theory. It was conjectured by D. W. Robinson and D. Ruelle[1] in 1966 and O. E. Lanford III and D. W. Robinson[2] in 1968 and proved in 1973 by E.H. Lieb and M.B. Ruskai,[3] building on results obtained by Lieb in his proof of the Wigner-Yanase-Dyson conjecture.[4]
The classical version of SSA was long known and appreciated in classical probability theory and information theory. The proof of this relation in the classical case is quite easy, but the quantum case is difficult because of the non-commutativity of the reduced density matrices describing the quantum subsystems.
Some useful references here include:
"Quantum Computation and Quantum Information"[5]
"Quantum Entropy and Its Use"[6]
Trace Inequalities and Quantum Entropy: An Introductory Course[7]
^Robinson, Derek W.; Ruelle, David (1967). "Mean entropy of states in classical statistical mechanics". Communications in Mathematical Physics. 5 (4). Springer Science and Business Media LLC: 288–300. Bibcode:1967CMaPh...5..288R. doi:10.1007/bf01646480. ISSN 0010-3616. S2CID 115134613.
^Lanford, Oscar E.; Robinson, Derek W. (1968). "Mean Entropy of States in Quantum‐Statistical Mechanics". Journal of Mathematical Physics. 9 (7). AIP Publishing: 1120–1125. Bibcode:1968JMP.....9.1120L. doi:10.1063/1.1664685. ISSN 0022-2488.
^Lieb, Elliott H.; Ruskai, Mary Beth (1973). "Proof of the strong subadditivity of quantum‐mechanical entropy" (PDF). Journal of Mathematical Physics. 14 (12). AIP Publishing: 1938–1941. Bibcode:1973JMP....14.1938L. doi:10.1063/1.1666274. ISSN 0022-2488.
^Lieb, Elliott H (1973). "Convex trace functions and the Wigner-Yanase-Dyson conjecture". Advances in Mathematics. 11 (3): 267–288. doi:10.1016/0001-8708(73)90011-X. ISSN 0001-8708.
^M. Nielsen, I. Chuang, Quantum Computation and Quantum Information, Cambr. U. Press, (2000)
^M. Ohya, D. Petz, Quantum Entropy and Its Use, Springer (1993)
^E. Carlen, Trace Inequalities and Quantum Entropy: An Introductory Course, Contemp. Math. 529 (2009).
and 12 Related for: Strong subadditivity of quantum entropy information
In quantum information theory, strongsubadditivityofquantumentropy (SSA) is the relation among the von Neumann entropiesof various quantum subsystems...
the Strong SubadditivityofEntropy in classical statistical mechanics and its quantum analog. Subadditivity is an essential property of some particular...
representations used in compilers Stationary Subspace Analysis Strongsubadditivityofquantumentropy SubStation Alpha and .ssa file format, a video subtitle...
and in relation to the strongsubadditivityof the von Neumann entropy. Efforts have been made to extend the definition ofquantum discord to continuous...
result. Entropic value at risk Quantum relative entropyStrongsubadditivity Classical information theory Min-entropy Watrous, J. Theory ofQuantum Information...
mathematics applicable to quantum mechanics. In 1972 she and Elliot Lieb proved the StrongSubadditivityofQuantumEntropy, which was described in 2005...
S(A:B|\Lambda )\geq 0} . This inequality is often called the strong-subadditivity property ofquantumentropy. Consider three random variables A , B , Λ {\displaystyle...
description to quantum teleportation. Wall AC. Maximin surfaces, and the strongsubadditivityof the covariant holographic entanglement entropy. Classical...