![]() 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. It is a basic theorem in modern quantum information theory. The classical version of SSA was long known and appreciated in classical probability theory and information theory. 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). As a result, different von Neumann entropies can be associated with the same state. The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a. Ruskai, building on results obtained by Lieb in his proof of the Wigner-Yanase-Dyson conjecture. Entropy of quantum states Paolo Facchi, Giovanni Gramegna, Arturo Konderak Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. ![]() Robinson in 1968 and proved in 1973 by E.H. In the classical framework, the probability distribution and partition function of the system allows us to compute all possible thermodynamic quantities. ![]() 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). 10.1.1Shannon entropy and data compression 2 10.1.2Joint typicality, conditional entropy, and mutual infor-mation 6 10.1.3Distributed source coding 8 10.1.4The noisy channel coding theorem 9 10.2 Von Neumann Entropy 16 10.2.1Mathematical properties of H() 18 10.2.2Mixing, measurement, and entropy 20 10.2. ![]()
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