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We still use qubits here as units, even though for classical communication the more appropriate units are classical bits. However, in our approach the quantum system is closed, so that we always deal with qubits (perhaps sometimes decohered).
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The alternative name is the "total" entanglement as it was used originally in [17].
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f denotes entanglement of formation, defined in Ref. [26].
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As a matter of fact, our information-thermodynamics analogy is akin to the Zurek approach [41] to the operations performed by the Maxwell demon as a kind of "demonic evolution" characterized by such special laws as the conservation of physical entropy. Zurek noted that the Shannon entropy and Kolmogorow randomness behave a bit similarly to kinetic and potential energy. We are also looking for a formal analogy between quantum information and energy, work, and other thermodynamical notions. The demonic evolution in our case is constituted by the operations of Alice and Bob over the quantum-communication systems.
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This concerns the first version of Vitanyi's paper. In the second version, Vitanyi independently introduced a definition similar to that of Ref. [44].
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