The non-conditional nature of the Cerf-Adami inequalities and implications for thermodynamics

Geometry of two-qubit states with negative conditional entropy

We review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by Cerf and Adami for two qubit states in comparison with entanglement and nonlocality of the states. We identify the region of negative conditional entropy in the tetrahedron of locally maximally mixed two-qubit states. Within this set of states, negative conditional entropy implies nonlocality and entanglement, but not vice versa, and we show that the Cerf-Adami conditional amplitude operator provides an entanglement witness equivalent to the Peres-Horodecki crit…

Limitations on entropic Bell inequalities

The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is considered. Inequalities of the Wigner form are derived but shown to be extremely limiting in their applicability due to the nature of the density matrices involved. This also helps to identify a limitation in the Cerf-Adami inequalities.

Are entropic Bell inequalities implied by the second law?

Bell's inequalities, in the form given by Cerf and Adami, are derived from the combination of the second law of thermodynamics and the Markov postulate. Violations of these inequalities are discussed in terms of the mixing characteristics of the density operators. A quantum mechanical bound for a system of three qubits, two of which are entangled, is found and is shown to lead to strong subadditivity in one case. Finally, in interpreting the results, the role the uncertainty relations play in the definition of entropy and the second law is discussed, demonstrating a link to Bell's inequalities…

关于Z. Van Herstraeten与N.J. Cerf近期提出的量子Wigner熵猜想

On a recent conjecture by Z. Van Herstraeten and N.J. Cerf for the quantum Wigner entropy

针对Z. Van Herstraeten和N.J. Cerf提出的正Wigner函数熵下界猜想，研究者提出适用于所有绝对可积Wigner函数的新熵定义，在任意维度下证明其存在接近猜想值的正常数下界，还证明了Rényi熵的对应结果及一个类Lieb的新不等式。