Markov熵分解：量子信念传播的变分对偶
Markov entropy decomposition: a variational dual for quantum belief propagation
摘要：
给出了有限温度下量子多体系统自由能的一个下界。这个下界被表示为一个线性约束的凸优化问题，并利用冯诺伊曼熵的强次可加性和局部密度算子的一致性条件的松弛而导出。这个最小化问题的对偶导致了一组量子信念传播方程，从而为该方法提供了坚实的理论基础。最小化问题是数值上易于处理的，我们发现很好的协议与量子蒙特卡罗自旋半海森堡反铁磁体在二维。这个下界补充了其他变分上界。我们讨论了应用到Hamilton复杂性理论，并给出了一个概括的结构定理的海登，Jozsa，Petz和冬天的树在附录中。
英文摘要：
We present a lower bound for the free energy of a quantum many-body system at finite temperature. This lower bound is expressed as a convex optimization problem with linear constraints, and is derived using strong subadditivity of von Neumann entropy and a relaxation of the consistency condition of local density operators. The dual to this minimization problem leads to a set of quantum belief propagation equations, thus providing a firm theoretical foundation to that approach. The minimization problem is numerically tractable, and we find good agreement with quantum Monte Carlo for the spin-half Heisenberg anti-ferromagnet in two dimensions. This lower bound complements other variational upper bounds. We discuss applications to Hamiltonian complexity theory and give a generalization of the structure theorem of Hayden, Jozsa, Petz and Winter to trees in an appendix.
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