The quantum null energy condition (QNEC) is a quantum generalization of the null energy condition, which gives a lower bound on the null energy in terms of the second derivative of the von Neumann entropy or entanglement entropy of some region with respect to a null direction. The QNEC states that ? T k k ? p ≥ lim A → 0 ( ? 2 π A S out ′′ ) , where S out is the entanglement entropy restricted to one side of a codimension-2 surface Σ , which is deformed in the null direction about a neighborhood of point p with area A . A proof of QNEC has been given before, which applies to free and super-renormalizable bosonic field theories, and to any points that lie on a stationary null surface. Using similar assumptions and methods, we prove the QNEC for fermionic field theories.
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机译：量子空能量条件（QNEC）是空能量条件的量子概括，其在von Neumann熵的第二导数相对于空方向的von Neumann熵的第二导数或某个区域的缠结熵的术语中给出了下限 。 QNEC规定了吗？ t k k？ P≥0 一种 。 以前给出了QNEC的证据，其适用于自由和超级更新的振动域理论，以及任何位于固定空表面的点。 使用类似的假设和方法，我们证明了QNEC用于Fermionic野性理论。
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