Institute of Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.
Phys Rev Lett. 2013 Aug 23;111(8):080503. doi: 10.1103/PhysRevLett.111.080503.
A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum state |ψ], we obtain an upper bound on the number of distinct states that are locally indistinguishable from |ψ]. The upper bound is determined only by the entanglement entropy of some local subsystems. As an example, we show that log N≤2γ for a large class of topologically ordered systems on a torus, where N is the number of topologically protected states and γ is the constant subcorrection term of the entanglement entropy. We discuss applications to quantum many-body systems that do not have any low-energy topological quantum field theory description, as well as tradeoff bounds for general quantum error correcting codes.
即使不使用母哈密顿量的性质或拓扑量子场论的形式，也推导出了纠缠熵和一些拓扑有序态之间的一般不等式。对于一个量子态 |ψ]，我们得到了与 |ψ] 在局部上不可区分的不同态的数量的上界。这个上界仅由一些局部子系统的纠缠熵决定。作为一个例子，我们表明对于环面上的一大类拓扑有序系统，log N≤2γ，其中 N 是拓扑保护态的数量，γ 是纠缠熵的常数次修正项。我们讨论了它在没有任何低能拓扑量子场论描述的量子多体系统中的应用，以及一般量子纠错码的权衡界限。
