Improved algorithm for quantum separability and entanglement detection

Abstract

Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard, suggesting that an efficient, general solution does not exist. There is a highly inefficient ``basic algorithm'' for solving the quantum separability problem which follows from the definition of a separable state. By exploiting specific properties of the set of separable states, we introduce a classical algorithm that solves the problem significantly faster than the ``basic algorithm,'' allowing a feasible separability test where none previously existed, e.g., in $3\ifmmode\times\else\texttimes\fi{}3$-dimensional systems. Our algorithm also provides a unique tool in the experimental detection of entanglement.