Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In quantum mechanics, separable quantum states are states without quantum entanglement.For simplicity, the following assumes all relevant state spaces are finite dimensional. First, consider separability for pure states. When the state spaces are infinite dimensional, density matrices are replaced by positive trace class operators with trace 1, and a state is separable if it can be approximated, in trace norm, by states of the above form. If there is only a single non-zero pk, then the state is called simply separable (or it is called a "product state").