Here we provide a list of open research problems. The problems classified by area and difficulty (easy, medium, difficult). Please add problems that you are interested in below. We suggest you follow the format of Howard's problem.

A suggestion for would-be problem solvers: It might be nice to let the person who proposed the problem know that you are working on it (or have solved it).

Problem: N&S conditions for mixed states
Rating: difficult
Problem Author: Howard Wiseman (interested in collaborating for a solution)
Problem Description: In the book it is shown that Eqs.(6.265)-(6.267) are simple necessary and sufficient condition for a covariance matrix to be that of a Gaussian pure state which is a possible steady-state solution of the filtering equation for a LG quantum system. (a) Are there analogous simple N&S conditions for mixed states? (b) Is there a way to impose a constraint on the efficiency with which the various output channels can be measured, while still having simple matrix equations as the N&S conditions?— Howard Wiseman 2009/11/21 00:18
Comments: Re (a), if one removes the condition of Eq. (6.267) one does not obtain the sufficient condition for mixed states. That is, surprisingly, there are mixed states that satisfy Eqs.(6.265)-(6.266) but that are not possible stationary solutions.— Howard Wiseman 2009/11/21 00:18