  The cocktail party problem refers to the famous selective attention problem
of how to find out the signal of each individual sources from signals of a
number of detectors. In the classical cocktail party problem, the signal of
each source is a sequence of data such as the voice from a speaker, and each
detector detects signal as a linear combination of all sources. This problem
can be solved by a unsupervised machine learning algorithm known as the
independent component analysis. In this work we propose a quantum analog of the
cocktail party problem. Here each source is a density matrix of a pure state
and each detector detects a density matrix as a linear combination of all pure
state density matrix. The quantum cocktail party problem is to recover the pure
state density matrix from a number observed mixed state density matrices. We
propose the physical realization of this problem, and how to solve this problem
through either classical Newton's optimization method or by mapping the problem
to the ground state of an Ising type of spin Hamiltonian.
