# The Quantum Cocktail Party Problem

## TL;DR

This paper introduces a quantum analog of the classical cocktail party problem, focusing on recovering pure quantum states from mixed states using classical and quantum optimization methods.

## Contribution

It formulates the quantum cocktail party problem, proposes physical realizations, and offers solution strategies including classical optimization and quantum Hamiltonian mapping.

## Key findings

- Formulation of the quantum cocktail party problem.
- Proposed physical realization methods.
- Solution approaches using classical and quantum techniques.

## Abstract

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.