The paper by Asher Peres discusses the separability criterion for density matrices in quantum systems. A quantum system is separable if its density matrix can be expressed as a sum of products of density matrices for its subsystems. The author introduces a necessary condition for separability: the matrix obtained by partial transposition of the density matrix must have only non-negative eigenvalues. This criterion is more stringent than Bell's inequality, which is a necessary condition for separability but not sufficient. The paper provides examples to illustrate the application of this criterion, including a Werner state and a mixed state introduced by Gisin. It also highlights that while the criterion is necessary, it may not be sufficient for higher-dimensional systems. The paper concludes by discussing the limitations of Bell's inequality and the potential for stronger criteria using higher tensor products of density matrices.The paper by Asher Peres discusses the separability criterion for density matrices in quantum systems. A quantum system is separable if its density matrix can be expressed as a sum of products of density matrices for its subsystems. The author introduces a necessary condition for separability: the matrix obtained by partial transposition of the density matrix must have only non-negative eigenvalues. This criterion is more stringent than Bell's inequality, which is a necessary condition for separability but not sufficient. The paper provides examples to illustrate the application of this criterion, including a Werner state and a mixed state introduced by Gisin. It also highlights that while the criterion is necessary, it may not be sufficient for higher-dimensional systems. The paper concludes by discussing the limitations of Bell's inequality and the potential for stronger criteria using higher tensor products of density matrices.