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## Main Question or Discussion Point

say an ensemble consisting of N

A) Two particles in a bipartite system are entangled as |psi>= 1/sqrt(2) ( |00> + |11> )

so the density matrix is

rho1 = |psi> <psi| = 1/2 *{1 0 0 1} * {1; 0; 0; 1}

= 0.5* { 1 0 0 1; 0 0 0 0; 0 0 0 0; 1 0 0 1}

B) The bipartite system is in a mixed state. But the initial states of the two particles are the same.

they are either in |00> or |11> with probability 1/2 respectively.

So, the density matrix is

rho2= 0.5 {1 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 1}

In summary, there are either N pairs of entangled particles or N pairs of independent but in-the-same-initial-state particles. Assume N is large enough.

How to design measurements on the ensemble, so that I can tell whether it is entangled?

**IDENTICAL**bipartite systems. The system can be in either of the two situations.A) Two particles in a bipartite system are entangled as |psi>= 1/sqrt(2) ( |00> + |11> )

so the density matrix is

rho1 = |psi> <psi| = 1/2 *{1 0 0 1} * {1; 0; 0; 1}

= 0.5* { 1 0 0 1; 0 0 0 0; 0 0 0 0; 1 0 0 1}

B) The bipartite system is in a mixed state. But the initial states of the two particles are the same.

they are either in |00> or |11> with probability 1/2 respectively.

So, the density matrix is

rho2= 0.5 {1 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 1}

In summary, there are either N pairs of entangled particles or N pairs of independent but in-the-same-initial-state particles. Assume N is large enough.

How to design measurements on the ensemble, so that I can tell whether it is entangled?