How can you test if a bipartite system is entangled?

In summary, an ensemble consisting of N identical bipartite systems can be in either N pairs of entangled particles or N pairs of independent but in-the-same-initial-state particles. To determine whether the ensemble is entangled, we can use an observable (A) that yields different mean values for the two cases. However, the technical realization of such a measurement is still unknown.
  • #1
ouacc
6
0
say an ensemble consisting of N 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?
 
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  • #2
ouacc said:
say an ensemble consisting of N 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?

So we have:
rho1 = 1/2*(|00>+|11>)(<00|+<11|)= shorter notation =1/2*|00+11><00+11|
rho2 = 1/2*(|00><00| + |11><11|)

Consider observable:
A = 1/2*|00+11><00+11| -1/2*|00-11><00-11|

Tr(A*rho1) = 1/2
Tr(A*rho2) = 0
=> we get different mean values, for more measurements we can distinguish between the two cases.
However, this is just a theoretical observable. If you mean the actual technical realisation of such a measurement on the system I have no idea how to do it.
 
  • #3
Thanks. But I couldn't figure out how to get the observables you mentioned in a real experiment.

tomasko789 said:
So we have:
rho1 = 1/2*(|00>+|11>)(<00|+<11|)= shorter notation =1/2*|00+11><00+11|
rho2 = 1/2*(|00><00| + |11><11|)

Consider observable:
A = 1/2*|00+11><00+11| -1/2*|00-11><00-11|

Tr(A*rho1) = 1/2
Tr(A*rho2) = 0
=> we get different mean values, for more measurements we can distinguish between the two cases.
However, this is just a theoretical observable. If you mean the actual technical realisation of such a measurement on the system I have no idea how to do it.
 

1. What is a bipartite system?

A bipartite system is a quantum system composed of two separate subsystems, such as two particles or two qubits, that interact with each other but do not interact with anything else. This means that the state of the system as a whole cannot be described by the individual states of each subsystem.

2. How can you tell if a bipartite system is entangled?

To test for entanglement in a bipartite system, one can perform a Bell inequality test. This involves measuring certain correlations between the two subsystems and comparing them to a specific threshold value. If the measured correlations exceed this threshold, the system is considered to be entangled.

3. What is a Bell inequality test?

A Bell inequality test is a way to experimentally determine if a bipartite system is entangled. It involves measuring correlations between the two subsystems in different configurations and comparing them to a threshold value. If the measured correlations exceed this threshold, the system is considered to be entangled.

4. Can a bipartite system be entangled even if the individual subsystems are not entangled?

Yes, it is possible for a bipartite system to be entangled even if the individual subsystems are not entangled. This is because entanglement is a property of the overall system, not just the individual parts. The subsystems may appear to be in a separable state, but their combined state may still exhibit entangled behavior.

5. How is entanglement measured in a bipartite system?

Entanglement in a bipartite system is typically measured using a quantifier called entanglement entropy. This measures the amount of entanglement present in the system by calculating the amount of information shared between the two subsystems. A higher entanglement entropy indicates a stronger level of entanglement in the system.

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