What is the Relationship Between Concurrence and Three Tangle in Quantum States?

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SUMMARY

The discussion focuses on the relationship between three tangle and concurrence in quantum states, specifically addressing the formula for three tangle, which is defined as $$\tau=\tau_{A(BC)}-\tau_{AB}-\tau_{AC}$$. It is established that three tangle can be expressed in terms of concurrence with the equation $$\tau=C^2_{A(BC)}-C^2_{AB}-C^2_{AC}$$, where concurrence is calculated using $$C^2=2-(Tr\rho^2_1+Tr\rho^2_2)$$. The participants express confusion regarding the expected values of three tangle for GHZ and W states, noting that $$\tau>0$$ for GHZ states and $$\tau=0$$ for W states. Additionally, there is a request for examples and code to calculate the density matrix and three tangle.

PREREQUISITES
  • Understanding of quantum mechanics concepts, particularly entanglement.
  • Familiarity with the mathematical definitions of three tangle and concurrence.
  • Knowledge of density matrices and partial trace operations.
  • Basic programming skills for implementing calculations in code.
NEXT STEPS
  • Study the derivation of the three tangle formula in quantum mechanics.
  • Learn how to compute the density matrix for various quantum states.
  • Explore numerical methods for calculating concurrence and three tangle using Python or MATLAB.
  • Review examples of GHZ and W states to understand their properties and implications for entanglement measures.
USEFUL FOR

Quantum physicists, researchers in quantum information theory, and students studying quantum entanglement who require a deeper understanding of three tangle and concurrence calculations.

munirah
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Good day,

May anyone help me to confirm the formula use for three tangle using concurrence.

From my reading,

three tangle,

$$\tau=\tau_{A(BC)}-\tau_{AB}-\tau_{AC}$$

and it can be related to concurrence

$$\tau=C^2_{A(BC)}-C^2_{AB}-C^2_{AC}$$

and I used formula for C is

$$C^2=2-(Tr\rho^2_1+Tr\rho^2_2)$$ where $$\rho$$ is partial trace.
[FONT=Georgia, Times New Roman, Times, serif]
When I calculate the GHZ state, I get zero. It suppose $$\tau>0$$ for GHZ state and $$\tau=0$$ for W state
[FONT=Georgia, Times New Roman, Times, serif]
May I know, what it mean by the $$\tau$$ here. Please help me.

And How I can calculated the density matrix of the state using three tangle. May anyone show me an example. I'm really stuck. Please help me.

Thank you.

 
Thank you Greg Bernhardt. It is ok for this. I will make other question.
 
munirah said:
Good day,

May anyone help me to confirm the formula use for three tangle using concurrence.

From my reading,

three tangle,

$$\tau=\tau_{A(BC)}-\tau_{AB}-\tau_{AC}$$

and it can be related to concurrence

$$\tau=C^2_{A(BC)}-C^2_{AB}-C^2_{AC}$$

and I used formula for C is

$$C^2=2-(Tr\rho^2_1+Tr\rho^2_2)$$ where $$\rho$$ is partial trace.
[FONT=Georgia, Times New Roman, Times, serif]
When I calculate the GHZ state, I get zero. It suppose $$\tau>0$$ for GHZ state and $$\tau=0$$ for W state
[FONT=Georgia, Times New Roman, Times, serif]
May I know, what it mean by the $$\tau$$ here. Please help me.

And How I can calculated the density matrix of the state using three tangle. May anyone show me an example. I'm really stuck. Please help me.

Thank you.
can you share me how to calculate the tangle. Its very urgent thing for me. And if possible please send me the code for that.
 
Hello,, even I am also struck in this. It is very needed for me. can you please share me how to calculate tangle manually and if you have code please send me. It will be a great helpfull for me. please send me today. Most wanted problem.
 
Appu said:
Hello,, even I am also struck in this. It is very needed for me. can you please share me how to calculate tangle manually and if you have code please send me. It will be a great helpfull for me. please send me today. Most wanted problem.
Welcome to PF. :smile:

This thread is over 5 years old, and the Original Poster (OP) has not been here since 2017. If this is a question for your work, start a new thread in the appropriate technical forum, and show what you have found so far. If this is for schoolwork, start a new thread in the Homework Help forums, and show your work on the problem.

BTW, please do not use text speak like "please" at PF. It is not allowed. Thank you.
 
Sorry for the mistake Sir. It won't repeat again.
Thank you.
 
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