# How to calculate tri-partite entanglement or mutual information
**URL:** https://itensor.discourse.group/t/how-to-calculate-tri-partite-entanglement-or-mutual-information/1115
**Category:** ITensor Julia Questions
**Tags:** mps, entanglement, julia
**Created:** [August 25, 2023, 9:41am UTC](https://itensor.discourse.group/t/how-to-calculate-tri-partite-entanglement-or-mutual-information/1115 "2023-08-25T09:41:53Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@singhroy.monalisa](https://itensor.discourse.group/u/singhroy.monalisa)
#### Post date: [August 25, 2023, 9:41am UTC](https://itensor.discourse.group/t/how-to-calculate-tri-partite-entanglement-or-mutual-information/1115/1 "2023-08-25T09:41:53Z")
Hi,
I am trying to calculate the tri-partite entanglement entropy or mutual information (I) in a one dimension (1D) spin-1/2 chain, defined as,
I (A, B, C) ≡ S(A) + S(B) + S(C) − S(A ∪ B) − S(A ∪ C) − S(B ∪ C) + S(A ∪ B ∪ C).
where, A, B, C are three regions (connected or disconnected) in the 1D chain.
c.f.: [Phys. Rev. B 101, 060301(R) (2020)](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.101.060301), [PRE 98 052205 (2018)](https://doi.org/10.1103/PhysRevE.98.052205),
I am not sure how SVD can help in this case, especially for the S(A ∪ B ∪ C) term.
Can you please point me in the right direction of thinking?
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### Author:  [@moony](https://itensor.discourse.group/u/moony)
#### Post date: [August 25, 2023, 9:52am UTC](https://itensor.discourse.group/t/how-to-calculate-tri-partite-entanglement-or-mutual-information/1115/2 "2023-08-25T09:52:02Z")
One way could be to divide the system into “connected” A,B,C,D region as shown in the paper you referred [Phys. Rev. B 101, 060301(R) (2020)](https://doi.org/10.1103/PhysRevB.101.060301).
Except… make sure that length of (no. of spin sites in) A+B+C is less than D.
Then S(A ∪ B ∪ C) can be calculated by doing an SVD at site between the regions A+B+C and D.