# Quantum Bayesian Networks

## October 12, 2019

### Squashed Entanglement can now be calculated

Filed under: Uncategorized — rrtucci @ 7:55 pm

I’m doing a small publicity blitz for my free open source software Entanglish. I’ve posted this story here and on Reddit, Medium, Rigetti Slack, and DataScienceCentral.

A question about the future that I wonder about is: which company and nation of the world will calculate squashed entanglement (a purely classical HPC calculation) for the largest physical system. Will it be the US (Google, IBM-Summit-Oakridge), China(Alibaba) , EU, etc.

## 2 Comments »

1. Dear Tucci,

I’ve tried to use your code to calculate the squashed entanglement of qubit isotropic states. The used code can be found here: https://pastebin.com/MLgCHztC
The resultant squashed entanglement seems to go to zero only as p approaches 1, while I would expect it to go to zero as p approaches 2/3, since qubit isotropic states become separable at that point (see https://dl.acm.org/citation.cfm?id=2011328). Do you have any explanation for this?

Best,
Kenneth

Comment by kdgoodenough — October 24, 2019 @ 4:55 pm

2. Thanks, I will look into it. The algo is delicate because it requires taking a log of possibly a singular matrix followed by an exp of it, exp log (0) = 0 is very prone to numerical noise. There are quite possibly multiple local minima but only one global one so it matters where you start the recursion. There is also the question of whether the number of hidden states is large enough.

For peace of mind and completeness sake, I think we should also write a conjugate gradient calculation and a comparison between the two.
Conjugate gradient calculations have been done for entanglement of formation and, as you are probably aware of, Wootters found a closed formula for it for an arbitrary density matrix of 2 qubits

https://arxiv.org/abs/quant-ph/0006128

https://arxiv.org/abs/quant-ph/0302018

Comment by rrtucci — October 24, 2019 @ 5:28 pm

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