Building separable approximations for quantum states via neural networks
- URL: http://arxiv.org/abs/2112.08055v1
- Date: Wed, 15 Dec 2021 11:50:25 GMT
- Title: Building separable approximations for quantum states via neural networks
- Authors: Antoine Girardin, Nicolas Brunner and Tam\'as Kriv\'achy
- Abstract summary: We parametrize separable states with a neural network and train it to minimize the distance to a given target state.
By examining the output of the algorithm, we can deduce whether the target state is entangled or not, and construct an approximation for its closest separable state.
We show our method to be efficient in the multipartite case, considering different notions of separability.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Finding the closest separable state to a given target state is a notoriously
difficult task, even more difficult than deciding whether a state is entangled
or separable. To tackle this task, we parametrize separable states with a
neural network and train it to minimize the distance to a given target state,
with respect to a differentiable distance, such as the trace distance or
Hilbert-Schmidt distance. By examining the output of the algorithm, we can
deduce whether the target state is entangled or not, and construct an
approximation for its closest separable state. We benchmark the method on a
variety of well-known classes of bipartite states and find excellent agreement,
even up to local dimension of $d=10$. Moreover, we show our method to be
efficient in the multipartite case, considering different notions of
separability. Examining three and four-party GHZ and W states we recover known
bounds and obtain novel ones, for instance for triseparability. Finally, we
show how to use the neural network's results to gain analytic insight.
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