Entanglement entropy of pure bipartite states

[astralcai]

Context:

Quantifying the entanglement for example by determining the entropy of entanglement of bipartite quantum states can be useful for applications of quantum information (e.g., in quantum cryptography).

One way of determining entanglement entropy is to compute the von Neumann entropy of one of the reduced states (see reduced density matrix feature here).

It could be useful to add a user interface for such a measure specifically for the bipartite quantum state case.

Description of the Change:

The von Neumann entanglement entropy feature is now added to math and qinfo. qml.math.vn_entanglement_entropy() returns the Von Neumann entanglement entropy between two subsystems in a given density matrix. qml.qinfo.vn_entanglement_entropy() computes the Von Neumann entanglement entropy from a QNode returning a state().

Benefits:

It enables users to find the entanglement entropy of a pure bipartite state.

Possible Drawbacks:

The von Neumann entanglement entropy is only defined for pure bipartite states. The current implementation does not perform any checks on if the overall input state is pure or mixed, since such a check would be jax.jit-unfriendly.

Related GitHub Issues:
#3150

Related Shortcut Story
[sc-55206]

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.69%. Comparing base (9151477) to head (398470e).
Report is 9 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5306      +/-   ##
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- Coverage   99.69%   99.69%   -0.01%     
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  Files         410      412       +2     
  Lines       38278    38159     -119     
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- Hits        38161    38041     -120     
- Misses        117      118       +1     

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[PietropaoloFrisoni]

Thanks, @astralcai! It looks great to me. I just left a few minor comments. Since this branch is 37 commits behind master, maybe updating it to see if all tests are fine would be appropriate.

[PietropaoloFrisoni]

👍👍👍