qml.math.vn_entropy¶
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vn_entropy(state, indices, base=None, check_state=False, c_dtype='complex128')[source]¶ Compute the Von Neumann entropy from a density matrix on a given subsystem. It supports all interfaces (NumPy, Autograd, Torch, TensorFlow and Jax).
\[S( \rho ) = -\text{Tr}( \rho \log ( \rho ))\]- Parameters
state (tensor_like) – Density matrix of shape
(2**N, 2**N)or(batch_dim, 2**N, 2**N).indices (list(int)) – List of indices in the considered subsystem.
base (float) – Base for the logarithm. If None, the natural logarithm is used.
check_state (bool) – If True, the function will check the state validity (shape and norm).
c_dtype (str) – Complex floating point precision type.
- Returns
Von Neumann entropy of the considered subsystem.
- Return type
float
Example
The entropy of a subsystem for any state vectors can be obtained. Here is an example for the maximally entangled state, where the subsystem entropy is maximal (default base for log is exponential).
>>> x = [1, 0, 0, 1] / np.sqrt(2) >>> x = dm_from_state_vector(x) >>> vn_entropy(x, indices=[0]) 0.6931472
The logarithm base can be switched to 2 for example.
>>> vn_entropy(x, indices=[0], base=2) 1.0