code: def vn_entropy(
      state, indices, base=None, check_state=False, c_dtype="complex128"
  ):
      r"""Compute the Von Neumann entropy from a density matrix on a given subsystem. It supports all
      interfaces (Numpy, Autograd, Torch, Tensorflow and Jax).
  
      .. math::
          S( \rho ) = -\text{Tr}( \rho \log ( \rho ))
  
      Args:
          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:
          float: Von Neumann entropy of the considered subsystem.
  
      **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
  
      .. seealso:: :func:`pennylane.qinfo.transforms.vn_entropy` and :func:`pennylane.vn_entropy`
      """
      density_matrix = reduce_dm(state, indices, check_state, c_dtype)
      entropy = _compute_vn_entropy(density_matrix, base)
      return entropy
  
imports: import itertools
  import functools
  from string import ascii_letters
  from autoray import numpy
  from numpy import float64
  import pennylane
  from .None import single_dispatch
  from .multi_dispatch import diag, dot, scatter_element_add, einsum, get_interface
  from .utils import is_abstract, allclose, cast, convert_like, cast_like
  from .matrix_manipulation import _permute_dense_matrix
label_desc: Use image node_id 10 for calling a global function with example usage: vn_entropy(state, indices, base, check_state, c_dtype) and returns: entropy