code: def _compute_max_entropy(density_matrix, base):
      """Compute the maximum entropy from a density matrix
  
      Args:
          density_matrix (tensor_like): ``(2**N, 2**N)`` or ``(batch_dim, 2**N, 2**N)`` tensor for an integer `N`.
          base (float, int): Base for the logarithm. If None, the natural logarithm is used.
  
      Returns:
          float: Maximum entropy of the density matrix.
  
      **Example**
  
      >>> x = [[1/2, 0], [0, 1/2]]
      >>> _compute_max_entropy(x)
      0.6931472
  
      >>> x = [[1/2, 0], [0, 1/2]]
      >>> _compute_max_entropy(x, base=2)
      1.0
  
      """
      # Change basis if necessary
      if base:
          div_base = np.log(base)
      else:
          div_base = 1
  
      evs = qml.math.eigvalsh(density_matrix)
      evs = qml.math.real(evs)
      rank = qml.math.sum(
          evs / qml.math.where(evs > 1e-8, evs, 1.0), -1
      )
      maximum_entropy = qml.math.log(rank) / div_base
  
      return maximum_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 20 for calling a global function with example usage: _compute_max_entropy(density_matrix, base) and returns: maximum_entropy