How to calculate the Von Neuman entropy on qiskit with the module quantum_info?

Short answer

You are getting that error because your example does not use a valid (normalized) statevector. If you remove the decimals=3 kwarg where you call result.get_statevector it will work.

Long Answer

The Von-Neuman entropy function in the qiskit.quantum_info works with either Statevector or DensityMatrix object inputs, or inputs that can be implicitly converted to those objects (ie a list or np.array for a vector or a square matrix). So you can do any of the following for example:

import numpy as np
from qiskit.quantum_info import entropy, Statevector, DensityMatrix

# Pure state entropy (Note this is always 0)
# The following are equivalent:

s1 = entropy([1, 0, 0, 0])  # Statevector as list
s2 = entropy(np.array([1, 0, 0, 0])) # Statevector as array
s3 = entropy(Statevector([1, 0, 0, 0]))  # Statevector object

print(s1, s2, s3)

# Mixed state entropy
# The following are equivalent

s1 = entropy([[0.75, 0], [0, 0.25]])  # Density matrix as list
s2 = entropy(np.array([[0.75, 0], [0, 0.25]])) # density matrix as array
s3 = entropy(DensityMatrix([[0.75, 0], [0, 0.25]]))  # Density matrix object

print(s1, s2, s3)

As for your specific issue: the entropy is only well-defined for a valid quantum state, so the function checks the input state is valid. In the case of a statevector this is checking it has norm 1, in the case of a density matrix that it is trace 1 and postive-semidefinite.

Your example does not have a norm-1 input state because you truncated the decimals when you got the output state from the simulator. You can check this using the statevector object for example:

# Returns True:
Statevector([1 / np.sqrt(2), 1 / np.sqrt(2)]).is_valid()

# Returns False:
Statevector([0.707, 0.707]).is_valid()

Entropy base: Another thing you should keep in mind if you didn't already notice is that the qiskit.quantum_info.entropy function takes logarithms in base 2 by default (and you can use a different base using the base kwarg). The deprecated qiskit.tools.qi.entropy function was always taken in log base e:

import numpy as np
from qiskit.quantum_info import entropy
from qiskit.tools.qi import entropy as old_entropy

rho = [[0.75, 0], [0, 0.25]]

s1 = entropy(rho)  # base-2
s2 = entropy(rho, base=np.e)  # base-e
s3 = old_entropy(rho)  # base-e

print(s1, s2, s3, s2 == s3)
```