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states.mutually_unbiased_basis¶
Construct a set of mutually unbiased bases.
Module Contents¶
Functions¶
Generate list of MUBs for a given dimension [1]. |
|
Determine if a number is a prime power. |
- states.mutually_unbiased_basis.mutually_unbiased_basis(dim)¶
Generate list of MUBs for a given dimension [1].
Note that this function only works if the dimension provided is prime or a power of a prime. Otherwise, we don’t know how to generate general MUBs.
Examples
For the case of dimension 2, the three mutually unbiased bases are provided by:
\[\begin{split}M_0 = \left\{|0\rangle, |1\rangle \right\}, \\ M_1 = \left\{\frac{|0\rangle + |1\rangle}{\sqrt{2}}, \frac{|0\rangle - |1\rangle}{\sqrt{2}}\right\} M_2 = \left\{\frac{|0\rangle + i|1\rangle}{\sqrt{2}}, \frac{|0\rangle - i|1\rangle}{\sqrt{2}}\right\}\end{split}\]References
- Parameters:
dim (int) – The dimension of the mutually unbiased bases to produce.
- Returns:
The set of mutually unbiased bases of dimension
dim(if known).- Return type:
list[numpy.ndarray]
- states.mutually_unbiased_basis._is_prime_power(n)¶
Determine if a number is a prime power.
A number is a prime power if it can be written as p^k, where p is a prime number and k is an integer greater than 0.
- Parameters:
n (int) – An integer to check for being a prime power.
- Returns:
True if n is a prime power, False otherwise.
- Return type:
bool