diamond_norm¶

diamond_norm(choi, **kwargs)[source]¶

Return the diamond norm of the input quantum channel object.

This function computes the completely-bounded trace-norm (often referred to as the diamond-norm) of the input quantum channel object using the semidefinite-program from reference [1].

Parameters

choi (Choi or QuantumChannel) – a quantum channel object or Choi-matrix array.
kwargs – optional arguments to pass to CVXPY solver.

Returns

The completely-bounded trace norm: \(\|\mathcal{E}\|_{\diamond}\).

Return type

float

Raises

QiskitError – if CVXPY package cannot be found.

Additional Information:: The input to this function is typically not a CPTP quantum channel, but rather the difference between two quantum channels \(\|\Delta\mathcal{E}\|_\diamond\) where \(\Delta\mathcal{E} = \mathcal{E}_1 - \mathcal{E}_2\).
Reference:: J. Watrous. “Simpler semidefinite programs for completely bounded norms”, arXiv:1207.5726 [quant-ph] (2012).

Note

This function requires the optional CVXPY package to be installed. Any additional kwargs will be passed to the cvxpy.solve function. See the CVXPY documentation for information on available SDP solvers.