Partial Transpose Negativity

qnetvo.negativity_cost_fn(network_ansatz, m, n, wires, qnode_kwargs={})[source]

Constructs an ansatz-specific negativity cost function.

Negativity can be used to identify if two subsystems \(A\) and \(B\) are entangled, through the PPT criterion. Negativity is an upper bound for distillable entanglement.

This entanglement measure is expressed as

\[\mathcal{N}(\rho) = |\sum_{\lambda_i < 0}\lambda_i|,\]

where \(\rho^{\Gamma_B}\) is the partial transpose of the joint state with respect to the \(B\) party, and \(\lambda_i\) are all of the eigenvalues of \(\rho^{\Gamma_B}\).

For more information on negativity and its applications in quantum information theory, (see Vidal and Werner, 2001).

Parameters:

  • ansatz (NetworkAnsatz) – The ansatz circuit on which the negativity is evaluated.

  • m (int) – The size of the \(A\) subsystem.

  • n (int) – The size of the \(B\) subsystem.

  • wires (list[int]) – The wires which define the joint state.

  • qnode_kwargs (dictionary) – Keyword arguments passed to the execute qnodes.

Returns:

A cost function negativity_cost(*network_settings) parameterized by the ansatz-specific scenario settings.

Return type:

Function

Raises:

ValueError – If the sum of the sizes of the two subsystems (m + n) does not match the length of wires.