seesaw.SeesawLO¶

seesaw.SeesawLO.SeesawDecoupling(JF, J_in, m, opt_sys)¶

CONVENTION: please read before modify this function!

The data of variables are encoded as follows:

• Suppose qp decomposition terms are arranged by decreasing order of the coefficients

  • m is then the largest index such that the corresponding coefficient is non-negative.

  • n is the number of decomposed terms

• JF is the target channel.

• J_in is the fixed variable and J_out is the opt varible in this iteration.

Depending on opt_sys, variable J_in and J_out could have different meanings:

• If opt_sys = 1, then J_in = JA and J_out = JB;

• If opt_sys = 2, then J_in = JB and J_out = JA.

• a is the coefficient of this optimization, where a(i) corresponds to

  • the coefficient of i-th term for 1 <= i <= m;

  • the negative coefficient of i-th term for m <= i <= n.

• For 1 <= i <= n:

  • JA/JB(:, :, i, 1) corresponds to the positve part of i-th decomposition term;

  • JA/JB(:, :, i, 2) corresponds to the negative part of i-th decomposition term.

• dim_A/B are the dimensions of system A and B, respectively.

seesaw.SeesawLO.SeesawLO(JN_target, dA, dB, varargin)¶

\[\gamma_{LO}(\mathcal{N}_{AB \rightarrow A'B'}) = \min \sum_j |\alpha_j| \ s.t. \ \mathcal{M}^{(A/B)}_j \in \operatorname{CPTN}(A/B \rightarrow A'/B') \ \mathcal{N}_{AB\rightarrow A'B'} = \sum_j \alpha_j \mathcal{M}^{(A)}_j \otimes \mathcal{M}^{(B)}_j\]

Parameters:¶

• JN_target (numeric) – The Choi matrix of the bipartite channel.

• dA (numeric) – The dimension of subsystem A.

• dB (numeric) – The dimension of subsystem B.

• varargin (numeric) – The hyperparameters for the optimization algorithm.

Returns:¶

The optimized decomposition of the target channel.

Return type:¶

numeric

seesaw.SeesawLO.SeesawMinimizing(JF, J_in, err, m, opt_sys)¶

CONVENTION: please read before modify this function!

The data of variables are encoded as follows:

• Suppose qp decomposition terms are arranged by decreasing order of the coefficients

  • m is then the largest index such that the corresponding coefficient is non-negative.

  • n is the number of decomposed terms

• JF is the target channel.

• err is the error tolerance for qp simulation.

• J_in is the fixed variable and J_out is the opt varible in this iteration.

Depending on opt_sys, variable J_in and J_out could have different meanings: - If opt_sys = 1, then J_in = JA and J_out = JB; - If opt_sys = 2, then J_in = JB and J_out = JA.

• a is the coefficient of this optimization, where a(i) corresponds to

  • the coefficient of i-th term for 1 <= i <= m;

  • the negative coefficient of i-th term for m <= i <= n.

• For 1 <= i <= n:

  • JA/JB(:, :, i, 1) corresponds to the positve part of i-th decomposition term;

  • JA/JB(:, :, i, 2) corresponds to the negative part of i-th decomposition term.

• dim_A/B are the dimensions of system A and B, respectively.