This project contains Matlab codes that supplement the results of the article Geometric Rényi Divergence and its Applications in Quantum Channel Capacities (https://arxiv.org/abs/1909.05758).

Please contact Kun Fang at (fangfred11@gmail.com) if there is any bug in the codes :)

You will need the following packages to run the scripts in this project:

CVX(http://cvxr.com/cvx/) QETLAB(http://www.qetlab.com/Main_Page) CVXQUAD(https://github.com/hfawzi/cvxquad)

1. HolevoWernerBound: Computing the Holevo-Werner bound of a channel [FF19, Equation 65]
2. MaxRainsInfo: Computing the max-Rains information of a channel [FF19, Equation 60]
3. MaximalRenyiRainsInfo: Computing the geometric/maximal Rényi Rains information of a channel [FF19, Equation 62]
4. MaximalRenyiRainsThetaInfo: Computing the geometric/maximal Rényi Theta-information of a channel [FF19, Equation 86]
5. RainsInfoCovariant: Computing the Rains information of a covariant channel [FF19, Equation 59]
6. REE_GADC_channel + REE_GADC_data + REE_qubit_X: Computing the Rains information of the generalized amplitude damping channel [FF19, Equation 59]
7. biHolevoWernerbound: Computing the Holevo-Werner bound of a bidirectional channel [FF19, Equation 89]
8. biMaxRainsInfo: Computing the max-Rains information of a bidirectional channel [FF19, Equation 87]
9. biMaxRainsThetaInfo: Computing the max-Rains Theta-information of a bidirectional channel [FF19, Equation 91]
10. biMaximalRenyiRainsThetaInfo: Computing the geometric/maximal Rényi Theta-information of a bidirectional channel [FF19, Equation 97]

1. CBetaBound: Computing the CBeta bound of a channel [FF19, Equation 152]
2. CZetaBound: Computing the CZeta bound of a channel [FF19, Equation 156]
3. MaxUpsilonInfo: Computing the max-Upsilon information of a channel [FF19, Equation 154]
4. MaximalRenyiUpsilonInfo: Computing the geometric/maximal Rényi Upsilon-information of a channel [FF19, Equation 162]
5. UpsilonInfoCovariant: Computing the Upsilon-information of a covariant channel [FF19, Equation 153]

1. ManaInfo: Computing the mana of a channel [FF19, Equation 172]
2. MaxThaumaInfo: Computing the max-Thauma of a channel [FF19, Equation 175]
3. MaximalRenyiThaumaInfo: Computing the geometric/maximal Rényi Thauma of a channel [FF19, Equation 176]
4. WignerTraceNorm: Computing the Wigner trace norm of a state [FF19, Equation 167]

1. ExampleDPchannel: Choi matrix of the depolarizing channel [FF19, Equation 98]
2. ExampleERchannel: Choi matrix of the erasure channel [FF19, Equation 99]
3. ExampleDePhchannel: Choi matrix of the dephasing channel [FF19, Equation 100]
4. ExampleADchannel: Choi matrix of the amplitude damping channel [FF19, Equation 101]
5. ExampleGADchannel: Choi matrix of the generalized amplitude damping channel [FF19, Equation 101]
6. ExampleDephrasureChannel: Choi matrix of the dephrasure channel [FF19, Page 34]