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Geometric Rényi Divergence and its Applications in Quantum Channel Capacities

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 :)

Dependencies:

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)

QCapacity_Bounds

  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]

CCapacity_Bounds

  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]

Magic_Bounds

  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]

Example_Channels

  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]

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