Improved Decoy-state and Flag-state Squashing Methods

This is a public version of the code used in Improved Decoy-state and Flag-state Squashing Methods [Arxiv]. This was built for a modified version of openQKDsecurity v1.0 and all changes have been included in this repository.

Installation Instructions

[!CAUTION] This repository is for archival and transparency purposes; we do not guarantee compatibility with other versions of the Open QKD Security package beyond the ones listed above.

1. Clone or download the repository.
2. Follow all further install instructions.
3. Also follow the additional Mosek install instructions if you want an exact match.

Figure Instructions

The functions below are required to generate the plots in the paper. For each plot we describe below which settings need to be chosen. For all plots the change from two to one decoy intensity is done as follows 1. Comment out the parameters with two decoy intensities in the preset file, 2. Comment out the variable names with two decoy intesities in the channel module, 3. Comment out the variable 'decoys' containing two decoy intensities in the channel module.

Here are the specific minor modificaitons required to reproduce the data of figures in the paper.

Figure 1

Requires functions Main_BB84 and pmBB84WCP_nodecoy for the correct parameters. For comparing different decoy methods, in the pmBB84WCP_nodecoy preset change the channel model to pmBB84WCPChannel_constr_nodecoy for the yellow triangles, and to pmBB84WCPChannel_Choi_nodecoy for the red circles.

Figure 2

Requires functions Main_BB84 and pmBB84WCP_decoy for the correct parameters. To recreate the curves using the decoy-state methods from Wang et.al. [4] change the channel to pmBB84WCPChannel (green diamonds and red circles) and comment out the decoy intensities appropriately. For the improved decoy methods (yellow stars) choose pmBB84WCPChannel_Choi in the same preset and comment out the decoy intensities appropriately.

Figure 3

This uses the same data as in figure 2.

Figure 7

Requires functions Main_SixState and pmSixStateWCP_decoy for the correct parameters of the qubit squasher [2, 3]. The channel models pmSixStateWCPChannel or pmSixStateWCPChannel_improved_decoy implement the decoy methods from Ref [4] and the improved decoy methods decoy methods, respectively. To change the number of decoy intensities comment out the intensities as described above. The files Main_SixState_Flag and pmSixStateLossyDescription_Flag_Reduced with the parameters $pz^A = \dots = py^A = pz^B = \dots = py^B = \frac{1}{3}$ are required for the flag-state squasher. The improved decoy methods from pmSixStateWCPChannel_Flag_improved create the curve corresponding to the flag-state squasher (red diamonds). Since this plot uses two decoy intensities a almost indistinguishable curve can be generated using the decoy methods from Ref [4] in pmSixStateWCPChannel_Flag_Reduced. To switch between any of these channel models they need to be commented out appropriately in the presets.

Figure 8

Main_SixState_Flag and pmSixStateLossyDescription_Flag_Reduced with $pz^A= pz^B = 0.8, py^A = py^B = px^A = px^B = 0.1$ setup the protocol using the flag-state squasher. The channel module pmSixStateWCPChannel_Flag_improved creates the curve corresponding to the improved decoy methods (red stars) and the channel module pmSixStateWCPChannel_Flag_Reduced is used for the standard decoy methods [4], creating the curve with green circles. Again, in the preset the channel modules and intensities have to be commented out appropriately.

Figure 9

Main_SixState_Flag and pmSixStateLossyDescription_Flag_Reduced with $pz^A= pz^B = 0.8, py^A = py^B = px^A = px^B = 0.1$ while commenting out all unncessary decoy intensities sets up the protocol. The channel modules pmSixStateWCPChannel_Flag_improved and pmSixStateWCPChannel_Flag_nodecoy create the curves using the improved decoy methods from this work and applying $e_0 = 1/2$ from Rusca et. al. [1], respectively.

Figure 10

This figure requires Main_SixState_Flag with the preset pmSixStateWCP_decoy_Flag_dif_int while setting $pz^A = \dots = py^A = pz^B = \dots = py^B = \frac{1}{3}$. The description file pmSixStateLossyDescription_Flag_dif_int and the channel pmSixStateWCPChannel_Flag_dif_int are create the curve without a bit bias. The description file pmSixStateLossyDescription_Flag_bit_bias and the channel pmSixStateWCPChannel_Flag_bit_bias create the curve with a bit bias. In both channel modules one can switch between improved decoy methods and standard decoy methods [4] by commenting out the lines 128 (w/o bit bias) or 109 (with bit bias).

Figure 11

This figure uses the same data as figure 10, but each key rate curve is divided by the sigle photon probability.

Functions

BB84:

Main_BB84: main file for any version of the BB84 protocol

no decoy:

• pmBB84WCP_nodecoy: preset for decoy analysis without decoy intensities
• pmBB84WCPChannel_Choi_nodecoy: channel for no decoy intensities using improved decoy methods
• pmBB84WCPChannel_constr_nodecoy: channel for no decoy intensities using results from Rusca et. al. [1], i.e. e_0 = 1/2

decoy:

• pmBB84WCP_decoy: preset for BB84 protocol with decoy states
• pmBB84WCPChannel_Choi: channel with decoy intensities using improved decoy methods

Six-State:

Qubit squasher from Refs [2, 3]:

Main_SixState: main file for the six-state protocol with the squashing map from Refs [2, 3]

• pmSixStateWCP_decoy: preset for six-state protocol with decoy state
• pmSixStateLossyDescription: Description file for six-state protocol with decoy state
• pmSixStateWCPChannel: Channel model for six-state protocol implementing decoy analysis from Wang et.al. [4]
• pmSixStateWCPChannel_improved_decoy: Channel model for six-state protocol implementing improved decoy methods

Flag-state squasher:

Main_SixState_Flag: main file for the six-state protocol with the flag-state squasher from Theorem 1 together with Eq. (78)

equal intensities:

• pmSixStateWCP_decoy_Flag: preset for six-state protocol with decoy state with equal intensities (clean and correct intervals)
• pmSixStateLossyDescription_Flag_Reduced: description file for six-state protocol with decoy states and the flag-state squasher from Theorem 1 together with Eq. (78)
• pmSixStateWCPChannel_Flag_Reduced: Channel model for six-state protocol implementing decoy analysis from Wang et. al. [4] with flag-state squasher
• pmSixStateWCPChannel_Flag_improved: Channel model for six-state protocol using improved decoy methods with flag-state squasher
• pmSixStateWCPChannel_Flag_nodecoy: Channel model for six-state protocol with no decoy intensities using results from Rusca et. al. [1], i.e. e_0 = 1/2

different intensities:

• pmSixStateWCP_decoy_Flag_dif_int: preset for six-state protocol with decoy state with different intensities (used with and without bit bias)
• pmSixStateLossyDescription_Flag_dif_int: description file for six-state protocol with decoy states and different intensities
• pmSixStateLossyDescription_Flag_bit_bias: description file for six-state protocol with decoy states and different intensities applying a bit bias
• pmSixStateWCPChannel_Flag_dif_int: Channel model for six-state protocol using improved decoy methods or decoy analysis from Wang et. al. [4] for different intensities
• pmSixStateWCPChannel_Flag_bit_bias: Channel model for six-state protocol using improved decoy methods or decoy analysis from Wang et. al. [4] for different intensities and applies a bit bias

References

[1] D. Rusca, A. Boaron, F. Grünenfelder, A. Martin, and H. Zbinden, Finite-key analysis for the 1-decoy state QKD protocol, Applied Physics Letters 112, 171104 (2018).

[2] O. Gittsovich, N. J. Beaudry, V. Narasimhachar, R. R. Alvarez, T. Moroder, and N. Lütkenhaus, Squashing model for detectors and applications to quantum-key-distribution protocols, Physical Review A 89, 012325 (2014).

[3] N. J. Beaudry, T. Moroder, and N. Lütkenhaus, Squashing Models for Optical Measurements in Quantum Communication, Physical Review Letters 101, 093601 (2008).

[4] W. Wang and N. Lütkenhaus, Numerical security proof for the decoy-state BB84 protocol and measurement-device-independent quantum key distribution resistant against large basis misalignment, Phys. Rev. Res. 4, 043097 (2022).