qkd_key_rate.protocols.quantum package

Quantum protocols

class qkd_key_rate.protocols.quantum.BB84AsymptoticKeyRateEstimate(detector, number_of_decoy=2, **kwargs)[source]

Bases: AsymptoticKeyRateEstimate

The situation for an asymptotic number of pulses.

We consider a fixed number of intensities (number_of_decoy + 1)

__init__(detector, number_of_decoy=2, **kwargs)[source]
Parameters:

  • detector (Detector) – The detector used at Bob’s side

  • number_of_decoy (int) – Number of decoy intensities used

compute_last_positive_distance(x)[source]

Computes the last positive distance.

The optimization routine sometimes considers a parameter setting outside of the valid region. This function is used to push the parameters back to the valid regime.

Return type:

float

compute_rate(mu, attenuation)[source]

Computes the key-rate given intensity-settings and an attenuation

Parameters:

  • mu (ArrayLike) – Intensity

  • attenuation (float) – Attenuation

Return type:

float

Returns:

Key-rate

optimize_rate(*, attenuation, x_0=None, bounds=None)[source]

Function to optimize the key-rate

For certain input parameters it can happen that the resulting lp problem is unfeasible. In that case the attenuation is slightly modified (+1e-6) in an attempt to obtain a feasible lp problem that can be solved.

Parameters:

  • attenuation (float) – Loss in dB for the channel

  • x_0 (Optional[ArrayLike]) – Initial search value, default midpoint search bounds

  • bounds (Optional[List[ArrayLike]]) – Bounds on search range

Return type:

Tuple[ndarray[Any, dtype[float64]], float]

Returns:

Optimized intensity and key-rate

Raises:

  • ValueError – When x_0 or bounds are given with invalid dimensions.

  • ValueError – when the found key-rate is negative.

  • OptimizationError – When lp solver is unsuccessful due to infeasible problem. Multiple attempts are made with slightly modified attenuation before error is raised.

class qkd_key_rate.protocols.quantum.BB84FiniteKeyRateEstimate(detector, number_of_pulses=1000000000000.0, number_of_decoy=2, **kwargs)[source]

Bases: FiniteKeyRateEstimate

The situation for a finite number of pulses

A fixed number of intensities is considered. The probabilities for both bases might vary.

__init__(detector, number_of_pulses=1000000000000.0, number_of_decoy=2, **kwargs)[source]
Parameters:

  • detector (Detector) – The detector used at Bob’s side

  • number_of_pulses (Optional[int]) – Number of pulses sent

  • number_of_decoy (Optional[int]) – Number of decoy intensities used

compute_last_positive_distance(x)[source]

Computes the last positive distance.

The optimization routine sometimes considers a parameter setting outside of the valid region. This function is used to push the parameters back to the valid regime.

Return type:

float

compute_rate(mu, attenuation, probability_basis_X, probability_basis_Z, n_X=None)[source]

Compute the key-rate for a specific set of parameters

Parameters:

  • mu (ArrayLike) – Used intensities

  • attenuation (float) – Attenuation of the channel

  • probability_basis_X (ArrayLike) – Probabilities for each intensity in the X-basis

  • probability_basis_Z (ArrayLike) – Probabilities for each intensity in the Z-basis

  • n_X (Optional[int]) – Number of pulses in the X-basis.

Return type:

float

Returns:

key-rate

optimize_rate(*, attenuation, x_0=None, bounds=None)[source]

Function to optimize the key-rate

The laser intensities should be ordered and the probabilities should sum to one. Probabilities for both X and Z-basis are considered simultaneously. We consider the Z-basis for error estimation and the X-basis for key-rate estimation, so no sifting rate is considered.

For certain input parameters it can happen that the resulting lp problem is unfeasible. In that case the attenuation is slightly modified (+1e-6) in an attempt to obtain a feasible lp problem that can be solved.

Parameters:

  • attenuation (float) – Loss in dB for the channel

  • x_0 (Optional[ArrayLike]) – Initial search value

  • bounds (Optional[List[ArrayLike]]) – Bounds on search range

  • args – Other variables to be optimized, for instance the attenuation

Return type:

Tuple[ndarray[Any, dtype[float64]], float]

Returns:

Optimized x=[intensity, probability_basis_X, probability_basis_Z] and found optimal key-rate

Raises:

  • ValueError – When x_0 or bounds are given with invalid dimensions.

  • ValueError – when the found key-rate is negative.

  • OptimizationError – When lp solver is unsuccessful due to infeasible problem. Multiple attempts are made with slightly modified attenuation before error is raised.

class qkd_key_rate.protocols.quantum.BB84FullyAsymptoticKeyRateEstimate(detector, **kwargs)[source]

Bases: AsymptoticKeyRateEstimate

The situation for an asymptotic number of intensity settings and pulses.

In the fully asymptotic case we only have to consider a single intensity

__init__(detector, **kwargs)[source]
Parameters:

  • detector (Detector) – The detector used at Bob’s side

  • kwargs – Protocol specific input

compute_rate(mu, attenuation)[source]

Computes the key-rate given an intensity and an attenuation.

Only the vacuum states and single photon states can be safely used. The error rate for vacuum states is 0.5. For single photon states we must upper bound it.

Parameters:

  • mu (ArrayLike) – Intensity

  • attenuation (float) – Attenuation

Return type:

float

Returns:

Key-rate

optimize_rate(*, attenuation, x_0=None, bounds=None)[source]

Function to optimize the key-rate

Parameters:

  • attenuation (float) – Loss in dB for the channel

  • x_0 (Optional[ArrayLike]) – Initial search value, default value [0.5] is chosen.

  • bounds (Optional[List[ArrayLike]]) – Bounds on search range, default [(0.1, 0.9)]

Raises:

  • ValueError – When x_0 or bounds are given with invalid dimensions.

  • ValueError – when the found key-rate is negative.

Return type:

Tuple[ndarray[Any, dtype[float64]], float]

Returns:

Optimized intensity and key-rate

class qkd_key_rate.protocols.quantum.BB84SingleAsymptoticKeyRateEstimate(detector, **kwargs)[source]

Bases: AsymptoticKeyRateEstimate

Key-rate modules when a single photon source is used. We may then assume all states remain save and photon number splitting attacks are impossible.

__init__(detector, **kwargs)[source]
Parameters:

  • detector (Detector) – The detector used at Bob’s side

  • kwargs – protocol specific input

compute_rate(mu, attenuation)[source]

Computes the key-rate given an intensity and an attenuation.

Parameters:

  • mu (ArrayLike) – Intensity

  • attenuation (float) – Attenuation

Return type:

float

Returns:

Key-rate

optimize_rate(*, attenuation, x_0=None, bounds=None)[source]

Function to optimize the key-rate

Parameters:

  • attenuation (float) – Loss in dB for the channel

  • x_0 (Optional[ArrayLike]) – Initial search value, default value [0.5] is chosen.

  • bounds (Optional[List[ArrayLike]]) – Bounds on search range, default [(0.1, 0.9)]

Return type:

Tuple[ndarray[Any, dtype[float64]], float]

Returns:

Optimized intensity and key-rate

Raises:

  • ValueError – When x_0 or bounds are given with invalid dimensions.

  • ValueError – when the found key-rate is negative.

class qkd_key_rate.protocols.quantum.BBM92AsymptoticKeyRateEstimate(detector, detector_alice=None, **kwargs)[source]

Bases: AsymptoticKeyRateEstimate

BBM92 Asymptotic Key Rate

__init__(detector, detector_alice=None, **kwargs)[source]

Class for asymptotic key-rate estimation

Parameters:

  • detector (Detector) – The detector used at Bob’s side

  • detector_alice (Optional[Detector]) – The detector used at Alice’s side. default same detector as Bob.

compute_rate(mu, attenuation)[source]

Compute the key-rate for a specific intensity and attenuation.

Note, the source can be placed anywhere between the two parties. If the source is placed at one party, we effectively have the BB84 protocol. The optimal gain is achieved with the source placed in middle between the two parties.

Parameters:

  • mu (ArrayLike) – Intensity

  • attenuation (float) – Attenuation

Return type:

float

Returns:

Key-rate

Raises:

ValueError – When mu is given with invalid dimensions

optimize_rate(*, attenuation, x_0=None, bounds=None)[source]

Function to optimize the key-rate

Parameters:

  • attenuation (float) – Loss in dB for the channel

  • x_0 (Optional[ArrayLike]) – Initial search value, default value [0.5] is chosen.

  • bounds (Optional[List[ArrayLike]]) – Bounds on search range, default [(0.001, 0.5)]

Return type:

Tuple[ndarray[Any, dtype[float64]], float]

Returns:

Optimized intensity and key-rate

Raises:

  • ValueError – When x_0 or bounds are given with invalid dimensions.

  • ValueError – when the found key-rate is negative.

class qkd_key_rate.protocols.quantum.BBM92FiniteKeyRateEstimate(detector, number_of_pulses=1000000000000.0, detector_alice=None, **kwargs)[source]

Bases: FiniteKeyRateEstimate

BBM92 Finite key-rate.

__init__(detector, number_of_pulses=1000000000000.0, detector_alice=None, **kwargs)[source]

Class for finite key-rate estimation

Parameters:

  • detector (Detector) – The detector used at Bob’s side

  • number_of_pulses (float) – Number of pulses sent in total

  • detector_alice (Optional[Detector]) – The detector used at Alice’s side. default same detector as Bob.

compute_last_positive_distance(x)[source]

Computes the last positive distance.

The optimization routine sometimes considers a parameter setting outside of the valid region. This function is used to push the parameters back to the valid regime.

Return type:

float

compute_rate(mu, attenuation, probability_basis_X, probability_basis_Z, n_X=None)[source]

Compute the key-rate for a specific set of variables

Note, the source can be placed anywhere between the two parties. If the source is placed at one party, we effectively have the BB84 protocol. The optimal gain is achieved with the source placed in middle between the two parties.

Parameters:

  • mu (ArrayLike) – Used intensities

  • attenuation (float) – Attenuation of the channel

  • probability_basis_X (ArrayLike) – Probabilities for each intensity in X-basis

  • probability_basis_Z (ArrayLike) – Probabilities for each intensity in Z-basis

  • n_X (Optional[int]) – Number of pulses in the X-basis

Return type:

float

Returns:

key-rate

Raises:

ValueError – When mu is given with invalid dimensions

optimize_rate(*, attenuation, x_0=None, bounds=None)[source]

Function to optimize the key-rate

Parameters:

  • attenuation (float) – Loss in dB for the channel

  • x_0 (Optional[ArrayLike]) – Initial search value

  • bounds (Optional[List[ArrayLike]]) – Bounds on search range

Return type:

Tuple[ndarray[Any, dtype[float64]], float]

Returns:

Optimized x=[intensity, probability_basis_X, probability_basis_Z] and found optimal key-rate

Raises:

  • ValueError – when x_0 or bounds are given with invalid dimensions.

  • ValueError – when the found key-rate is negative.