Single-photon transmission determination

A computer-implemented method for determining a lower-bound for a number of successful single-photon transmissions from a transmitter to a receiver,

• wherein for a plurality of transmissions, one or more parameters of each of the transmissions may be selected from a plurality of predetermined discrete values, and the method comprises:
• determining, for each value of each of the one or more parameters, the number of transmissions transmitted by the transmitter having said value;
• determining, for each value of each of the one or more parameters, the number of transmissions received by the receiver having said value;
• and
• determining an estimator based on:
• the determined number of transmitted transmissions corresponding to each of the values of the one or more parameters,
• the determined number of received transmissions corresponding to each of the values of the one or more parameters, and
• a plurality of statistical parameters, wherein each statistical parameter is associated with a statistical model of the number of photons transmitted per transmission from the transmitter for a respective value of the one or more parameters, wherein determining the estimator comprises:
• for each of the plurality of statistical parameters, λi, determining a respective coefficient,
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• determining the estimator, Y=ΣiciMi/Ni,
• wherein Ni represents the determined number of transmitted transmissions corresponding to each of the values of the one or more parameters and Mi represents the determined number of received transmissions corresponding to each of the values of the one or more parameters,
• wherein the estimator is a lower-bound for the number of successful single-photon transmissions between the transmitter and the receiver, and
• wherein the estimator is strictly non-positively biased.

A non-transitory computer-readable medium comprising logic which, when executed by a computer, causes the computer to determine a lower-bound for a number of successful single-photon transmissions from a transmitter to a receiver, wherein for a plurality of transmissions, one or more parameters of each of the transmissions may be selected from a plurality of predetermined discrete values, wherein the computer is further configured to:

• determine, for each value of each of the one or more parameters, the number of transmissions transmitted by the transmitter having said value;
• determine, for each value of each of the one or more parameters, the number of transmissions received by the receiver having said value;
• and
• determine an estimator based on:
• the determined number of transmitted transmissions corresponding to each of the values of the one or more parameters,
• the determined number of received transmissions corresponding to each of the values of the one or more parameters, and
• a plurality of statistical parameters, wherein each statistical parameter is associated with a statistical model of the number of photons transmitted per transmission from the transmitter for a respective value of the one or more parameters, wherein determining the estimator comprises:
• for each of the plurality of statistical parameters, λi, determining a respective coefficient,
• c
• i
• =
• e
• λ
• i
• ×
• ∑
• j
• ≠
• i
• λ
• j
• 2
• ∏
• j
• ≠
• i
• ⁢
• (
• -
• 1
• )
• j
• -
• i
• ⁢
• (
• λ
• j
• -
• λ
• i
• )
• ;
• and
• determining the estimator, Y=ΣciMi/Ni,
• wherein N;
• represents the determined number of transmitted transmissions corresponding to each of the values of the one or more parameters and M;
• represents the determined number of received transmissions corresponding to each of the values of the one or more parameters,
• wherein the estimator is a lower-bound for the number of successful single-photon transmissions between the transmitter and the receiver, and
• wherein the estimator is strictly non-positively biased.