Secure multi-state quantum key distribution with wavelength division multiplexing
The performance of quantum key distribution by systems and methods that use wavelength division multiplexing and encode information using both wavelength and polarization of photons of two or more wavelengths. Multi-wavelength polarization state encoding schemes allow ternary-coded digits, quaternary-coded digits and higher-radix digits to be represented by single photons. Information expressed in a first radix can be encoded in a higher radix and combined with a string of key values to produce a datastream having all allowed digit values of that radix in a manner that allows eavesdropping to be detected without requiring the sender and receiver to exchange additional information after transmission of the information.
1. A method, comprising:
receiving incoming photons representing digit values of a datastream that includes at least three distinct digit values, the incoming photons including photons having a first wavelength and photons having a second wavelength;
selecting between first and second measurement bases for each photon, each measurement basis defining a pair mutually orthogonal polarization axes;
performing a polarization measurement on each photon that determines a polarization axis of that photon in the measurement basis selected for that photon and a wavelength of that photon; and
decoding the datastream using the wavelength and polarization of each of the polarized photon, including generating a signal indicating whether at least a portion of the datastream was altered;
wherein the first measurement basis defines, for each of the first and second wavelengths, a first polarization axis in a plane for that wavelength and a second polarization axis in that plane that is perpendicular to the first polarization axis for that wavelength;
wherein the second measurement basis defines, for each of the first and second wavelengths, a third polarization axis in the plane for that wavelength and a fourth polarization axis in the plane for that wavelength that is perpendicular to the third polarization axis for that wavelength; and
wherein the third and the fourth polarization axes for each wavelength are equally-weighted vector combinations of the first and second polarization axes for that wavelength.
2. The method of claim 1 , wherein decoding the datastream using the wavelength and polarization of each of the polarized photon comprises:
performing the polarization measurement on a first portion of the incoming photons according to the first measurement basis and on a second portion of the incoming photons according to the second measurement basis for each wavelength;
determining, according to the polarization measurement, a number erratic of photons of the first portion having the second wavelength having a measured polarization axis that differs from an expected polarization axis of the first measurement basis for the second wavelength;
determining, according to the polarization measurement, a number of erratic photons of the second portion having the first wavelength that have a measured polarization axis that differs from an expected polarization axis of the first measurement basis for the second wavelength; and
wherein generating the signal indicating whether at least a portion of the datastream was altered includes causing the signal to indicate whether a sum of the number of erratic photons of the first portion and the number of erratic photons of the second portion exceeds a predetermined threshold.
3. The method of claim 2 , wherein decoding the datastream using the wavelength and polarization of each of the polarized photon further comprises:
associating a first digit value with photons having the first wavelength that belong to the first portion and are polarized along the first polarization axis for the first wavelength according to the polarization measurement;
associating a second digit value with photons having the first wavelength that belong to the first portion and are polarized along the second polarization axis for the first wavelength according to the polarization measurement;
associating the first digit value with photons having the second wavelength that belong to the second portion and are polarized along the third polarization axis for the first wavelength according to the polarization measurement; and
associating the second digit value with photons having the second wavelength that belong to the second portion and are polarized along the fourth polarization axis for the first wavelength according to the polarization measurement.
4. The method of claim 3 , wherein decoding the datastream using the wavelength and polarization of each of the polarized photon further comprises:
associating the first digit value with photons having the second wavelength that belong to the first portion and are polarized along the first polarization axis for the second wavelength according to the polarization measurement.
5. The method of claim 1 , wherein decoding the datastream using the wavelength and polarization of each of the polarized photon comprises:
performing the polarization measurement on a first portion of the incoming photons according to the first measurement basis and on a second portion of the incoming photons according to the second measurement basis for each wavelength;
associating a first digit value with photons having the first wavelength that belong to the first portion and are polarized along the first polarization axis for the first wavelength according to the polarization measurement;
associating a second digit value with photons having the first wavelength that belong to the first portion and are polarized along the second polarization axis for the first wavelength according to the polarization measurement;
associating a third digit value with photons having the second wavelength that belong to the first portion and are polarized along the first polarization axis for the second wavelength according to the polarization measurement; and
providing the datastream and a key string that includes the first, second, and third digit values as inputs to a decoding function that outputs a decoded message.
6. The method of claim 5 , wherein generating the signal indicating whether at least a portion of the datastream was altered includes:
determining that the decoded message includes one or more digits having the third digit value; and
causing the signal to indicate that the datastream was altered.
7. The method of claim 5 , wherein decoding the datastream using the wavelength and polarization of each of the polarized photon further comprises:
associating the first digit value with photons having the second wavelength that belong to the first portion and are polarized along the first polarization axis for the second wavelength according to the polarization measurement.
8. An optical communication device, comprising:
a first photon detector configured to detect photons having a first wavelength and to signal polarization orientations of those photons and a first optical polarization controller coupled to the first optical detector;
a second photon detector configured to detect photons having a second wavelength and to signal polarization orientations of those photons and a second optical polarization controller coupled to the second optical detector;
an optical interface coupled to the first and second polarization controllers configured receive incoming photons representing a datastream and to maintain orientation of a polarization of a first incoming photon with respect to polarizations of subsequent incoming photons; and
a processor coupled to the first and second optical detectors and to the first and second polarization controllers, the processor configured to:
select a chosen measurement basis between first and second measurement bases for each incoming photon, each measurement basis defining a of pair mutually orthogonal polarization axes for the each of the first and second wavelengths;
configure the first and second polarization controllers such that the first and second optical detectors measure polarization with respect to the measurement basis selected for that photon;
perform a polarization measurement on each photon that determines a polarization axis of that photon in the measurement basis selected for that photon and a wavelength of that photon; and
decode the datastream using the wavelengths and polarizations of the incoming photon, including generating a signal indicating whether at least a portion of the datastream was altered;
wherein the first measurement basis defines, for each of the first and second wavelengths, a first polarization axis in a plane for that wavelength and a second polarization axis in that plane that is perpendicular to the first polarization axis for that wavelength;
wherein the second measurement basis defines, for each of the first and second wavelengths, a third polarization axis in the plane for that wavelength and a fourth polarization axis in the plane for that wavelength that is perpendicular to the third polarization axis for that wavelength; and
wherein the third and the fourth polarization axes for each wavelength are equally-weighted vector combinations of the first and second polarization axes for that wavelength.
9. The device of claim 8 , wherein the processor is further configured to:
perform the polarization measurement on a first portion of the incoming photons according to the first measurement basis and on a second portion of the incoming photons according to the second measurement basis for each wavelength;
determine, according to the polarization measurement, a number erratic of photons of the first portion having the second wavelength having a measured polarization axis that differs from an expected polarization axis of the first measurement basis for the second wavelength;
determine, according to the polarization measurement, a number of erratic photons of the second portion having the first wavelength that have a measured polarization axis that differs from an expected polarization axis of the first measurement basis for the second wavelength; and
generate the signal indicating whether at least a portion of the datastream was altered by causing the signal to indicate whether a sum of the number of erratic photons of the first portion and the number of erratic photons of the second portion exceeds a predetermined threshold.
10. The device of claim 9 , wherein, when the processor decodes the datastream using the wavelength and polarization of each of the incoming photons, the processor is configured to:
associate a first digit value with photons having the first wavelength that belong to the first portion and are polarized along the first polarization axis for the first wavelength according to the polarization measurement;
associate a second digit value with photons having the first wavelength that belong to the first portion and are polarized along the second polarization axis for the first wavelength according to the polarization measurement;
associate the first digit value with photons having the second wavelength that belong to the second portion and are polarized along the third polarization axis for the first wavelength according to the polarization measurement; and
associate the second digit value with photons having the second wavelength that belong to the second portion and are polarized along the fourth polarization axis for the first wavelength according to the polarization measurement.
11. The device of claim 10 , wherein, when the processor decodes the datastream using the wavelength and polarization of each of the incoming photons, the processor is further configured to:
associating the first digit value with photons having the second wavelength that belong to the first portion and are polarized along the first polarization axis for the second wavelength according to the polarization measurement.
12. The device of claim 8 , wherein, when the processor decodes the datastream using the wavelength and polarization of each of the incoming photons, the processor is configured to:
perform the polarization measurement on a first portion of the incoming photons according to the first measurement basis and on a second portion of the incoming photons according to the second measurement basis for each wavelength;
associate a first digit value with photons having the first wavelength that belong to the first portion and are polarized along the first polarization axis for the first wavelength according to the polarization measurement;
associate a second digit value with photons having the first wavelength that belong to the first portion and are polarized along the second polarization axis for the first wavelength according to the polarization measurement;
associate a third digit value with photons having the second wavelength that belong to the first portion and are polarized along the first polarization axis for the second wavelength according to the polarization measurement; and
provide the datastream and a key string that includes the first, second, and third digit values as inputs to a decoding function that outputs a decoded message.
13. The device of claim 12 , wherein, when the processor decodes the datastream using the wavelength and polarization of each of the incoming photons, the processor is configured to:
determine that the decoded message includes one or more digits having the third digit value; and
cause the signal to indicate that the datastream was altered.
14. The device of claim 12 , wherein, when the processor decodes the datastream using the wavelength and polarization of each of the incoming photons, the processor is further configured to:
associate the first digit value with photons having the second wavelength that belong to the first portion and are polarized along the first polarization axis for the second wavelength according to the polarization measurement.