Quantum tokens

1. An agency system comprising:

a hardware device that generates or receives, at a first space-time point, a plurality of random quantum states, each of the quantum states chosen from a set of non-orthogonal quantum states;

a measurement apparatus that applies a pre-determined measurement, from a plurality of possible pre-determined measurements, to the quantum states in order to obtain a token comprising a sequence of classical measurement outcomes, wherein the sequence of classical measurement outcomes is valid at a single space-time point; and

a communications system that sends the token to a second agency system at a second space-time point in the causal future of the first space-time point, wherein the second agency system verifies whether the token corresponds to a statistically plausible result for the pre-determined measurement applied to the plurality of quantum states, before allowing access to a resource.

2. The system of claim 1 , wherein the quantum states are chosen independently randomly from among pure states of a plurality of possible bases for a quantum state space.

3. The system of claim 2 , wherein the quantum state space is a two-dimensional qubit space and the quantum states represent quantum bits (qubits).

4. The system of claim 3 , wherein each of the plurality of quantum states comprises BB84 states for the two-dimensional qubit space.

5. The system of claim 3 or claim 4 , wherein each of the qubits is encoded in a photon of electromagnetic energy.

6. The system of claim 5 , wherein each of the qubits is encoded as a polarization state of the photon.

7. The system of claim 6 , wherein each qubit is represented by the polarization state of a weak light pulse with a low expected photon number.

8. The system of claim 2 , wherein the pre-determined measurement comprises a projection of each of the plurality of quantum states onto one of the pure states of the corresponding quantum state space.

9. The system of claim 1 , wherein the pre-determined measurement is applied at the first space-time point.

10. The system of claim 1 , wherein the quantum states represent quantum bits (qubits).

11. The system of claim 1 , wherein the pre-determined measurement is such that possible measurement outcomes give a valid token for the second space-time point.

12. The system of claim 11 , wherein a probability that the result of the pre-determined measurement gives a valid token for a third space-time point separated from the second space-time point is small.

13. The system of claim 12 , wherein the probability that the result of the pre-determined measurement gives a valid token for the third space-time point is negligible.

14. The system of claim 1 , wherein the communications system encrypts the token prior to sending the token.

15. The system of claim 1 , wherein the plurality of quantum states are entangled.

16. The system of claim 1 , wherein the token comprises only the measurement outcomes corresponding to quantum states of the plurality of random quantum states, for which the measurements were successful.

17. The system of claim 1 , wherein the communications system sends data identifying quantum states of the plurality of random quantum states, for which the measurements were successful.

18. The system of claim 1 , wherein the hardware device:

receives, at a fourth space-time point in the future of the first space-time point and in the past of the second space-time point, a second plurality of quantum states;

applies a second pre-determined measurement to the second plurality of quantum states to obtain a second sequence of classical measurement outcomes;

appends the second sequence of classical measurement outcomes to the token, forming an extended token; and

sends the extended token to the second agency system at the second space-time point.

19. The system of claim 18 , wherein the hardware device iterates, at each of a plurality of successive time-like separated space-time points in the future of the first space-time point and in the past of the second space-time point, the steps of:

receiving a further plurality of quantum states;

applying a pre-determined measurement to the plurality of quantum states to obtain a further sequence of classical measurement outcomes; and

appending the further sequence of classical measurement outcomes to the token, such that the extended token presented at the second space-time point comprises each of the plurality of sequences of classical measurement outcomes.

20. The system of claim 1 , wherein the hardware device generates, at a fourth space-time point in the future of the first space-time point and in the past of the second space-time point, a second plurality of quantum states, and wherein the second agency system verifies whether the token includes a statistically plausible result for a first pre-determined measurement on the first plurality of quantum states and a statistically plausible result for a second pre-determined measurement on the second plurality of quantum states.

21. The system of claim 20 , wherein the hardware device literates, at each of a plurality of successive time-like separated space-time points in the future of the first space-time point and in the past of the second space-time point, the step of generating a further plurality of quantum states, wherein the communications system sends an extended token comprising a plurality of sequences of classical measurement outcomes, and wherein the second agency system verifies whether the extended token includes a statistically plausible result for each of a plurality of respective pre-determined measurements on each generated plurality of quantum states.

22. The system of claim 1 , 19 , or 21 , wherein the hardware device:

receives, at the first space-time point, multiple pluralities of random quantum states, each of the quantum states chosen from a respective set of non-orthogonal quantum states;

applies a respective pre-determined measurement to the quantum states to obtain an extended token comprising a number of sequences of classical measurement outcomes; and

sends a portion of the extended token to the second agency system at the second space-time point.

23. The system of claim 1 , 19 , or 21 , wherein the hardware device:

generates, at the first space-time point, multiple pluralities of random quantum states, each of the quantum states chosen from a respective set of non-orthogonal quantum states; and

sends an extended token comprising a number of sequences of classical measurement outcomes to the second agency system at the second space-time point, wherein the second agency system verifies whether the extended token corresponds to a statistically plausible result for respective pre-determined measurements on each of the pluralities of quantum states.

24. The system of claim 1 , wherein a unique pre-determined measurement from the plurality of possible pre-determined measurements is assigned to each space-time point.

25. The system of claim 1 , wherein the pre-determined measurement comprises a pre-determined sequence of measurements based on a pre-agreed set of measurement strings.