Low loss partial photon number-resolution detection
Methods are disclosed for performing projective measurements combining continuous-variable quadrature and discrete photon-number-basis detections on bosonic quantum modes. Some embodiments use single-photon detectors to perform photon subtraction on a bosonic mode propagating along a waveguide prior to field measurements with homodyne detection. Methods of implementation and specific applications for quantum computation, Gaussian boson sampling, and full quantum state tomography are also disclosed.
1. A method for performing partial photon-number-resolving (PNR) detection on a bosonic mode to generate results of measuring the bosonic mode in photon number basis and at least one other basis, the method comprising:
coupling a portion of the bosonic mode to a plurality of single-photon detectors (SPDs), wherein a first portion of the coupled portion of the bosonic mode is absorbed by the plurality of SPDs to generate a result of measuring the bosonic mode in the photon number basis;
combining a second portion of the coupled portion of the bosonic mode with an uncoupled portion of the bosonic mode to generate a first transmitted portion of the bosonic mode, the second portion of the coupled portion of the bosonic mode comprising an unabsorbed portion of the coupled portion of the bosonic mode; and
performing an operation on a final transmitted portion of the bosonic mode to generate the result of measuring the bosonic mode in the at least one other basis, wherein the final transmitted portion of the bosonic mode comprises at least the first transmitted portion of the bosonic mode.
2. The method of claim 1 , wherein the operation comprises homodyne detection.
3. The method of claim 1 , wherein the at least one other basis comprises a quadrature basis.
4. The method of any of claim 2 , wherein performing the operation comprises interfering the final transmitted portion with an ancillary bosonic mode to generate two output bosonic modes and performing a balanced homodyne detection based on the two output bosonic modes.
5. The method of claim 4 , wherein the ancillary bosonic mode comprises a local oscillator.
6. The method of claim 4 , wherein the ancillary bosonic mode comprises a non-Gaussian mode.
7. The method of claim 4 , wherein the ancillary bosonic mode comprises a squeezed vacuum state.
8. The method of claim 1 , wherein a first coupling coefficient between the bosonic mode and at least one of the SPDs is adjustable.
9. The method of claim 8 , wherein coupling a portion of the bosonic mode to the plurality of single-photon detectors (SPDs) comprises adjusting at least the first coupling coefficient to increase the first transmitted portion of the bosonic mode.
10. The method of claim 1 , further comprising coupling the first transmitted portion of the bosonic mode to the plurality of SPDs to generate a second transmitted portion of the bosonic mode, wherein the final transmitted portion of the bosonic mode comprises the second transmitted portion of the bosonic mode.
11. The method of claim 1 , further comprising generating a plurality of transmitted portions of the bosonic mode wherein a transmitted portion of the plurality of transmitted portions of the bosonic mode is generated by coupling a portion of a previously generated transmitted portion of the bosonic mode to the plurality of SPDs.
12. The method of claim 1 , wherein the bosonic mode comprises a guided bosonic mode.
13. The method of claim 1 , wherein the bosonic mode comprises an optical mode.
14. The method of claim 13 , wherein the optical mode is confined and propagates in an optical waveguide.
15. The method of claim 14 , wherein the optical waveguide comprises an on-chip optical waveguide.
16. The method of claim 15 , wherein the optical waveguide comprises a silicon waveguide.
17. The method of claim 15 , wherein performing the operation comprises splitting the final transmitted portion of the bosonic mode using at least one beam splitter.
18. The method of claim 15 , wherein performing the operation comprises detecting photons using an on-chip photodetector.
19. The method of claim 18 , wherein the on-chip photodetector is integrated with the optical waveguide.
20. The method of claim 2 , wherein the bosonic mode is entangled to one or more other bosonic modes, the bosonic mode and the one or more other bosonic modes having a joint quantum state, wherein the result of measuring the bosonic mode in the photon number basis comprises detection of at least one photon.