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Reliability of photon NOON-state production schemes

Università degli Studi di Bari Dip. di Fisica. Reliability of photon NOON-state production schemes. Milena D ’ Angelo, Augusto Garuccio and Vincenzo Tamma. Vincenzo Tamma. CEWQO 2007 – Palermo, 1-5 June. Outline. What is a NOON state?

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Reliability of photon NOON-state production schemes

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  1. Università degli Studi di Bari Dip. di Fisica Reliability of photon NOON-state production schemes Milena D’Angelo, Augusto Garuccio and Vincenzo Tamma Vincenzo Tamma CEWQO 2007 – Palermo, 1-5 June

  2. Outline • What is a NOON state? • Production of NOON states by projection measurements: • Non detection • Single-photon detection • Importance of the detectors efficiency for the effective production of NOON states • Reliability of NOON state production schemes • Conclusions

  3. What is a N-photons NOON state? Given a system of N = 1, 2, … photons distributed into two modes (a and b) N-photons NOON State:

  4. Quantum lithography (Boto et al.; PRL, 85:2733 (2000)) Quantum optics Quantummetrology (Bollinger et al.; PRA, 54:4649(1996)) Quantum criptography(W. Tittel; PRL, 84:4737 (2000)) Quantum information Quantum teleportation (H. de Riedmatten;PRL, 92: 047904 (2004)) Applications of photons NOON states All these applications strongly rely on the purity of NOON states!

  5. Production of NOON states by Non Destructive Projection Measurement (NDPM) N single-photon detections (“Nsd”) “NDPM” ck dk N non detections (“Nnd”) • -2 input modes: ak-1, bk-1 • - 4 output modes: ak, bk (next cell) + ck, dk (detectors) • linear optics elements: • 1 phase shifter (f k= 2 πk / N) • 2 beam splitters with transmission probability Tk. N/2 cells (for N even)containing linear optical elements + single-photon detectors: Importance of the detector efficiency!

  6. Does NDPM really produce a NOON state? Realistic NDPM Detectors efficiency ƞ <1: “ignorance” about the produced state “ignorance” about the detected states NDPM does not necessarily produce a NOON state!

  7. Reliability of NOON state production schemes based on NDPM Definition It is the conditional probabilityof producing a NOON state upon occurrence of NDPM:

  8. Non-detection technique Nnd Projector(ƞ=1): ck dk (Fiurasek; PRA, 65:053818(2002)) What happens for realistic detectors (ƞ < 1)?

  9. Reliability of the non-detection technique ƞ < 1 Non detection doesn’t mean absence of photons! Nnd POVM: Probability that n photons give no click Reliability Rnd In general … N = 2 The reliability of the non-detection technique decreases as N increases, for any ƞ< 1! N = 4 N = 6

  10. Single-photon detection technique Nsd Projector(ƞ=1): ck dk (Kok, Lee, Dowling; PRA, 65:052104(2002)) What happens for realistic detectors (ƞ < 1)?

  11. Reliability of single-photon detection technique Photon detection doesn’t mean only one-photon impinges on the detector! ƞ < 1 Nsd POVM: Probability that n photons give a single click Reliability Rsd N = 2, 4, 6 In general … N=2 The reliabilityofsingle-photon detection technique decreases as N increases, for any ƞ< 1 ! N=4 N=6

  12. Which technique is more reliable ? N = 2: __= non detection scheme __= single-photon detection scheme N = 4: N = 6: Non detection technique is more reliable than single-photon detection technique, for any ƞ < 1 !

  13. Why is the non detection technique more reliable? • two Physical Reasons: • 1) the probability that zero photons give no click is 1, i.e., is independent of h, while the probability that one photon gives a single click is h • P(NOON ∩ Nsd) ƞNP(NOON ∩ Nnd) • 2) the detectors in the first cell of the non-detection protocol are not involved in the projection measurement (T1 = 0)

  14. Moreover… • The NON-DETECTION scheme works with SPCMs(sensitive tosingle photons but unable to resolvesingle photons) • while • the SINGLE-PHOTON DETECTION scheme requires photon-number resolving detectors • 2) The non-detection scheme requires N/2 |1,1› states • while • the single-photon detection scheme requires one |N,N› state Revaluation of the non detection technique!

  15. Conclusions We have found how much the effective NOON state production is affected by the efficiency of photon detectors, for both non detection and single-photon detection techniques. Reliability of non-detection protocol > reliability of single-photon detection protocol, for any ƞ < 1 ! Future developments • Finding the reliability for any even number N of photons • Alternative detection schemes • Experiments Revaluation of the non detection technique!

  16. Thank you for your attention!

  17. Production of NOON states by Non Destructive Projective Measurement (NDPM) Bipartite system, composed of two subsystems 1 and 2, in the entangled state: “NDPM” c(α,β) arbitrary normalized not factorable complex function Working Principle In practice …

  18. Probability of N non-detection events: Probability of both NOON state and N non-detections events:

  19. Probability of N single-photon detections events: Probability of both NOON state and N single-photon detections events:

  20. Maximum of Maximum of events associated with no photons at the input channel of each detector. Non Detection scheme: Single-photon Detection scheme: Maximum of events associated with one photon at the input channel of each detector. Maximum of

  21. The reliability of N-photon NOON state production decreases at N increasing for any ƞ < 1. Necessity to check the effective NOON state production, specially for large values of N.

  22. N single-photon detections: “NDPM” ≡“N sd” N non detections: “NDPM”≡“N nd”

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