## Entangled photon polarimetry |

Optics Express, Vol. 19, Issue 27, pp. 26011-26016 (2011)

http://dx.doi.org/10.1364/OE.19.026011

Acrobat PDF (1767 KB)

### Abstract

We construct an entangled photon polarimeter capable of monitoring a two-qubit quantum state in real time. Using this polarimeter, we record a nine frames-per-second video of a two-photon state’s transition from separability to entanglement.

© 2011 OSA

## 1. Introduction

2. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Yanhua Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. **75**, 4337–4341 (1995). [CrossRef] [PubMed]

5. M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science **301**, 5633 (2003). [CrossRef]

6. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. **94**, 053601 (2005). [CrossRef] [PubMed]

10. M. Medic, J. B. Altepeter, M. A. Hall, M. Patel, and P. Kumar, “Fiber-based telecommunication-band source of degenerate entangled photons,” Opt. Lett. **35**, 802–804 (2010). [CrossRef] [PubMed]

11. U. Leonhardt, “Quantum-state tomography and discrete Wigner function,” Phys. Rev. Lett. **74**, 4101–4105 (1995). [CrossRef] [PubMed]

16. M. S. Kaznady and D. F. V. James, “Numerical strategies for quantum tomography: Alternatives to full optimization,” Phys. Rev. A **79**, 022109 (2009). [CrossRef]

*polarimeter*is a common tool which is used to debug unwanted polarization rotations or depolarization effects, which provides an experimenter with a real-time picture of the optical field’s polarization state. An

*entangled photon polarimeter*—a measurement device capable of performing quantum tomographies and displaying the reconstructed two-qubit states in real time—would be a valuable tool for optimizing and deploying entangled photon sources.

## 2. Two-qubit polarimetry

*quantum state tomography*, a procedure for reconstructing an unknown quantum state from a series of measurements (generally either 9 or 36 coincidence measurements performed using two single-photon detectors per qubit [14

14. R. T. Thew, K. Nemoto, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A **66**, 012303 (2002). [CrossRef]

*T*, is given by

*T*≡

*M*× (

*τ*+

_{m}*τ*) +

_{s}*τ*, where

_{a}*M*is the number of two-qubit measurement settings taken per reconstruction,

*τ*is the time per measurement setting,

_{m}*τ*is the the time to switch between measurement settings, and

_{s}*τ*is the time to numerically reconstruct the unknown density matrix from an analysis of the measurement results.

_{a}*Two-qubit polarimetry*is an application of two-qubit polarization tomography which maximizes precision for very short

*T*(≤ 1s), allowing an experimenter to manipulate an entangled photon source using real-time tomographic feedback (by updating after every measurement, the time between updates can be reduced to

*T*/9). (In this paper,

*entangled photon polarimetery*refers to the application of two-qubit polarimetry to entangled photon states.) Because maximizing precision requires maximizing

*N*, the ideal entangled photon polarimeter will minimize both the time between measurements (

*τ*) and the time for numerical analysis (

_{s}*τ*):

_{a}*τ*<

_{a}*M*(

*τ*+

_{m}*τ*), a complete set of

_{s}*M*measurements can be analyzed at the same time the next set of

*M*measurements are being performed, leading to one tomographic result being displayed to the experimenter every

*M*(

*τ*+

_{m}*τ*) seconds. For

_{s}*τ*<

_{a}*τ*+

_{m}*τ*, a tomographic result can be analyzed and displayed after every

_{s}*measurement*, rather than after every complete set of

*M*measurements. In other words, after every measurement, the

*previous M measurements*are used to reconstruct an updated density matrix, leading to a faster refresh rate based on a tomographic “rolling average”. Similarly, this configuration can be altered in real time to utilize even more measurements (e.g., 4

*M*) for increased precision (analagous to averaging multiple traces on an oscilloscope).

## 3. Experimental details

10. M. Medic, J. B. Altepeter, M. A. Hall, M. Patel, and P. Kumar, “Fiber-based telecommunication-band source of degenerate entangled photons,” Opt. Lett. **35**, 802–804 (2010). [CrossRef] [PubMed]

14. R. T. Thew, K. Nemoto, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A **66**, 012303 (2002). [CrossRef]

*F*as a function of total tomography time

_{p}*T*.

### 3.1. Entangled photon source

10. M. Medic, J. B. Altepeter, M. A. Hall, M. Patel, and P. Kumar, “Fiber-based telecommunication-band source of degenerate entangled photons,” Opt. Lett. **35**, 802–804 (2010). [CrossRef] [PubMed]

**35**, 802–804 (2010). [CrossRef] [PubMed]

### 3.2. Polarization measurements

14. R. T. Thew, K. Nemoto, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A **66**, 012303 (2002). [CrossRef]

*τ*will in general be very large (≈ 5s). For the fiber-based source above, this type of polarization analyzer will lead to a single-qubit loss of ≈ 1.5 dB (including the fiber to free-space to fiber coupling losses).

_{s}*τ*, we have constructed an all-fiber/waveguide polarization analyzer based on electro-optic modulators (EOMs). These LiNbO

_{s}_{3}EOMs (EOSpace, model PC-B4-00-SFU-SFU-UL) allow precise control of both the retardance and optic axis of a birefringent crystalline waveguide using the fringe fields from three electrodes. In general, this process has an extremely short response time leading to EOM switching rates of up to 10 MHz. In practice, we are able to implement arbitrary polarization measurements at 125 kHz, which is a limit set by the speed of our computer-controlled voltage sources.

### 3.3. Single-photon detection

*τ*= 20 ms. By upgrading the detector control software to eliminate extraneous electronic delays, we anticipate that this will approach the EOM’s 125 kHz limit (

_{s}*τ*= 10

_{s}*μ*s). The quantum efficiency of each detector at 1550-nm is ≈20%, with a measured dark-count rate of 1–4 × 10

^{−4}per pulse.

### 3.4. Tomographic reconstruction

*ρ*most likely to reproduce the measured counts [13

13. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A **64**, 052312 (2001). [CrossRef]

**66**, 012303 (2002). [CrossRef]

*τ*≈ 5 s).

_{a}16. M. S. Kaznady and D. F. V. James, “Numerical strategies for quantum tomography: Alternatives to full optimization,” Phys. Rev. A **79**, 022109 (2009). [CrossRef]

*wM*·

*S*=

*wC*. Here,

*M*is the set of measurements, which can be arbitrary POVMs;

*C*is the measured counts, and

*S*is the Stokes vector we solve for;

*w*is a weight vector representing the distribution width for each measurement. We assume the counting process to be Poissonian, and use the large-N limit where the Poisson distribution is approximated as a Gaussian with width

16. M. S. Kaznady and D. F. V. James, “Numerical strategies for quantum tomography: Alternatives to full optimization,” Phys. Rev. A **79**, 022109 (2009). [CrossRef]

*M*measurements. For four-detector, complete-basis polarization analyzers (described above), only nine measurements are needed to perform a complete tomography. Note that it is often experimentally optimal to perform a redundant set of 36 measurements in order to detect and/or correct for systematic errors such as source intensity drift, detector efficiency drift, or polarizer crosstalk [14

**66**, 012303 (2002). [CrossRef]

## 4. Entangled photon polarimeter performance

*τ*= 80 ms,

_{m}*τ*= 20 ms, and

_{s}*τ*= 1 ms. Total single-qubit insertion loss is measured to be

_{a}*η*= 3–3.4 dB (not including detector inefficiency). The tomographic precision is estimated using a Monte Carlo simulation of this polarimeter’s application to the entanglement source pictured in Fig. 2 (≈ 1000 coincidences / second). For nine-measurement tomographies (

*T*≈ 1s),

*F*(

_{p}*N*= 1000,

*ρ*

_{ideal}) ≈ 92%. For 36-measurement tomographies (

*T*≈ 4s),

*F*(

_{p}*N*= 4000,

*ρ*

_{ideal}) ≈ 96%. Because long (30-minute) tomographies have previously verified the source’s fidelity to a maximally entangled state to be 99.7% ± 0.4% [10

**35**, 802–804 (2010). [CrossRef] [PubMed]

*ϕ*

^{+}〉 as an approximation to

*ρ*

_{ideal}.

*DV*〉 (see Fig. 3( Media 2)), and a maximally entangled state, |

*ϕ*

^{+}〉 (see Fig. 3( Media 3)). By analyzing each frame and comparing it to the target state, we directly measured the system precision to be 98% ± 1% (for |

*DV*〉) and 95% ± 2% (for |

*ϕ*

^{+}〉). Note that this experimentally measured system precision for |

*ϕ*

^{+}〉 is in good agreement with the theoretically predicted 96% (see the prediction for a 4-s, 36-measurement tomography above). Finally, we recorded a video of a two-photon state’s transition from separability to entanglement (the transition is physically implemented by rotating wave plate HWP in the entangled photon source setup—see Fig. 2). Selected frames from this video are shown in Fig. 3( Media 1).

## References and links

1. | M. Nielsen and I. Chuang, Quantum computation and quantum information (Cambridge Univ. Press2000). |

2. | P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Yanhua Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. |

3. | J. B. Altepeter, E. R. Jeffrey, and P. G. Kwiat, “Phase-compensated ultra-bright source of entangled photons,” Opt. Exp. |

4. | C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. |

5. | M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science |

6. | X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. |

7. | J. Fan, M. D. Eisaman, and A. Migdall, “Bright phase-stable broadband fiber-based source of polarization-entangled photon pairs,” Phys. Rev. A |

8. | H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Exp. |

9. | M. A. Hall, J. B. Altepeter, and P. Kumar, “Drop-in compatible entanglement for optical-fiber networks,” Opt. Exp. |

10. | M. Medic, J. B. Altepeter, M. A. Hall, M. Patel, and P. Kumar, “Fiber-based telecommunication-band source of degenerate entangled photons,” Opt. Lett. |

11. | U. Leonhardt, “Quantum-state tomography and discrete Wigner function,” Phys. Rev. Lett. |

12. | K. Banaszek, G. M. DAriano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A |

13. | D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A |

14. | R. T. Thew, K. Nemoto, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A |

15. | J. B. Altepeter, E. R. Jeffrey, and P. G. Kwiat, “Photonic state tomography,” Adv. At., Mol., Opt. Phys. |

16. | M. S. Kaznady and D. F. V. James, “Numerical strategies for quantum tomography: Alternatives to full optimization,” Phys. Rev. A |

17. | R. Jozsa, “Fidelity for mixed quantum states,” J. of Mod. Opt. |

**OCIS Codes**

(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry

(270.5565) Quantum optics : Quantum communications

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: August 31, 2011

Revised Manuscript: November 13, 2011

Manuscript Accepted: November 14, 2011

Published: December 6, 2011

**Citation**

Joseph B. Altepeter, Neal N. Oza, Milja Medić, Evan R. Jeffrey, and Prem Kumar, "Entangled photon polarimetry," Opt. Express **19**, 26011-26016 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26011

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### References

- M. Nielsen and I. Chuang, Quantum computation and quantum information (Cambridge Univ. Press2000).
- P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Yanhua Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995). [CrossRef] [PubMed]
- J. B. Altepeter, E. R. Jeffrey, and P. G. Kwiat, “Phase-compensated ultra-bright source of entangled photons,” Opt. Exp. 13, 8951–8959 (2005). [CrossRef]
- C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005). [CrossRef] [PubMed]
- M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 5633 (2003). [CrossRef]
- X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005). [CrossRef] [PubMed]
- J. Fan, M. D. Eisaman, and A. Migdall, “Bright phase-stable broadband fiber-based source of polarization-entangled photon pairs,” Phys. Rev. A 76, 043836 (2007). [CrossRef]
- H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Exp. 165721–5727 (2008). [CrossRef]
- M. A. Hall, J. B. Altepeter, and P. Kumar, “Drop-in compatible entanglement for optical-fiber networks,” Opt. Exp. 17, 14558–14566 (2009). [CrossRef]
- M. Medic, J. B. Altepeter, M. A. Hall, M. Patel, and P. Kumar, “Fiber-based telecommunication-band source of degenerate entangled photons,” Opt. Lett. 35, 802–804 (2010). [CrossRef] [PubMed]
- U. Leonhardt, “Quantum-state tomography and discrete Wigner function,” Phys. Rev. Lett. 74, 4101–4105 (1995). [CrossRef] [PubMed]
- K. Banaszek, G. M. DAriano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304(R) (1999). [CrossRef]
- D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef]
- R. T. Thew, K. Nemoto, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A 66, 012303 (2002). [CrossRef]
- J. B. Altepeter, E. R. Jeffrey, and P. G. Kwiat, “Photonic state tomography,” Adv. At., Mol., Opt. Phys. 52, 105–159 (2005).
- M. S. Kaznady and D. F. V. James, “Numerical strategies for quantum tomography: Alternatives to full optimization,” Phys. Rev. A 79, 022109 (2009). [CrossRef]
- R. Jozsa, “Fidelity for mixed quantum states,” J. of Mod. Opt. 41, 2315–2323 (1994). [CrossRef]

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