Reversing the weak quantum measurement for a photonic qubit
Optics Express, Vol. 17, Issue 14, pp. 11978-11985 (2009)
http://dx.doi.org/10.1364/OE.17.011978
Acrobat PDF (440 KB)
Abstract
We demonstrate the conditional reversal of a weak (partial-collapse) quantum measurement on a photonic qubit. The weak quantum measurement causes a nonunitary transformation of a qubit which is subsequently reversed to the original state after a successful reversing operation. Both the weak measurement and the reversal operation are implemented linear optically. The state recovery fidelity, determined by quantum process tomography, is shown to be over 94% for partial-collapse strength up to 0.9. We also experimentally study information gain due to the weak measurement and discuss the role of the reversing operation as an information erasure.
© 2009 Optical Society of America
1. Introduction
7. E. Knill, R. Laamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001). [CrossRef]
8. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002). [CrossRef]
9. P. Kok, W.J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–173 (2007). [CrossRef]
2. Theory
3. Experimental setup
10. C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. 56, 58–60 (1986). [CrossRef] [PubMed]
11. S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008). [CrossRef]
10. C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. 56, 58–60 (1986). [CrossRef] [PubMed]
11. S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008). [CrossRef]
12. M. Mitchell, J. Lundeen, and A. Steinberg, “Super-resolving phase measurements with a multi-photon entangled state,” Nature 429, 161–164 (2004). [CrossRef] [PubMed]
14. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits: Qubit state tomography,” Phys. Rev. A 64, 052312 (2001). [CrossRef]
4. Tomographic analysis of the experimental data
15. J. Fiurasek and Z. Hradil, “Maximum-likelihood estimation of quantum processes,” Phys. Rev. A 63, 020101(R) (2001). [CrossRef]
5. Information gain and optimal guessing strategy
16. K. Banaszek, “Fidelity Balance in Quantum Operations,” Phys. Rev. Lett. 86, 1366–1369 (2001). [CrossRef] [PubMed]
17. S.-Y. Baek, Y. W. Cheong, and Y.-H. Kim, “Minimum disturbance measurement without postselection,” Phys. Rev. A 77, 060308(R) (2008). [CrossRef]
4. A. N. Korotkov and A. N. Jordan, “Undoing a weak quantum measurement of a solid-state qubit,” Phys. Rev. Lett. 97, 166805 (2006). [CrossRef] [PubMed]
5. N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. Oconnell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a superconducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008). [CrossRef] [PubMed]
16. K. Banaszek, “Fidelity Balance in Quantum Operations,” Phys. Rev. Lett. 86, 1366–1369 (2001). [CrossRef] [PubMed]
17. S.-Y. Baek, Y. W. Cheong, and Y.-H. Kim, “Minimum disturbance measurement without postselection,” Phys. Rev. A 77, 060308(R) (2008). [CrossRef]
16. K. Banaszek, “Fidelity Balance in Quantum Operations,” Phys. Rev. Lett. 86, 1366–1369 (2001). [CrossRef] [PubMed]
17. S.-Y. Baek, Y. W. Cheong, and Y.-H. Kim, “Minimum disturbance measurement without postselection,” Phys. Rev. A 77, 060308(R) (2008). [CrossRef]
6. Conclusion
Acknowledgments
References and links
1. | R. Shankar, Principles of Quantum Mechanics, 2nd ed., (Plenum Press, New York, 1994). |
2. | M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000). |
3. | M. Koashi and M. Ueda, “Reversing measurement and probabilistic quantum error correction,” Phys. Rev. Lett. 82, 2598–2601 (1999). [CrossRef] |
4. | A. N. Korotkov and A. N. Jordan, “Undoing a weak quantum measurement of a solid-state qubit,” Phys. Rev. Lett. 97, 166805 (2006). [CrossRef] [PubMed] |
5. | N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. Oconnell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a superconducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008). [CrossRef] [PubMed] |
6. | The Physics of Quantum Information, edited by D. Bouwmeester, A. K. Ekert, and A. Zeilinger (Springer, Berlin, 2000). |
7. | E. Knill, R. Laamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001). [CrossRef] |
8. | N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002). [CrossRef] |
9. | P. Kok, W.J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–173 (2007). [CrossRef] |
10. | C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. 56, 58–60 (1986). [CrossRef] [PubMed] |
11. | S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008). [CrossRef] |
12. | M. Mitchell, J. Lundeen, and A. Steinberg, “Super-resolving phase measurements with a multi-photon entangled state,” Nature 429, 161–164 (2004). [CrossRef] [PubMed] |
13. | The calculated and measured p values for each BP set agreed well. For example, for two pieces of BP’s, they are 0.478 and 0.455, respectively, and for seven pieces of BP’s, they are 0.897 and 0.895. |
14. | D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits: Qubit state tomography,” Phys. Rev. A 64, 052312 (2001). [CrossRef] |
15. | J. Fiurasek and Z. Hradil, “Maximum-likelihood estimation of quantum processes,” Phys. Rev. A 63, 020101(R) (2001). [CrossRef] |
16. | K. Banaszek, “Fidelity Balance in Quantum Operations,” Phys. Rev. Lett. 86, 1366–1369 (2001). [CrossRef] [PubMed] |
17. | S.-Y. Baek, Y. W. Cheong, and Y.-H. Kim, “Minimum disturbance measurement without postselection,” Phys. Rev. A 77, 060308(R) (2008). [CrossRef] |
OCIS Codes
(270.5570) Quantum optics : Quantum detectors
(270.5565) Quantum optics : Quantum communications
(270.5585) Quantum optics : Quantum information and processing
ToC Category:
Quantum Optics
History
Original Manuscript: May 20, 2009
Revised Manuscript: June 17, 2009
Manuscript Accepted: June 21, 2009
Published: June 30, 2009
Citation
Yong-Su Kim, Young-Wook Cho, Young-Sik Ra, and Yoon-Ho Kim, "Reversing the weak quantum
measurement for a photonic qubit," Opt. Express 17, 11978-11985 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-11978
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References
- R. Shankar, Principles of Quantum Mechanics, 2nd ed., (Plenum Press, New York, 1994).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
- M. Koashi and M. Ueda, "Reversing measurement and probabilistic quantum error correction," Phys. Rev. Lett. 82, 2598-2601 (1999). [CrossRef]
- A. N. Korotkov and A. N. Jordan, "Undoing a weak quantum measurement of a solid-state qubit," Phys. Rev. Lett. 97, 166805 (2006). [CrossRef] [PubMed]
- N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. Oconnell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, "Reversal of the weak measurement of a quantum state in a superconducting phase qubit," Phys. Rev. Lett. 101, 200401 (2008). [CrossRef] [PubMed]
- The Physics of Quantum Information, edited by D. Bouwmeester, A. K. Ekert, and A. Zeilinger (Springer, Berlin, 2000).
- E. Knill, R. Laamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature (London) 409, 46-52 (2001). [CrossRef]
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
- P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, "Linear optical quantum computing with photonic qubits," Rev. Mod. Phys. 79, 135-173 (2007). [CrossRef]
- C. K. Hong and L. Mandel, "Experimental realization of a localized one-photon state," Phys. Rev. Lett. 56, 58-60 (1986). [CrossRef] [PubMed]
- S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Temporal shaping of a heralded single-photon wave packet," Phys. Rev. A 77, 013829 (2008). [CrossRef]
- M. Mitchell, J. Lundeen, and A. Steinberg, "Super-resolving phase measurements with a multi-photon entangled state," Nature 429, 161-164 (2004). [CrossRef] [PubMed]
- The calculated and measured p values for each BP set agreed well. For example, for two pieces of BP’s, they are 0.478 and 0.455, respectively, and for seven pieces of BP’s, they are 0.897 and 0.895.
- D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits: Qubit state tomography," Phys. Rev. A 64, 052312 (2001). [CrossRef]
- J. Fiurasek and Z. Hradil, "Maximum-likelihood estimation of quantum processes," Phys. Rev. A 63, 020101(R) (2001). [CrossRef]
- K. Banaszek, "Fidelity Balance in Quantum Operations," Phys. Rev. Lett. 86, 1366-1369 (2001). [CrossRef] [PubMed]
- S.-Y. Baek, Y. W. Cheong, and Y.-H. Kim, "Minimum disturbance measurement without postselection," Phys. Rev. A 77, 060308(R) (2008). [CrossRef]
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