Abstract

We present an efficient proposal to realize quantum nondestructive determination (QNDD) of unknown single-qubit states in two types of low-Q cavities, i.e., single-sided and double-sided cavity QED systems. In the dispersive regime, we demonstrate that the QNDD of single-qubit states can be realized by detecting qubit-state-dependent phase shifts (QSDPSs) of the reflected or transmitted photons from the cavity in the single-photon input-output process. Our proposal could be straightforwardly extended to the case of multiple-qubit states. Furthermore, the experimental feasibility of our proposal is also analyzed in experimentally-demonstrated circuit QED systems. The distinct feature of our proposal is that our proposal works in the dispersive regime of low-Q cavities and it is robust to both cavity decay and atomic spontaneous emission.

© 2016 Optical Society of America

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2014 (10)

See the supplementary information in T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (2014).
[Crossref] [PubMed]

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature 508, 237–240 (2014).
[Crossref] [PubMed]

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref] [PubMed]

J. Volz, M. Scheucher, C. Junge, and A. Rauschenbeutel, “Nonlinear π phase shift for single fibre-guided photons interacting with a single resonator-enhanced atom,” Nat. Photon. 8, 965–970 (2014).
[Crossref]

Y. X. Liu, X. W. Xu, A. Miranowicz, and F. Nori, “From blockade to transparency: controllable photon transmission through a circuit-QED system,” Phys. Rev. A 89, 043818 (2014).
[Crossref]

I. M. Georgescu, S. Ashhab, and F. Nori, “Quantum simulation,” Rev. Mod. Phys. 86, 153 (2014).
[Crossref]

M. L. Zhang, G. W. Deng, S. X. Li, H. O. Li, G. Cao, T. Tu, M. Xiao, G. C. Guo, H. Jiang, I. Siddiqi, and G. P. Guo, “Symmetric reflection line resonator and its quality factor modulation by a two-dimensional electron gas,” Appl. Phys. Lett. 104, 083511 (2014).
[Crossref]

A. Miranowicz, K. Bartkiewicz, J. Peřina, M. Koashi, N. Imoto, and F. Nori, “Optimal two-qubit tomography based on local and global measurements: maximal robustness against errors as described by condition numbers,” Phys. Rev. A 90, 062123 (2014).
[Crossref]

H. R. Wei and F. G. Deng, “Universal quantum gates on electron-spin qubits with quantum dots inside single-side optical microcavities,” Opt. Express 22, 593–607 (2014).
[Crossref] [PubMed]

C. Wang, T. J. Wang, Y. Zhang, R. Z. Jiao, and G. S. Jin, “Concentration of entangled nitrogen-vacancy centers in decoherence free subspace,” Opt. Express 22, 1551–1559 (2014).
[Crossref] [PubMed]

2013 (10)

C. Cao, C. Wang, L. Y. He, and R. Zhang, “Atomic entanglement purification and concentration using coherent state input-output process in low-Q cavity QED regime,” Opt. Express 21, 4093–4105 (2013).
[Crossref] [PubMed]

L. Y. Cheng, H. F. Wang, S. Zhang, and K. H. Yeon, “Quantum state engineering with nitrogen-vacancy centers coupled to low-Q microresonator,” Opt. Express 21, 5988–5997 (2013).
[Crossref] [PubMed]

H. R. Wei and F. G. Deng, “Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities,” Phys. Rev. A 87, 022305 (2013).
[Crossref]

H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Optically controlled phase gate and teleportation of a controlled-NOT gate for spin qubits in a quantum-dot-microcavity coupled system,” Phys. Rev. A 87, 062337 (2013).
[Crossref]

H. R. Wei and F. G. Deng, “Compact quantum gates on electron-spin qubits assisted by diamond nitrogen-vacancy centers inside cavities,” Phys. Rev. A 88, 042323 (2013).
[Crossref]

X. B. Wang, Z. W. Yu, J. Z. Hu, A. Miranowicz, and F. Nori, “Efficient tomography of quantum-optical Gaussian processes probed with a few coherent states,” Phys. Rev. A 88, 022101 (2013).
[Crossref]

Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
[Crossref]

B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser Phys. Lett. 10, 115201 (2013).
[Crossref]

H. Yuan and L. F. Wei, “Testing genuine tripartite quantum nonlocality with three two-level atoms in a driven cavity,” Phys. Rev. A 88, 042104 (2013).
[Crossref]

H. Yuan and L. F. Wei, “Testing Hardy’s ladder proof of nonlocality by joint measurements of qubits,” Quantum Inf. Process. 12, 3341 (2013).
[Crossref]

2012 (5)

H. Yuan, L. F. Wei, J. S. Huang, and V. Vedral, “Quantum nonlocality test by spectral joint measurements of qubits in driven cavity,” Europhys. Lett. 100, 10007 (2012).
[Crossref]

M. D. Shulman, O. E. Dial, S. P. Harvey, H. Bluhm, V. Umansky, and A. Yacoby, “Demonstration of entanglement of electrostatically coupled singlet-triplet qubits,” Science 336, 202–205 (2012).
[Crossref] [PubMed]

Z. H. Peng, J. Zou, X. J. Liu, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A 86, 034305 (2012).
[Crossref]

S. Ritter, C. Nölleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mücke, E. Figueroa, J. Bochmann, and G. Rempe, “An elementary quantum network of single atoms in optical cavities,” Nature 484, 195–200 (2012).
[Crossref] [PubMed]

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities,” Phys. Rev. A 86, 042337 (2012).
[Crossref]

2011 (3)

Q. Chen, W. Yang, M. Feng, and J. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
[Crossref]

C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011).
[Crossref]

J. Q. You and F. Nori, “Atomic physics and quantum optics using superconducting circuits,” Nature 474, 589–597 (2011).
[Crossref] [PubMed]

2010 (5)

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[Crossref] [PubMed]

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A 81, 042304 (2010).
[Crossref]

J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, L. S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Detecting highly entangled states with a joint qubit readout,” Phys. Rev. A 81, 062325 (2010).
[Crossref]

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[Crossref] [PubMed]

Q. Chen and M. Feng, “Quantum-information processing in decoherence-free subspace with low-Q cavities,” Phys. Rev. A 82, 052329 (2010).
[Crossref]

2009 (5)

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A 79, 032303 (2009).
[Crossref]

Q. Chen and M. Feng, “Quantum gating on neutral atoms in low-Q cavities by a single-photon input-output process,” Phys. Rev. A 79, 064304 (2009).
[Crossref]

R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, M. Göppl, P. J. Leek, L. Steffen, A. Blais, and A. Wallraff, “Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics,” Phys. Rev. A 80, 043840 (2009).
[Crossref]

L. Zhou, S. Yang, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum Zeno switch for single-photon coherent transport,” Phys. Rev. A 80, 062109 (2009).
[Crossref]

I. Buluta and F. Nori, “Quantum simulators,” Science 326, 108–111 (2009).
[Crossref] [PubMed]

2008 (3)

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[Crossref] [PubMed]

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A 78, 063827 (2008).
[Crossref]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[Crossref] [PubMed]

2007 (4)

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoǧlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450, 862–865 (2007).
[Crossref] [PubMed]

M. Atatüre, J. Dreiser, A. Badolato, and A. Imamoglu, “Observation of Faraday rotation from a single confined spin,” Nat. Phys. 3, 101–105 (2007).
[Crossref]

A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Quantum-information processing with circuit quantum electrodynamics,” Phys. Rev. A 75, 032329 (2007).
[Crossref]

2005 (4)

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Approaching unit visibility for control of a superconducting qubit with dispersive readout,” Phys. Rev. Lett. 95, 060501 (2005).
[Crossref] [PubMed]

J. Q. You and F. Nori, “Superconducting circuits and quantum information,” Phys. Today 58(11), 42–47 (2005).
[Crossref]

Y. X. Liu, L. F. Wei, and F. Nori, “Tomographic measurements on superconducting qubit states,” Phys. Rev. B 72, 014547 (2005).
[Crossref]

H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[Crossref] [PubMed]

2004 (4)

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, “Observation of the vacuum Rabi spectrum for one trapped atom,” Phys. Rev. Lett. 93, 233603 (2004).
[Crossref] [PubMed]

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

2001 (2)

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

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[Crossref]

1999 (1)

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, “Nonmaximally entangled states: production, characterization, and utilization,” Phys. Rev. Lett. 83, 3103–3107 (1999).
[Crossref]

1963 (1)

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[Crossref]

An, J. H.

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A 79, 032303 (2009).
[Crossref]

Aoki, T.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[Crossref] [PubMed]

Ashhab, S.

I. M. Georgescu, S. Ashhab, and F. Nori, “Quantum simulation,” Rev. Mod. Phys. 86, 153 (2014).
[Crossref]

Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
[Crossref]

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoǧlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

M. Atatüre, J. Dreiser, A. Badolato, and A. Imamoglu, “Observation of Faraday rotation from a single confined spin,” Nat. Phys. 3, 101–105 (2007).
[Crossref]

Badolato, A.

M. Atatüre, J. Dreiser, A. Badolato, and A. Imamoglu, “Observation of Faraday rotation from a single confined spin,” Nat. Phys. 3, 101–105 (2007).
[Crossref]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoǧlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Bartkiewicz, K.

A. Miranowicz, K. Bartkiewicz, J. Peřina, M. Koashi, N. Imoto, and F. Nori, “Optimal two-qubit tomography based on local and global measurements: maximal robustness against errors as described by condition numbers,” Phys. Rev. A 90, 062123 (2014).
[Crossref]

Baur, M.

R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, M. Göppl, P. J. Leek, L. Steffen, A. Blais, and A. Wallraff, “Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics,” Phys. Rev. A 80, 043840 (2009).
[Crossref]

Becher, C.

H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[Crossref] [PubMed]

Bechler, O.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref] [PubMed]

Benhelm, J.

H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[Crossref] [PubMed]

Bialczak, R. C.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[Crossref] [PubMed]

Bianchetti, R.

R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, M. Göppl, P. J. Leek, L. Steffen, A. Blais, and A. Wallraff, “Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics,” Phys. Rev. A 80, 043840 (2009).
[Crossref]

Birnbaum, K. M.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, “Observation of the vacuum Rabi spectrum for one trapped atom,” Phys. Rev. Lett. 93, 233603 (2004).
[Crossref] [PubMed]

Bishop, L. S.

J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, L. S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Detecting highly entangled states with a joint qubit readout,” Phys. Rev. A 81, 062325 (2010).
[Crossref]

Blais, A.

R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, M. Göppl, P. J. Leek, L. Steffen, A. Blais, and A. Wallraff, “Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics,” Phys. Rev. A 80, 043840 (2009).
[Crossref]

A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Quantum-information processing with circuit quantum electrodynamics,” Phys. Rev. A 75, 032329 (2007).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Approaching unit visibility for control of a superconducting qubit with dispersive readout,” Phys. Rev. Lett. 95, 060501 (2005).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

Blatt, R.

H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[Crossref] [PubMed]

Bluhm, H.

M. D. Shulman, O. E. Dial, S. P. Harvey, H. Bluhm, V. Umansky, and A. Yacoby, “Demonstration of entanglement of electrostatically coupled singlet-triplet qubits,” Science 336, 202–205 (2012).
[Crossref] [PubMed]

Boca, A.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, “Observation of the vacuum Rabi spectrum for one trapped atom,” Phys. Rev. Lett. 93, 233603 (2004).
[Crossref] [PubMed]

Bochmann, J.

S. Ritter, C. Nölleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mücke, E. Figueroa, J. Bochmann, and G. Rempe, “An elementary quantum network of single atoms in optical cavities,” Nature 484, 195–200 (2012).
[Crossref] [PubMed]

Boozer, A. D.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, “Observation of the vacuum Rabi spectrum for one trapped atom,” Phys. Rev. Lett. 93, 233603 (2004).
[Crossref] [PubMed]

Brune, M.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[Crossref]

Buluta, I.

I. Buluta and F. Nori, “Quantum simulators,” Science 326, 108–111 (2009).
[Crossref] [PubMed]

Cao, C.

Cao, G.

M. L. Zhang, G. W. Deng, S. X. Li, H. O. Li, G. Cao, T. Tu, M. Xiao, G. C. Guo, H. Jiang, I. Siddiqi, and G. P. Guo, “Symmetric reflection line resonator and its quality factor modulation by a two-dimensional electron gas,” Appl. Phys. Lett. 104, 083511 (2014).
[Crossref]

Chek-al-kar, D.

H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[Crossref] [PubMed]

Chen, Q.

Q. Chen, W. Yang, M. Feng, and J. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
[Crossref]

Q. Chen and M. Feng, “Quantum-information processing in decoherence-free subspace with low-Q cavities,” Phys. Rev. A 82, 052329 (2010).
[Crossref]

Q. Chen and M. Feng, “Quantum gating on neutral atoms in low-Q cavities by a single-photon input-output process,” Phys. Rev. A 79, 064304 (2009).
[Crossref]

Cheng, L. Y.

Chow, J. M.

J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, L. S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Detecting highly entangled states with a joint qubit readout,” Phys. Rev. A 81, 062325 (2010).
[Crossref]

Chwalla, M.

H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[Crossref] [PubMed]

Cleland, A. N.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[Crossref] [PubMed]

Cummings, F. W.

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[Crossref]

Dayan, B.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref] [PubMed]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[Crossref] [PubMed]

de Leon, N. P.

See the supplementary information in T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (2014).
[Crossref] [PubMed]

Deng, F. G.

H. R. Wei and F. G. Deng, “Universal quantum gates on electron-spin qubits with quantum dots inside single-side optical microcavities,” Opt. Express 22, 593–607 (2014).
[Crossref] [PubMed]

H. R. Wei and F. G. Deng, “Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities,” Phys. Rev. A 87, 022305 (2013).
[Crossref]

H. R. Wei and F. G. Deng, “Compact quantum gates on electron-spin qubits assisted by diamond nitrogen-vacancy centers inside cavities,” Phys. Rev. A 88, 042323 (2013).
[Crossref]

B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser Phys. Lett. 10, 115201 (2013).
[Crossref]

Deng, G. W.

M. L. Zhang, G. W. Deng, S. X. Li, H. O. Li, G. Cao, T. Tu, M. Xiao, G. C. Guo, H. Jiang, I. Siddiqi, and G. P. Guo, “Symmetric reflection line resonator and its quality factor modulation by a two-dimensional electron gas,” Appl. Phys. Lett. 104, 083511 (2014).
[Crossref]

Devoret, M. H.

J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, L. S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Detecting highly entangled states with a joint qubit readout,” Phys. Rev. A 81, 062325 (2010).
[Crossref]

A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Quantum-information processing with circuit quantum electrodynamics,” Phys. Rev. A 75, 032329 (2007).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Approaching unit visibility for control of a superconducting qubit with dispersive readout,” Phys. Rev. Lett. 95, 060501 (2005).
[Crossref] [PubMed]

Dial, O. E.

M. D. Shulman, O. E. Dial, S. P. Harvey, H. Bluhm, V. Umansky, and A. Yacoby, “Demonstration of entanglement of electrostatically coupled singlet-triplet qubits,” Science 336, 202–205 (2012).
[Crossref] [PubMed]

DiCarlo, L.

J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, L. S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Detecting highly entangled states with a joint qubit readout,” Phys. Rev. A 81, 062325 (2010).
[Crossref]

Dong, H.

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A 78, 063827 (2008).
[Crossref]

Dreiser, J.

M. Atatüre, J. Dreiser, A. Badolato, and A. Imamoglu, “Observation of Faraday rotation from a single confined spin,” Nat. Phys. 3, 101–105 (2007).
[Crossref]

Du, J.

Q. Chen, W. Yang, M. Feng, and J. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
[Crossref]

Duan, L. M.

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[Crossref] [PubMed]

Dür, W.

H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[Crossref] [PubMed]

Eberhard, P. H.

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, “Nonmaximally entangled states: production, characterization, and utilization,” Phys. Rev. Lett. 83, 3103–3107 (1999).
[Crossref]

Englund, D.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[Crossref] [PubMed]

Fält, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoǧlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Feng, M.

Q. Chen, W. Yang, M. Feng, and J. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
[Crossref]

Q. Chen and M. Feng, “Quantum-information processing in decoherence-free subspace with low-Q cavities,” Phys. Rev. A 82, 052329 (2010).
[Crossref]

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A 79, 032303 (2009).
[Crossref]

Q. Chen and M. Feng, “Quantum gating on neutral atoms in low-Q cavities by a single-photon input-output process,” Phys. Rev. A 79, 064304 (2009).
[Crossref]

Figueroa, E.

S. Ritter, C. Nölleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mücke, E. Figueroa, J. Bochmann, and G. Rempe, “An elementary quantum network of single atoms in optical cavities,” Nature 484, 195–200 (2012).
[Crossref] [PubMed]

Filipp, S.

R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, M. Göppl, P. J. Leek, L. Steffen, A. Blais, and A. Wallraff, “Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics,” Phys. Rev. A 80, 043840 (2009).
[Crossref]

Fink, J. M.

R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, M. Göppl, P. J. Leek, L. Steffen, A. Blais, and A. Wallraff, “Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics,” Phys. Rev. A 80, 043840 (2009).
[Crossref]

Forchel, A.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Frunzio, L.

J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, L. S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Detecting highly entangled states with a joint qubit readout,” Phys. Rev. A 81, 062325 (2010).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Approaching unit visibility for control of a superconducting qubit with dispersive readout,” Phys. Rev. Lett. 95, 060501 (2005).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

Gambetta, J.

A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Quantum-information processing with circuit quantum electrodynamics,” Phys. Rev. A 75, 032329 (2007).
[Crossref]

Gambetta, J. M.

J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, L. S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Detecting highly entangled states with a joint qubit readout,” Phys. Rev. A 81, 062325 (2010).
[Crossref]

Georgescu, I. M.

I. M. Georgescu, S. Ashhab, and F. Nori, “Quantum simulation,” Rev. Mod. Phys. 86, 153 (2014).
[Crossref]

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoǧlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Girvin, S. M.

J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, L. S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Detecting highly entangled states with a joint qubit readout,” Phys. Rev. A 81, 062325 (2010).
[Crossref]

A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Quantum-information processing with circuit quantum electrodynamics,” Phys. Rev. A 75, 032329 (2007).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Approaching unit visibility for control of a superconducting qubit with dispersive readout,” Phys. Rev. Lett. 95, 060501 (2005).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

Gong, Z. R.

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A 81, 042304 (2010).
[Crossref]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[Crossref] [PubMed]

Göppl, M.

R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, M. Göppl, P. J. Leek, L. Steffen, A. Blais, and A. Wallraff, “Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics,” Phys. Rev. A 80, 043840 (2009).
[Crossref]

Guendelman, G.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref] [PubMed]

Gühne, O.

H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[Crossref] [PubMed]

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoǧlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Guo, G. C.

M. L. Zhang, G. W. Deng, S. X. Li, H. O. Li, G. Cao, T. Tu, M. Xiao, G. C. Guo, H. Jiang, I. Siddiqi, and G. P. Guo, “Symmetric reflection line resonator and its quality factor modulation by a two-dimensional electron gas,” Appl. Phys. Lett. 104, 083511 (2014).
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Figures (8)

Fig. 1
Fig. 1 Schematic of the generic models investigated in this paper. (a) Type-I cavity QED system wherein a qubit is dispersively coupled to a single-mode and single-sided cavity with one mirror partially reflective and another mirror perfectly reflective. (b) Type-II cavity QED system consisting of a qubit dispersively coupled to a single-mode and double-sided cavity with both mirror partially reflective. In (a) and (b), the QNDD of unknown single-qubit states can be realized by detecting the QSDPSs of the reflected or transmitted photons from the cavity. κ denotes the cavity decay rate, and γ is the qubit decay rate.
Fig. 2
Fig. 2 The numerically simulated phases ϕ1 of the reflected photons from the cavity as a function of the detuning Δdc for the EC (black line), the computational basis states |1〉 (green line) and |0〉 (red line), and an arbitrary state ρ with the diagonal elements of its density matrix as diag(0.7, 0.3) (blue line). The available experimental parameters are chosen as Γ = −2π × 7.38MHz and κ = 2π × 1.69MHz [34].
Fig. 3
Fig. 3 The numerically simulated QSDPSs ϕ1 of the reflected photons from the cavity as a function of the detuning Δdc. Panels (a)–(c) correspond to the exemplified detected states ρ1, ρ′1, and ρ″2, respectively. The detection of the QSDPSs is assumed to be performed at Δdc = 0. The available experimental parameters are the same as those in Fig. 2.
Fig. 4
Fig. 4 The numerically simulated QSDPSs θ1 of the transmitted photons through the cavity as a function of the detuning Δdc for the EC (black line), the computational basis states |1〉 (green line) and |0〉 (red line), and an arbitrary state ρ with the diagonal elements of its density matrix as diag(0.7, 0.3) (blue line). The available experimental parameters are the same as those in Fig. 2 and κl = κr = κ for simplicity.
Fig. 5
Fig. 5 The numerically simulated QSDPSs θ1 of the transmitted photons through the cavity as a function of the detuning Δdc. Panels (a)–(c) correspond to the exemplified detected states ρ1, ρ′1, and ρ″1, respectively. The detection of the QSDPSs is assumed to be performed at Δdc = 0. The available experimental parameters are the same as those in Fig. 2 and κl = κr = κ for simplicity.
Fig. 6
Fig. 6 The numerically simulated QSDPSs ϕ2 of the reflected photons as a function of the detuning Δdc. Panels (a)–(o) correspond to the states ρ 2 k (k = 1, 2, ···, 15), respectively. The accessible experimental parameters are selected as (Γ1, Γ2) = 2π × (13, 4) MHz [37] and κ = 2π × 1.69MHz [34].
Fig. 7
Fig. 7 The numerically simulated QSDPSs θ2 of the transmitted photons vs. the detuning Δdc. Panels (a)–(o) correspond to the states ρ 2 k (k = 1, 2, ···, 15), respectively. The accessible experimental parameters are the same as those in Fig. 6 and κl = κr = κ for simplicity.
Fig. 8
Fig. 8 Schematic of two types of circuit QED systems. (a) Type-I circuit QED system wherein a superconducting qubit is dispersively coupled to a reflection-line resonator. (b) Type-II circuit QED system wherein a superconducting qubit is dispersively coupled to a transmission-line resonator. (c) The resonator output field in (a) and (b) is measured with the homodyne detection technique. The resonator output field is first mixed with the local oscillator (LO) and then the resulting signal out of the mixer is measured by the network analyzer in experiment.

Tables (1)

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Table 1 Correspondence relation between the required proper unitary operations (UOs) and the calculated quantity j = 1 , 2 Γ j σ z j ( 0 ) . See the text for details.

Equations (25)

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H = ω c a a + ω a 2 σ z + g ( a σ + σ + a ) ,
H eff = U H U ( ω c + Γ σ z ) a a + ( ω a + Γ ) σ z a
H eff RF = U H eff U i U U t = ( Δ d c Γ σ z ) a a ( Δ d a Γ ) σ z 2 ,
d σ z ( t ) d t = γ [ σ z ( t ) + 1 ] 2 γ [ c in ( t ) σ + σ + c in ( t ) ] ,
σ z ( t ) = e γ t [ σ z ( 0 ) + 1 ] 1 σ z ( 0 ) .
d a ( t ) d t = i [ Δ d c Γ σ z ( t ) ] a ( t ) κ 2 a ( t ) κ b in ( t ) ,
b out ( t ) = b in ( t ) + κ a ( t ) .
e i ϕ 1 b out ( t ) b in ( t ) = i [ Δ d c Γ σ z ( 0 ) ] + κ 2 i [ Δ d c Γ σ z ( 0 ) ] κ 2 .
e i ϕ 0 = i Δ d c + κ 2 i Δ d c κ 2 .
ρ 1 = 1 2 j = 0 , x , y , z r j σ j = 1 2 ( 1 + r z r x i r y r x + i r y 1 r z ) ,
ρ 1 = U x ( π 4 ) ρ 1 U x ( π 4 ) = 1 2 ( 1 r y r x i r z r x + i r z 1 + r y )
ρ 1 = U y ( π 4 ) ρ 1 U y ( π 4 ) = 1 2 ( 1 + r x r z i r y r z + i r y 1 r x )
ρ 1 = ( 0.6 0.25 0.3 i 0.25 + 0.3 i 0.4 )
ρ 1 = ( 0.2 0.25 0.1 i 0.25 + 0.1 i 0.8 )
ρ 1 = ( 0.75 0.1 0.3 i 0.1 + 0.3 i 0.25 )
d a ( t ) d t = i [ Δ d c Γ σ z ( t ) ] a ( t ) 1 2 ( κ l + κ r ) a ( t ) κ l b in l ( t ) κ r b in r ( t ) ,
b out l ( t ) = b in l ( t ) + κ l a ( t ) , b out r ( t ) = b in r ( t ) + κ r a ( t ) .
T 1 e i θ 1 b out r ( t ) b in l ( t ) = κ l κ r i [ Δ d c Γ σ z ( 0 ) ] 1 2 ( κ l + κ r ) ,
T 0 e i θ 0 = κ l κ r i Δ d c 1 2 ( κ l + κ r ) ,
eff RF = ( Δ d c j = 1 N Γ j σ z j ) a a j = 1 N ( Δ d a j Γ j ) σ z j 2 ,
d a ( t ) d t = i [ Δ d c j = 1 N Γ j σ z j ( t ) ] a ( t ) κ 2 a ( t ) κ b in ( t ) .
e i ϕ N b out ( t ) b in ( t ) = i [ Δ d c j = 1 N Γ j σ z j ( 0 ) ] + κ 2 i [ Δ d c j = 1 N Γ j σ z j ( 0 ) ] κ 2 .
d a ( t ) d t = i i [ Δ d c j = 1 N Γ j σ z j ( t ) ] a ( t ) 1 2 ( κ l + κ r ) a ( t ) κ l b in l ( t ) κ r b in r ( t ) .
T N e i θ N b out r ( t ) b in l ( t ) = κ l κ r i [ Δ d c j = 1 N Γ j σ z j ( 0 ) ] κ l + κ r 2 ,
ρ N = 1 2 N j 1 , j 2 , j N = 0 , x , y , z r j 1 j 2 j N σ j 1 σ j 2 σ j N ,

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