Skip to main content
Top
Published in: Quantum Information Processing 2/2017

01-02-2017

Overcoming experimental limitations in a nonlinear two-qubit gate through postselection

Author: Julián Martínez-Rincón

Published in: Quantum Information Processing | Issue 2/2017

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We introduce a modular-value two-qubit gate and explore its advantages in experimentally limited situations. The gate is defined such that the final state of a qubit is fully controlled by a pre- and postselection procedure in an ancillary qubit given an (imperfect or technically limited) intermediate conditional qubit–qubit interaction. As an example of the gate and its benefit, we make the connection to a postselected cross-phase modulation scenario when a undesired absorption is present. Probabilistic amplification of a small cross phase while mitigating relative absorption is possible, and a complementary behavior between phase and amplitude emerges.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
1.
go back to reference Dressel, J., Malik, M., Miatto, F.M., Jordan, A.N., Boyd, R.W.: Colloquium : understanding quantum weak values: basics and applications. Rev. Mod. Phys. 86, 307–316 (2014)ADSCrossRef Dressel, J., Malik, M., Miatto, F.M., Jordan, A.N., Boyd, R.W.: Colloquium : understanding quantum weak values: basics and applications. Rev. Mod. Phys. 86, 307–316 (2014)ADSCrossRef
2.
go back to reference Kofman, A.G., Ashhab, S., Nori, F.: Nonperturbative theory of weak pre- and post-selected measurements. Phys. Rep. 520, 43–133 (2012)ADSMathSciNetCrossRef Kofman, A.G., Ashhab, S., Nori, F.: Nonperturbative theory of weak pre- and post-selected measurements. Phys. Rep. 520, 43–133 (2012)ADSMathSciNetCrossRef
3.
go back to reference Shikano, Y.: Theory of ”Weak Value” and Quantum Mechanical Measurements, Measurements in Quantum Mechanics (InTech, 2012) prof. Mohammad Reza Pahlavani (Ed.), doi:10.5772/32810 Shikano, Y.: Theory of ”Weak Value” and Quantum Mechanical Measurements, Measurements in Quantum Mechanics (InTech, 2012) prof. Mohammad Reza Pahlavani (Ed.), doi:10.​5772/​32810
4.
go back to reference Svensson, B.: Pedagogical review of quantum measurement theory with an emphasis on weak measurements. Quanta 2, 18–49 (2013)CrossRefMATH Svensson, B.: Pedagogical review of quantum measurement theory with an emphasis on weak measurements. Quanta 2, 18–49 (2013)CrossRefMATH
5.
go back to reference Torres, J.P., Salazar-Serrano, L.J.: Weak value amplification: a view from quantum estimation theory that highlights what it is and what isn’t. Sci. Rep. 6, 19702 (2016) Torres, J.P., Salazar-Serrano, L.J.: Weak value amplification: a view from quantum estimation theory that highlights what it is and what isn’t. Sci. Rep. 6, 19702 (2016)
6.
go back to reference Brunner, N., Simon, C.: Measuring small longitudinal phase shifts: weak measurements or standard interferometry? Phys. Rev. Lett. 105, 010405 (2010)ADSCrossRef Brunner, N., Simon, C.: Measuring small longitudinal phase shifts: weak measurements or standard interferometry? Phys. Rev. Lett. 105, 010405 (2010)ADSCrossRef
7.
go back to reference Starling, D.J., Dixon, P.B., Jordan, A.N., Howell, J.C.: Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values. Phys. Rev. A. 80, 041803 (2009)ADSCrossRef Starling, D.J., Dixon, P.B., Jordan, A.N., Howell, J.C.: Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values. Phys. Rev. A. 80, 041803 (2009)ADSCrossRef
8.
go back to reference Feizpour, A., Xing, X., Steinberg, A.M.: Amplifying single-photon nonlinearity using weak measurements. Phys. Rev. Lett. 107, 133603 (2011)ADSCrossRef Feizpour, A., Xing, X., Steinberg, A.M.: Amplifying single-photon nonlinearity using weak measurements. Phys. Rev. Lett. 107, 133603 (2011)ADSCrossRef
9.
go back to reference Jordan, A.N., Martínez-Rincón, J., Howell, J.C.: Technical advantages for weak-value amplification: when less is more. Phys. Rev. X 4, 011031 (2014) Jordan, A.N., Martínez-Rincón, J., Howell, J.C.: Technical advantages for weak-value amplification: when less is more. Phys. Rev. X 4, 011031 (2014)
10.
go back to reference Viza, G.I., Martínez-Rincón, J., Alves, G.B., Jordan, A.N., Howell, J.C.: Experimentally quantifying the advantages of weak-value-based metrology. Phys. Rev. A 92, 032127 (2015)ADSCrossRef Viza, G.I., Martínez-Rincón, J., Alves, G.B., Jordan, A.N., Howell, J.C.: Experimentally quantifying the advantages of weak-value-based metrology. Phys. Rev. A 92, 032127 (2015)ADSCrossRef
11.
go back to reference Lundeen, J.S., Sutherland, B., Patel, A., Stewart, C., Bamber, Charles: Direct measurement of the quantum wavefunction. Nature 474, 188–191 (2011)CrossRef Lundeen, J.S., Sutherland, B., Patel, A., Stewart, C., Bamber, Charles: Direct measurement of the quantum wavefunction. Nature 474, 188–191 (2011)CrossRef
12.
go back to reference Lundeen, J.S., Bamber, C.: Procedure for direct measurement of general quantum states using weak measurement. Phys. Rev. Lett. 108, 070402 (2012)ADSCrossRef Lundeen, J.S., Bamber, C.: Procedure for direct measurement of general quantum states using weak measurement. Phys. Rev. Lett. 108, 070402 (2012)ADSCrossRef
13.
go back to reference Malik, M., Mirhosseini, M., Lavery, M.P.J., Leach, J., Padgett, M.J., Boyd, R.W.: Direct measurement of a 27-dimensional orbital-angular-momentum state vector. Nat. Commun. 5, 3115 (2014) Malik, M., Mirhosseini, M., Lavery, M.P.J., Leach, J., Padgett, M.J., Boyd, R.W.: Direct measurement of a 27-dimensional orbital-angular-momentum state vector. Nat. Commun. 5, 3115 (2014)
14.
go back to reference Zou, P., Zhang, Z.-M., Song, W.: Direct measurement of general quantum states using strong measurement. Phys. Rev. A. 91, 052109 (2015)ADSCrossRef Zou, P., Zhang, Z.-M., Song, W.: Direct measurement of general quantum states using strong measurement. Phys. Rev. A. 91, 052109 (2015)ADSCrossRef
15.
go back to reference Vallone, G., Dequal, D.: Strong measurements give a better direct measurement of the quantum wave function. Phys. Rev. Lett. 116, 040502 (2016)ADSCrossRef Vallone, G., Dequal, D.: Strong measurements give a better direct measurement of the quantum wave function. Phys. Rev. Lett. 116, 040502 (2016)ADSCrossRef
16.
go back to reference Salvail, J., Agnew, M., Johnson, A., Bolduc, E., Leach, J., Boyd, R.: Full characterization of polarization states of light via direct measurement. Nat. Photonics 7, 316–321 (2013)ADSCrossRef Salvail, J., Agnew, M., Johnson, A., Bolduc, E., Leach, J., Boyd, R.: Full characterization of polarization states of light via direct measurement. Nat. Photonics 7, 316–321 (2013)ADSCrossRef
17.
go back to reference Qin, L., Xu, L., Feng, W., Li, X.-Q.: “Qubit state tomography in superconducting circuit via weak measurements,” ArXiv e-prints (2016), arXiv:1606.04659 [quant-ph] Qin, L., Xu, L., Feng, W., Li, X.-Q.: “Qubit state tomography in superconducting circuit via weak measurements,” ArXiv e-prints (2016), arXiv:​1606.​04659 [quant-ph]
18.
go back to reference Aharonov, Y., Albert, D.Z., Vaidman, L.: How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351–1354 (1988)ADSCrossRef Aharonov, Y., Albert, D.Z., Vaidman, L.: How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351–1354 (1988)ADSCrossRef
20.
go back to reference Pryde, G.J., O’Brien, J.L., White, A.G., Ralph, T.C., Wiseman, H.M.: Measurement of quantum weak values of photon polarization. Phys. Rev. Lett. 94, 220405 (2005)ADSCrossRef Pryde, G.J., O’Brien, J.L., White, A.G., Ralph, T.C., Wiseman, H.M.: Measurement of quantum weak values of photon polarization. Phys. Rev. Lett. 94, 220405 (2005)ADSCrossRef
21.
22.
go back to reference Dressel, J., Broadbent, C.J., Howell, J.C., Jordan, A.N.: Experimental violation of two-party Leggett–Garg inequalities with semiweak measurements. Phys. Rev. Lett. 106, 040402 (2011)ADSCrossRef Dressel, J., Broadbent, C.J., Howell, J.C., Jordan, A.N.: Experimental violation of two-party Leggett–Garg inequalities with semiweak measurements. Phys. Rev. Lett. 106, 040402 (2011)ADSCrossRef
23.
go back to reference Groen, J.P., Ristè, D., Tornberg, L., Cramer, J., de Groot, P.C., Picot, T., Johansson, G., DiCarlo, L.: Partial-measurement backaction and nonclassical weak values in a superconducting circuit. Phys. Rev. Lett. 111, 090506 (2013)ADSCrossRef Groen, J.P., Ristè, D., Tornberg, L., Cramer, J., de Groot, P.C., Picot, T., Johansson, G., DiCarlo, L.: Partial-measurement backaction and nonclassical weak values in a superconducting circuit. Phys. Rev. Lett. 111, 090506 (2013)ADSCrossRef
24.
go back to reference White, T.C., Mutus, J.Y., Dressel, J., Kelly, J., Barends, R., Jeffrey, E., Sank, D., Megrant, A., Campbell, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Hoi, I.-C., Neill, C., O’Malley, P.J.J., Roushan, P., Vainsencher, A., Wenner, J., Korotkov, A.N., Martinis, J.M.: Preserving entanglement during weak measurement demonstrated with a violation of the Bell-Leggett-Garg inequality. Npj Quantum Inf. 2, 15022 (2016)ADSCrossRef White, T.C., Mutus, J.Y., Dressel, J., Kelly, J., Barends, R., Jeffrey, E., Sank, D., Megrant, A., Campbell, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Hoi, I.-C., Neill, C., O’Malley, P.J.J., Roushan, P., Vainsencher, A., Wenner, J., Korotkov, A.N., Martinis, J.M.: Preserving entanglement during weak measurement demonstrated with a violation of the Bell-Leggett-Garg inequality. Npj Quantum Inf. 2, 15022 (2016)ADSCrossRef
25.
go back to reference Denkmayr, T., Geppert, H., Sponar, S., Lemmel, H., Matzkin, A, Tollaksen, J., Hasegawa, Y.: Observation of a quantum Cheshire cat in a matter-wave interferometer experiment. Nat. Commun. 5, 4492 (2014) Denkmayr, T., Geppert, H., Sponar, S., Lemmel, H., Matzkin, A, Tollaksen, J., Hasegawa, Y.: Observation of a quantum Cheshire cat in a matter-wave interferometer experiment. Nat. Commun. 5, 4492 (2014)
26.
go back to reference Sponar, S., Denkmayr, T., Geppert, H., Lemmel, H., Matzkin, A., Tollaksen, J., Hasegawa, Y.: Weak values obtained in matter-wave interferometry. Phys. Rev. A 92, 062121 (2015)ADSCrossRef Sponar, S., Denkmayr, T., Geppert, H., Lemmel, H., Matzkin, A., Tollaksen, J., Hasegawa, Y.: Weak values obtained in matter-wave interferometry. Phys. Rev. A 92, 062121 (2015)ADSCrossRef
27.
go back to reference Corra, Raul, Santos, Marcelo Frana, Monken, C.H., Saldanha, Pablo L.: Quantum cheshire cat as simple quantum interference. New J. Phys. 17, 053042 (2015)ADSMathSciNetCrossRef Corra, Raul, Santos, Marcelo Frana, Monken, C.H., Saldanha, Pablo L.: Quantum cheshire cat as simple quantum interference. New J. Phys. 17, 053042 (2015)ADSMathSciNetCrossRef
28.
go back to reference Brun, T.A., Diósi, L., Strunz, W.T.: Test of weak measurement on a two- or three-qubit computer. Phys. Rev. A 77, 032101 (2008)ADSCrossRef Brun, T.A., Diósi, L., Strunz, W.T.: Test of weak measurement on a two- or three-qubit computer. Phys. Rev. A 77, 032101 (2008)ADSCrossRef
30.
go back to reference Cormann, M., Remy, M., Kolaric, B., Caudano, Y.: Revealing geometric phases in modular and weak values with a quantum eraser. Phys. Rev. A 93, 042124 (2016)ADSCrossRef Cormann, M., Remy, M., Kolaric, B., Caudano, Y.: Revealing geometric phases in modular and weak values with a quantum eraser. Phys. Rev. A 93, 042124 (2016)ADSCrossRef
31.
go back to reference Lund, A.P.: Efficient quantum computing with weak measurements. New J. Phys. 13, 053024 (2011)ADSCrossRef Lund, A.P.: Efficient quantum computing with weak measurements. New J. Phys. 13, 053024 (2011)ADSCrossRef
32.
go back to reference Lu, D., Brodutch, A., Li, J., Li, H., Laflamme, R.: Experimental realization of post-selected weak measurements on an NMR quantum processor. New J. Phys. 16, 053015 (2014)ADSCrossRef Lu, D., Brodutch, A., Li, J., Li, H., Laflamme, R.: Experimental realization of post-selected weak measurements on an NMR quantum processor. New J. Phys. 16, 053015 (2014)ADSCrossRef
33.
go back to reference Nazir, A., Barrett, S.D.: Overcoming non-Markovian dephasing in single-photon sources through postselection. Phys. Rev. A 79, 011804 (2009)ADSCrossRef Nazir, A., Barrett, S.D.: Overcoming non-Markovian dephasing in single-photon sources through postselection. Phys. Rev. A 79, 011804 (2009)ADSCrossRef
35.
go back to reference Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)ADSCrossRefMATH Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)ADSCrossRefMATH
36.
go back to reference Kedem, Y., Vaidman, L.: Modular values and weak values of quantum observables. Phys. Rev. Lett. 105, 230401 (2010)ADSCrossRef Kedem, Y., Vaidman, L.: Modular values and weak values of quantum observables. Phys. Rev. Lett. 105, 230401 (2010)ADSCrossRef
37.
38.
go back to reference Kirby, B.T., Franson, J.D.: Macroscopic state interferometry over large distances using state discrimination. Phys. Rev. A 89, 033861 (2014)ADSCrossRef Kirby, B.T., Franson, J.D.: Macroscopic state interferometry over large distances using state discrimination. Phys. Rev. A 89, 033861 (2014)ADSCrossRef
39.
go back to reference Hallaji, M., Feizpour, A., Dmochowski, G., Sinclair, J., Steinberg, A.M.: How a single photon can act like many photons. In CLEO: 2015 (Optical Society of America, 2015) p.FM1E.3 Hallaji, M., Feizpour, A., Dmochowski, G., Sinclair, J., Steinberg, A.M.: How a single photon can act like many photons. In CLEO: 2015 (Optical Society of America, 2015) p.FM1E.3
Metadata
Title
Overcoming experimental limitations in a nonlinear two-qubit gate through postselection
Author
Julián Martínez-Rincón
Publication date
01-02-2017
Publisher
Springer US
Published in
Quantum Information Processing / Issue 2/2017
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-016-1485-7

Other articles of this Issue 2/2017

Quantum Information Processing 2/2017 Go to the issue