Skip to main content
Top
Published in: Quantum Information Processing 4/2021

01-04-2021

Quantum thermometry by single qubit-probe in a thermal XY spin-chain bath

Authors: Lionel Tenemeza Kenfack, William Degaulle Waladi Gueagni, Martin Tchoffo, Lukong Cornelius Fai

Published in: Quantum Information Processing | Issue 4/2021

Log in

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

search-config
loading …

Abstract

We address the estimation of temperature in a thermal XY spin-chain through quantum probe and tools of parameter estimation theory, namely the quantum Fisher information and signal to noise ratio. We focus on the situation where the probe is weakly coupled to the bath to ensure its coherent time-evolution as long as possible and, in turn, an accurate estimation of the bath temperature. Our results provide clear evidence that the estimation precision can be effectively improved by properly adjusting the probe–bath and bath-spins coupling strength. Indeed, we demonstrate that the optimum precision in the estimation of the bath temperature is achieved when the probe–bath and bath spins coupling strength are equals, leading to a long-time interaction of the probe with the bath.

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!

Literature
1.
go back to reference Paris, M.G.A.: Quantum estimation for quantum technology. Int. J. Quantum Inf. 07, 125–137 (2009)MATHCrossRef Paris, M.G.A.: Quantum estimation for quantum technology. Int. J. Quantum Inf. 07, 125–137 (2009)MATHCrossRef
2.
go back to reference Giovannetti, V., Lloyd, S., Maccone, L.: Advances in quantum metrology. Nat. Photon. 5, 222 (2011)ADSCrossRef Giovannetti, V., Lloyd, S., Maccone, L.: Advances in quantum metrology. Nat. Photon. 5, 222 (2011)ADSCrossRef
3.
go back to reference Braun, D., Adesso, G., Benatti, F., Floreanini, R., Marzolino, U., Mitchell, M.W., Pirandola, S.: Quantum-enhanced measurements without entanglement. Rev. Mod. Phys. 90, 035006 (2018)ADSMathSciNetCrossRef Braun, D., Adesso, G., Benatti, F., Floreanini, R., Marzolino, U., Mitchell, M.W., Pirandola, S.: Quantum-enhanced measurements without entanglement. Rev. Mod. Phys. 90, 035006 (2018)ADSMathSciNetCrossRef
4.
go back to reference Kurizki, G., Bertet, P., Kubo, Y., Mølmer, K., Petrosyan, D., Rabl, P., Schmiedmayer, J.: Quantum technologies with hybrid systems. Proc. Natl. Acad. Sci. 112, 3866–3873 (2015)ADSCrossRef Kurizki, G., Bertet, P., Kubo, Y., Mølmer, K., Petrosyan, D., Rabl, P., Schmiedmayer, J.: Quantum technologies with hybrid systems. Proc. Natl. Acad. Sci. 112, 3866–3873 (2015)ADSCrossRef
5.
go back to reference Hauke, P., Heyl, M., Tagliacozzo, L., Zoller, P.: Measuring multipartite entanglement through dynamic susceptibilities. Nat. Phys. 12, 778 (2016)CrossRef Hauke, P., Heyl, M., Tagliacozzo, L., Zoller, P.: Measuring multipartite entanglement through dynamic susceptibilities. Nat. Phys. 12, 778 (2016)CrossRef
6.
go back to reference Strobel, H., Muessel, W., Linnemann, D., Zibold, T., Hume, D.B., Pezzè, L., Oberthaler, M.K.: Fisher information and entanglement of non-gaussian spin states. Science 345, 424 (2014)ADSCrossRef Strobel, H., Muessel, W., Linnemann, D., Zibold, T., Hume, D.B., Pezzè, L., Oberthaler, M.K.: Fisher information and entanglement of non-gaussian spin states. Science 345, 424 (2014)ADSCrossRef
8.
go back to reference Kenfack, L.T., Tchoffo, M., Fai, L.C.: Estimation of the disorder degree of the classical static noise using. Phys. Lett. A 383, 1123–1131 (2019)ADSCrossRef Kenfack, L.T., Tchoffo, M., Fai, L.C.: Estimation of the disorder degree of the classical static noise using. Phys. Lett. A 383, 1123–1131 (2019)ADSCrossRef
10.
go back to reference Rossi, M.A., Paris, M.G.A.: Entangled quantum probes for dynamical environmental noise. Phys. Rev. A 92, 010302 (2015)ADSCrossRef Rossi, M.A., Paris, M.G.A.: Entangled quantum probes for dynamical environmental noise. Phys. Rev. A 92, 010302 (2015)ADSCrossRef
11.
go back to reference Benedetti, C., Buscemi, F., Bordone, P., Paris, M.G.A.: Quantum probes for the spectral properties of a classical environment. Phys. Rev. A 89, 032114 (2014)ADSCrossRef Benedetti, C., Buscemi, F., Bordone, P., Paris, M.G.A.: Quantum probes for the spectral properties of a classical environment. Phys. Rev. A 89, 032114 (2014)ADSCrossRef
12.
go back to reference Latune, C.L., Sinayskiy, I., Petruccione, F.: Quantum force estimation in arbitrary non-Markovian Gaussian baths. Phys. Rev. A 94, 052115 (2016)ADSCrossRef Latune, C.L., Sinayskiy, I., Petruccione, F.: Quantum force estimation in arbitrary non-Markovian Gaussian baths. Phys. Rev. A 94, 052115 (2016)ADSCrossRef
13.
go back to reference Benedetti, C., Sehdaran, F.S., Zandi, M.H., Paris, M.G.A.: Quantum probes for the cutoff frequency of Ohmic environments. Phys. Rev. A 97, 012126 (2018)ADSCrossRef Benedetti, C., Sehdaran, F.S., Zandi, M.H., Paris, M.G.A.: Quantum probes for the cutoff frequency of Ohmic environments. Phys. Rev. A 97, 012126 (2018)ADSCrossRef
14.
go back to reference Salari Sehdaran, F., Bina, M., Benedetti, C., Paris, M.G.A.: Quantum probes for Ohmic environments at thermal equilibrium. Entropy 21, 486 (2019)ADSMathSciNetCrossRef Salari Sehdaran, F., Bina, M., Benedetti, C., Paris, M.G.A.: Quantum probes for Ohmic environments at thermal equilibrium. Entropy 21, 486 (2019)ADSMathSciNetCrossRef
15.
go back to reference Tamascelli, D., Benedetti, C., Breuer, H.P., Paris, M.G.: Quantum probing beyond pure dephasing. New J. Phys. 22, 083027 (2020)ADSMathSciNetCrossRef Tamascelli, D., Benedetti, C., Breuer, H.P., Paris, M.G.: Quantum probing beyond pure dephasing. New J. Phys. 22, 083027 (2020)ADSMathSciNetCrossRef
16.
go back to reference Zwick, A., Álvarez, G.A., Kurizki, G.: Criticality of environmental information obtainable by dynamically controlled quantum probes. Phys. Rev. A 94, 042122 (2016)ADSCrossRef Zwick, A., Álvarez, G.A., Kurizki, G.: Criticality of environmental information obtainable by dynamically controlled quantum probes. Phys. Rev. A 94, 042122 (2016)ADSCrossRef
17.
go back to reference Correa, L.A., Perarnau-Llobet, M., Hovhannisyan, K.V., Hernandez-Santana, S., Mehboudi, M., Sanpera, A.: Enhancement of low-temperature thermometry by strong coupling. Phys. Rev. A 96, 062103 (2017)ADSCrossRef Correa, L.A., Perarnau-Llobet, M., Hovhannisyan, K.V., Hernandez-Santana, S., Mehboudi, M., Sanpera, A.: Enhancement of low-temperature thermometry by strong coupling. Phys. Rev. A 96, 062103 (2017)ADSCrossRef
18.
go back to reference Zwick, A., Álvarez, G.A., Kurizki, G.: Maximizing information on the environment by dynamically controlled qubit probes. Phys. Rev. Appl. 5, 014007 (2016)ADSCrossRef Zwick, A., Álvarez, G.A., Kurizki, G.: Maximizing information on the environment by dynamically controlled qubit probes. Phys. Rev. Appl. 5, 014007 (2016)ADSCrossRef
19.
go back to reference Hofer, P.P., Brask, J.B., Perarnau-Llobet, M., Brunner, N.: Quantum thermal machine as a thermometer. Phys. Rev. Lett. 119, 090603 (2017)ADSCrossRef Hofer, P.P., Brask, J.B., Perarnau-Llobet, M., Brunner, N.: Quantum thermal machine as a thermometer. Phys. Rev. Lett. 119, 090603 (2017)ADSCrossRef
20.
go back to reference Mehboudi, M., Sanpera, A., Correa, L.A.: Thermometry in the quantum regime: recent theoretical progress. J. Phys. A Math. Theor. 52, 303001 (2019)MathSciNetCrossRef Mehboudi, M., Sanpera, A., Correa, L.A.: Thermometry in the quantum regime: recent theoretical progress. J. Phys. A Math. Theor. 52, 303001 (2019)MathSciNetCrossRef
21.
go back to reference Schwab, K., Henriksen, E.A., Worlock, J.M., Roukes, M.L.: Measurement of the quantum of thermal conductance. Nature 404, 974 (2000)ADSCrossRef Schwab, K., Henriksen, E.A., Worlock, J.M., Roukes, M.L.: Measurement of the quantum of thermal conductance. Nature 404, 974 (2000)ADSCrossRef
22.
go back to reference Linden, N., Popescu, S., Skrzypczyk, P.: How small can thermal machines be? The smallest possible refrigerator. Phys. Rev. Lett. 105, 130401 (2010)ADSCrossRef Linden, N., Popescu, S., Skrzypczyk, P.: How small can thermal machines be? The smallest possible refrigerator. Phys. Rev. Lett. 105, 130401 (2010)ADSCrossRef
23.
go back to reference Klinkert, B., Narberhaus, F.: Microbial thermosensors. Cell. Mol. Life Sci. 66, 2661 (2009)CrossRef Klinkert, B., Narberhaus, F.: Microbial thermosensors. Cell. Mol. Life Sci. 66, 2661 (2009)CrossRef
24.
go back to reference Schirhagl, R., Chang, K., Loretz, M., Degen, C.L.: Nitrogen-vacancy centers in diamond: nanoscale sensors for physics and biology. Annu. Rev. Phys. Chem. 65, 83 (2014)ADSCrossRef Schirhagl, R., Chang, K., Loretz, M., Degen, C.L.: Nitrogen-vacancy centers in diamond: nanoscale sensors for physics and biology. Annu. Rev. Phys. Chem. 65, 83 (2014)ADSCrossRef
25.
26.
go back to reference Campisi, M., Hänggi, P., Talkner, P.: Rev. Mod. Phys. 83, 771 (2011). Erratum: Rev. Mod. Phys. Quantum fluctuation relations: Foundations and applications 83, 1653 (2011) Campisi, M., Hänggi, P., Talkner, P.: Rev. Mod. Phys. 83, 771 (2011). Erratum: Rev. Mod. Phys. Quantum fluctuation relations: Foundations and applications 83, 1653 (2011)
27.
go back to reference Horodecki, M., Oppenheim, J.: Fundamental limitations for quantum and nanoscale thermodynamics. Nat. Commun. 4, 2059 (2013)ADSCrossRef Horodecki, M., Oppenheim, J.: Fundamental limitations for quantum and nanoscale thermodynamics. Nat. Commun. 4, 2059 (2013)ADSCrossRef
28.
go back to reference Carrega, M., Solinas, P., Braggio, A., Sassetti, M., Weiss, U.: Functional integral approach to time-dependent heat exchange in open quantum systems: general method and applications. New J. Phys. 17, 045030 (2015)ADSMathSciNetCrossRef Carrega, M., Solinas, P., Braggio, A., Sassetti, M., Weiss, U.: Functional integral approach to time-dependent heat exchange in open quantum systems: general method and applications. New J. Phys. 17, 045030 (2015)ADSMathSciNetCrossRef
29.
go back to reference Carrega, M., Solinas, P., Braggio, A., Sassetti, M., Weiss, U.: Energy exchange in driven open quantum systems at strong coupling. Phys. Rev. Lett. 116, 240403 (2016)ADSCrossRef Carrega, M., Solinas, P., Braggio, A., Sassetti, M., Weiss, U.: Energy exchange in driven open quantum systems at strong coupling. Phys. Rev. Lett. 116, 240403 (2016)ADSCrossRef
30.
go back to reference Boyd, R.: Nonlinear Optics. Academic Press, Cambridge (2008) Boyd, R.: Nonlinear Optics. Academic Press, Cambridge (2008)
31.
go back to reference Williams, N.S., Le Hur, K., Jordan, A.N.: Effective thermodynamics of strongly coupled qubits. J. Phys. A Math. Theor. 44, 385003 (2011)MathSciNetMATHCrossRef Williams, N.S., Le Hur, K., Jordan, A.N.: Effective thermodynamics of strongly coupled qubits. J. Phys. A Math. Theor. 44, 385003 (2011)MathSciNetMATHCrossRef
32.
go back to reference Kliesch, M., Gogolin, C., Kastoryano, M.J., Riera, A., Eisert, J.: Locality of Temperature Kliesch, M., Gogolin, C., Kastoryano, M.J., Riera, A., Eisert, J.: Locality of Temperature
33.
go back to reference Millen, J., Xuereb, A.: New J. Phys. 18, 011002 (2016). Perspective on quantum thermodynamics. Phys. Rev. X 4, 031019 (2014) Millen, J., Xuereb, A.: New J. Phys. 18, 011002 (2016). Perspective on quantum thermodynamics. Phys. Rev. X 4, 031019 (2014)
34.
35.
go back to reference Kenfack, L.T., Tchoffo, M., Gueagni, W.D.W., Fai, L.C.: Temperature estimation in a quantum spin bath through entangled and separable two-qubit probes. Eur. Phys. J. Plus 136, 220 (2021)CrossRef Kenfack, L.T., Tchoffo, M., Gueagni, W.D.W., Fai, L.C.: Temperature estimation in a quantum spin bath through entangled and separable two-qubit probes. Eur. Phys. J. Plus 136, 220 (2021)CrossRef
36.
go back to reference Mohr, P.J., Taylor, N.: CODATA recommended values of the fundamental physical constants: 2002. Rev. Mod. Phys. 77, 1 (2005)ADSCrossRef Mohr, P.J., Taylor, N.: CODATA recommended values of the fundamental physical constants: 2002. Rev. Mod. Phys. 77, 1 (2005)ADSCrossRef
37.
go back to reference Weng, W., Anstie, J.D., Stace, T.M., Campbell, G., Baynes, F.N., Luiten, A.N.: Nano-Kelvin thermometry and temperature control: beyond the thermal noise limit. Phys. Rev. Lett. 112, 160801 (2014)ADSCrossRef Weng, W., Anstie, J.D., Stace, T.M., Campbell, G., Baynes, F.N., Luiten, A.N.: Nano-Kelvin thermometry and temperature control: beyond the thermal noise limit. Phys. Rev. Lett. 112, 160801 (2014)ADSCrossRef
38.
go back to reference Razavian, S., Benedetti, C., Bina, M., Akbari-Kourbolagh, Y., Paris, M.G.A.: Quantum thermometry by single-qubit dephasing. Eur. Phys. J. Plus. 134, 284 (2019)CrossRef Razavian, S., Benedetti, C., Bina, M., Akbari-Kourbolagh, Y., Paris, M.G.A.: Quantum thermometry by single-qubit dephasing. Eur. Phys. J. Plus. 134, 284 (2019)CrossRef
39.
go back to reference Rangani Jahromi, H.: Quantum thermometry in a squeezed thermal bath. Phys. Scr. 95, 035107 (2020)CrossRef Rangani Jahromi, H.: Quantum thermometry in a squeezed thermal bath. Phys. Scr. 95, 035107 (2020)CrossRef
40.
go back to reference Gebbia, F., Benedetti, C., Benatti, F., Floreanini, R., Bina, M., Paris, M.G.A.: Two-qubit quantum probes for the temperature of an Ohmic environment. Phys. Rev. A 101, 032112 (2020)ADSMathSciNetCrossRef Gebbia, F., Benedetti, C., Benatti, F., Floreanini, R., Bina, M., Paris, M.G.A.: Two-qubit quantum probes for the temperature of an Ohmic environment. Phys. Rev. A 101, 032112 (2020)ADSMathSciNetCrossRef
41.
go back to reference Seveso, L., Paris, M.G.A.: Trade-off between information and disturbance in qubit thermometry. Phys. Rev. A 97, 032129 - Published 28 March 2018 Seveso, L., Paris, M.G.A.: Trade-off between information and disturbance in qubit thermometry. Phys. Rev. A 97, 032129 - Published 28 March 2018
42.
go back to reference Yuan, X.-Z., Zhu, K.-D., Goan, H.-S.: The dynamics of a central spin in quantum Heisenberg XY Model. Eur. Phys. J. D 46, 375–380 (2008)ADSCrossRef Yuan, X.-Z., Zhu, K.-D., Goan, H.-S.: The dynamics of a central spin in quantum Heisenberg XY Model. Eur. Phys. J. D 46, 375–380 (2008)ADSCrossRef
43.
go back to reference Yuan, X.-Z., Goan, H.-S., Zhu, K.-D.: Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment. Phys. Rev. B 75, 045331 (2007)ADSCrossRef Yuan, X.-Z., Goan, H.-S., Zhu, K.-D.: Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment. Phys. Rev. B 75, 045331 (2007)ADSCrossRef
44.
go back to reference Zhong, W., Sun, Z., Ma, J., Wang, X., Nori, F.: Fisher information under decoherence in Bloch representation. Phys. Rev. A 87, 022337 (2013)ADSCrossRef Zhong, W., Sun, Z., Ma, J., Wang, X., Nori, F.: Fisher information under decoherence in Bloch representation. Phys. Rev. A 87, 022337 (2013)ADSCrossRef
Metadata
Title
Quantum thermometry by single qubit-probe in a thermal XY spin-chain bath
Authors
Lionel Tenemeza Kenfack
William Degaulle Waladi Gueagni
Martin Tchoffo
Lukong Cornelius Fai
Publication date
01-04-2021
Publisher
Springer US
Published in
Quantum Information Processing / Issue 4/2021
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-021-03075-3

Other articles of this Issue 4/2021

Quantum Information Processing 4/2021 Go to the issue