Quantum metrology vs. quantum information science

Transcription

1 Quantum metrology vs. quantum information science I. Practical phase estimation II. Phase-preserving linear amplifiers III. Force detection IV. Probabilistic quantum metrology Carlton M. Caves Center for Quantum Information and Control, University of New Mexico Center for Engineered Quantum Systems, University of Queensland Noise, Information, and Quantum Scale, Erice, October 11, 2013 Collaborators: J. Combes, C. Ferrie, Z. Jiang, S. Pandey, M. D. Lang, M. Piani Center for Quantum Information and Control

2 Quantum information science A new way of thinking Computer science Computational complexity depends on physical law. New physics Quantum mechanics as liberator. What can be accomplished with quantum systems that can t be done in a classical world? Explore what can be done with quantum systems, instead of being satisfied with what Nature hands us. Quantum engineering Old physics Quantum mechanics as nag. The uncertainty principle restricts what can be done.

3 Metrology Taking the measure of things The heart of physics New physics Quantum mechanics as liberator. Explore what can be done with quantum systems, instead of being satisfied with what Nature hands us. Quantum engineering Old physics Quantum mechanics as nag. The uncertainty principle restricts what can be done. Old conflict in new guise Asking better questions Getting better answers

4 I. Practical phase estimation Tent Rocks Kasha-Katuwe National Monument Northern New Mexico

5 Optimal practical phase estimation M. D. Lang and C. M. Caves, PRL, to be published, arxiv: [quant-ph]. Straightforward application of Quantum Cramér-Rao Bound (QCRB).

6 Optimal practical phase estimation Straightforward application of Quantum Cramér-Rao Bound (QCRB).

7 Quantum metrology making a difference Squeezed light in the LIGO Hanford detector The LIGO Scientific Collaboration, Nat. Phot. 7, 613 (2013). ~ 2 db of shot-noise reduction

8 Entanglement in linear optical networks Use Bargmann-Fock representation. Z. Jiang, M. D. Lang, and C. M. Caves, PRA, to be published, arxiv: [quant-ph].

9 II. Phase-preserving linear amplifiers Holstrandir Peninsula overlooking Ísafjarðardjúp Westfjords, Iceland

10 Phase-preserving linear amplifiers Ball-and-stick (lollipop) diagram.

11 Phase-preserving linear amplifiers output noise addednoise operator gain input noise added noise Zero-point noise Refer noise to input Added noise number C. M. Caves, PRD 26, 1817 (1982). C. M. Caves, J. Combes, Z. Jiang, and S. Pandey, PRA 86, (2012). Noise temperature

12 Ideal phase-preserving linear amplifier The noise is Gaussian. Circles are drawn here at half the standard deviation of the Gaussian. A perfect linear amplifier, which only has the (blue) amplified input noise, is not physical.

13 NonGaussian amplification of initial coherent state Which of these are legitimate linear amplifiers?

14 What is a phase-preserving linear amplifier? Immaculate amplification of input coherent state Smearing probability distribution. Smears out the amplified coherent state and includes amplified input noise and added noise. For coherent-state input, it is the P function of the output. THE PROBLEM What are the restrictions on the smearing probability distribution that ensure that the amplifier map is physical (completely positive)?

15 Attacking the problem THE ANSWER Any phase-preserving linear amplifier is equivalent to a two-mode squeezing paramp with the smearing function being a rescaled Q function of a physical initial state σ of the ancillary mode.

16 NonGaussian amplification of initial coherent state To IV

17 When does the ancilla state have to be physical? Z. Jiang, M. Piani, and C. M. Caves, QIP 12, 1999 (2013). (orthogonal) Schmidt operators

18 When does the ancilla state have to be physical?

19 III. Force detection Westfjords Iceland

20 Standard quantum limit (SQL) for force detection Monitor position Back-action force Langevin force measurement (shot) noise

21 SQL for force detection Time domain Back-action force Langevin force measurement noise Frequency domain Back-action force measurement noise Langevin force

22 SQL for force detection Back-action force measurement noise Langevin force

23 SQL for force detection

24 SQL for force detection The right wrong story In an opto-mechanical setting, achieving the SQL at a particular frequency requires squeezing at that frequency, and achieving the SQL over a wide bandwidth requires frequency-dependent squeezing.

25 Quantum Cramér-Rao Bound (QCRB) Single-parameter estimation: Bound on the error in estimating a classical parameter that is coupled to a quantum system in terms of the inverse of the quantum Fisher information. Multi-parameter estimation: Bound on the covariance matrix in estimating a set of classical parameters that are coupled to a quantum system in terms of the inverse of a quantum Fisher-information matrix. Waveform estimation: Bound on the continuous covariance matrix for estimating a continuous waveform that is coupled to a quantum system in terms of the inverse of a continuous, two-time quantum Fisher-information matrix.

26 Waveform QCRB. Spectral uncertainty principle M. Tsang, H. M. Wiseman, and C. M. Caves, PRL 106, (2011). Prior-information term At frequencies where there is little prior information, Minimum-uncertainty noise No hint of SQL no back-action noise, only measurement noise but can the bound be achieved?

27 Beating the SQL M. Tsang and C. M. Caves, PRL 105, (2010). Quantum noise cancellation (QNC) using oscillator and negative-mass oscillator. Primary oscillator Negative-mass oscillator Monitor collective position Q Conjugate pairs QCRB Oscillator pairs

28 Quantum-mechanics-free subsystems Conjugate pairs Oscillator pairs M. Tsang and C. M. Caves, PRX 2, (2012).

29 Quantum-mechanics-free subsystems Conjugate variables Dynamically coupled variables

30 Quantum-mechanics-free subsystems Conjugate pairs Paired sidebands about a carrier frequency Oscillator pairs Paired collective spins polarized along opposite directions W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balbas, and E. S. Polzik, PRL 104, (2010). B. Julsgaardd, A. Kozhekin, and E. S. Polzik, Nature 413, 400 (2001).

31 IV. Probabilistic quantum metrology Bungle Bungle Range Western Australia

32 Probabilistic quantum metrology In probabilistic metrology, a selection measurement is made, outcomes unfavorable for estimation are discarded, and parameter(s) are estimated on the favorable outcomes. The selection measurement can be regarded as a state-preparation procedure that prepares states more sensitive to the parameter(s). Analysis should Use a fixed performance metric applied to all data available after postselection, with the data collected from optimal measurements and applied to optimal estimators. Include success probability properly in the performance metric. This should happen automatically if the problem is set up correctly. Compare with performance of optimal deterministic protocol using the same performance metric. We analyze single-parameter estimation using mean-square-error as the performance metric and employing the quantum Cramér-Rao bound as the quantum limit on estimation accuracy.

33 Probabilistic quantum metrology? Probably not J. Combes, C. Ferrie, Z. Jiang, and C. M. Caves, arxiv: [quant-ph]. MSE(x) 1 NI ½Q (x) MSE(x) 1 N X I ¾QAjX (x)

34 Probabilistic quantum metrology? Probably not J. Combes, C. Ferrie, Z. Jiang, and C. M. Caves, arxiv: [quant-ph]. MSE(x) 1 NI ½Q (x) MSE(x) 1 N X I ¾QAjX (x) Cherno bound : Pr[N XI ¾ NI ½ ] e Np(X) µ e p(x)i¾ I ½ NI½ =I ¾

35 Metrology with abstention B. Gendra, E. Ronco-Bonvehii, J. Calsamiglia, R. Muñoz-Tapia, and E. Bagan, NJP 14, (2012).

36 Thanks for your attention Variegated fairy wren Oxley Common, Brisbane Red-backed fairy wren Oxley Common, Brisbane