Abstract

In recent proposals for achieving optical super-resolution, variants of the quantum Fisher information (QFI) quantify the attainable precision. We find that claims about a strong enhancement of the resolution resulting from coherence effects are questionable because they refer to very small subsets of the data without proper normalization. When the QFI is normalized, accounting for the strength of the signal, there is no advantage of coherent sources over incoherent ones. Our findings have a bearing on further studies of the achievable precision of optical instruments.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. Tsang, “Resolving starlight: a quantum perspective,” arXiv:1906.02064[quant-ph] (2019).
  2. M. Tsang, R. Nair, and X.-M. Lu, Phys. Rev. X 6, 031033 (2016).
    [Crossref]
  3. M. Paúr, B. Stoklasa, Z. Hradil, L. L. Sánchez-Soto, and J. Řeháček, Optica 3, 1144 (2016).
    [Crossref]
  4. J. Řeháček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Phys. Rev. A 96, 062107 (2017).
    [Crossref]
  5. W. Larson and B. E. A. Saleh, Optica 5, 1382 (2018).
    [Crossref]
  6. M. Tsang and R. Nair, Optica 6, 400 (2019).
    [Crossref]
  7. W. Larson and B. E. A. Saleh, Optica 6, 402 (2019).
    [Crossref]
  8. C. M. Sparrow, Astrophys. J. 44, 76 (1916).
    [Crossref]
  9. B. L. Mehta, Nouvelle Revue d’Optique 5, 95 (1974).
    [Crossref]
  10. G. Cesini, G. Guattari, P. De Santis, and C. Palma, J. Opt. 10, 79(1979).
    [Crossref]
  11. T. Asakura, Nouvelle Revue d’Optique 5, 169 (1974).
    [Crossref]
  12. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005), p. 159.
  13. B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
    [Crossref]
  14. X.-F. Qian and J. H. Eberly, Opt. Lett. 36, 4110 (2011).
    [Crossref]

2019 (3)

M. Tsang and R. Nair, Optica 6, 400 (2019).
[Crossref]

W. Larson and B. E. A. Saleh, Optica 6, 402 (2019).
[Crossref]

B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
[Crossref]

2018 (1)

2017 (1)

J. Řeháček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Phys. Rev. A 96, 062107 (2017).
[Crossref]

2016 (2)

2011 (1)

1979 (1)

G. Cesini, G. Guattari, P. De Santis, and C. Palma, J. Opt. 10, 79(1979).
[Crossref]

1974 (2)

T. Asakura, Nouvelle Revue d’Optique 5, 169 (1974).
[Crossref]

B. L. Mehta, Nouvelle Revue d’Optique 5, 95 (1974).
[Crossref]

1916 (1)

C. M. Sparrow, Astrophys. J. 44, 76 (1916).
[Crossref]

Asakura, T.

T. Asakura, Nouvelle Revue d’Optique 5, 169 (1974).
[Crossref]

Cesini, G.

G. Cesini, G. Guattari, P. De Santis, and C. Palma, J. Opt. 10, 79(1979).
[Crossref]

Daiss, S.

B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
[Crossref]

De Santis, P.

G. Cesini, G. Guattari, P. De Santis, and C. Palma, J. Opt. 10, 79(1979).
[Crossref]

Eberly, J. H.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005), p. 159.

Grover, J.

J. Řeháček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Phys. Rev. A 96, 062107 (2017).
[Crossref]

Guattari, G.

G. Cesini, G. Guattari, P. De Santis, and C. Palma, J. Opt. 10, 79(1979).
[Crossref]

Hacker, B.

B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
[Crossref]

Hradil, Z.

J. Řeháček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Phys. Rev. A 96, 062107 (2017).
[Crossref]

M. Paúr, B. Stoklasa, Z. Hradil, L. L. Sánchez-Soto, and J. Řeháček, Optica 3, 1144 (2016).
[Crossref]

Krzic, A.

J. Řeháček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Phys. Rev. A 96, 062107 (2017).
[Crossref]

Larson, W.

Li, L.

B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
[Crossref]

Lu, X.-M.

M. Tsang, R. Nair, and X.-M. Lu, Phys. Rev. X 6, 031033 (2016).
[Crossref]

Mehta, B. L.

B. L. Mehta, Nouvelle Revue d’Optique 5, 95 (1974).
[Crossref]

Nair, R.

M. Tsang and R. Nair, Optica 6, 400 (2019).
[Crossref]

M. Tsang, R. Nair, and X.-M. Lu, Phys. Rev. X 6, 031033 (2016).
[Crossref]

Palma, C.

G. Cesini, G. Guattari, P. De Santis, and C. Palma, J. Opt. 10, 79(1979).
[Crossref]

Paúr, M.

J. Řeháček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Phys. Rev. A 96, 062107 (2017).
[Crossref]

M. Paúr, B. Stoklasa, Z. Hradil, L. L. Sánchez-Soto, and J. Řeháček, Optica 3, 1144 (2016).
[Crossref]

Qian, X.-F.

Rehácek, J.

J. Řeháček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Phys. Rev. A 96, 062107 (2017).
[Crossref]

M. Paúr, B. Stoklasa, Z. Hradil, L. L. Sánchez-Soto, and J. Řeháček, Optica 3, 1144 (2016).
[Crossref]

Rempe, G.

B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
[Crossref]

Ritter, S.

B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
[Crossref]

Saleh, B. E. A.

Sánchez-Soto, L. L.

J. Řeháček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Phys. Rev. A 96, 062107 (2017).
[Crossref]

M. Paúr, B. Stoklasa, Z. Hradil, L. L. Sánchez-Soto, and J. Řeháček, Optica 3, 1144 (2016).
[Crossref]

Shaukat, A.

B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
[Crossref]

Sparrow, C. M.

C. M. Sparrow, Astrophys. J. 44, 76 (1916).
[Crossref]

Stoklasa, B.

J. Řeháček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Phys. Rev. A 96, 062107 (2017).
[Crossref]

M. Paúr, B. Stoklasa, Z. Hradil, L. L. Sánchez-Soto, and J. Řeháček, Optica 3, 1144 (2016).
[Crossref]

Tsang, M.

M. Tsang and R. Nair, Optica 6, 400 (2019).
[Crossref]

M. Tsang, R. Nair, and X.-M. Lu, Phys. Rev. X 6, 031033 (2016).
[Crossref]

M. Tsang, “Resolving starlight: a quantum perspective,” arXiv:1906.02064[quant-ph] (2019).

Welte, S.

B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
[Crossref]

Astrophys. J. (1)

C. M. Sparrow, Astrophys. J. 44, 76 (1916).
[Crossref]

J. Opt. (1)

G. Cesini, G. Guattari, P. De Santis, and C. Palma, J. Opt. 10, 79(1979).
[Crossref]

Nat. Photonics (1)

B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
[Crossref]

Nouvelle Revue d’Optique (2)

T. Asakura, Nouvelle Revue d’Optique 5, 169 (1974).
[Crossref]

B. L. Mehta, Nouvelle Revue d’Optique 5, 95 (1974).
[Crossref]

Opt. Lett. (1)

Optica (4)

Phys. Rev. A (1)

J. Řeháček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Phys. Rev. A 96, 062107 (2017).
[Crossref]

Phys. Rev. X (1)

M. Tsang, R. Nair, and X.-M. Lu, Phys. Rev. X 6, 031033 (2016).
[Crossref]

Other (2)

M. Tsang, “Resolving starlight: a quantum perspective,” arXiv:1906.02064[quant-ph] (2019).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005), p. 159.

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Figures (2)

Fig. 1.
Fig. 1. Dependence of the QFI on the displacement s for the phase values φ = 0 , 1 4 π , 1 2 π , 3 4 π , and π . The QFI diverges for φ π . The plot is for a Gaussian PSF with the variances ( Δ X ) 2 = σ 2 and ( Δ P ) 2 = 1 / ( 4 σ 2 ) . The displacement is in units of σ , and F in units of σ 2 .
Fig. 2.
Fig. 2. Dependence of the total QFI on the displacement s for both constructive and destructive interference channels detected independently for phases φ = 0 , 1 4 π , and 1 2 π . This properly normalized QFI is always limited by its value for an incoherent superposition. Note that the upper bound is saturated for large displacements, and also for zero displacement for all the phases except when φ = 0 or π . The plot is for a Gaussian PSF with variances ( Δ x ) = σ 2 and ( Δ P ) 2 = 1 / ( 4 σ 2 ) .

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

( Δ θ ) 2 H 1 n F ,
ρ = 1 N | Φ Φ | with | Φ = | Ψ + + e i φ | Ψ .
F φ ( s ) = 4 N s Φ | s Φ 4 N 2 | Φ | s Φ | 2 .
F φ ( 0 ) = tan 2 ( φ / 2 ) ( Δ P ) 2 .
F π ( s ) = P 6 P 2 P 4 2 36 P 2 2 s 2
F 0 ( s ) = 1 4 ( Δ P 2 ) 2 s 2 ,
| φ = 2 1 / 2 ( | Ψ + | x + e i φ | Ψ | x ) = | Φ 1 | z + | Φ 2 | z ,
| Φ 1 = 1 2 ( | Ψ + + e i φ | Ψ ) , | Φ 2 = 1 2 ( | Ψ + e i φ | Ψ ) ,
F tot ( s ) = Φ 1 | Φ 1 F φ ( s ) + Φ 2 | Φ 2 F φ + π ( s ) P 2 = F ent = F inc .
ρ j = ( | Ψ + | Ψ ) R j ( Ψ + | Ψ | ) ,

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