Abstract

We propose to generate a single-mode-squeezing two-mode squeezed vacuum state via a single χ (2) nonlinear photonic crystal. The state is favorable for existing Gaussian entanglement distillation schemes, since local squeezing operations can enhance the final entanglement and the success probability. The crystal is designed for enabling three concurrent quasi-phase-matching parametric-down conversions, and hence relieves the auxiliary on-line bi-side local squeezing operations. The compact source opens up a way for continuous-variable quantum technologies and could find more potential applications in future large-scale quantum networks.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]

2015 (2)

G. Masada, K. Miyata, A. Politi, T. Hashimoto, J. L. O’Brien, and A. Furusawa, “Continuous-variable entanglement on a chip,” Nat. Photonics 9, 316–319 (2015).
[Crossref]

M. Lazoul, A. Boudrioua, L.-M. Simohamed, and L.-H. Peng, “Multi-resonant optical parametric oscillator based on 2D-PPLT nonlinear photonic crystal,” Opt. Lett. 40, 1861–1864 (2015).
[Crossref] [PubMed]

2014 (3)

L. Chen, P. Xu, Y. F. Bai, X. W. Luo, M. L. Zhong, M. Dai, M. H. Lu, and S. N. Zhu, “Concurrent optical parametric down-conversion in χ(2) nonlinear photonic crystals,” Opt. Express 22, 13164–13169 (2014).
[Crossref] [PubMed]

B.-Q. Chen, C. Zhang, R.-J. Liu, and Z.-Y. Li, “Multi-direction high-efficiency second harmonic generation in ellipse structure nonlinear photonic crystals,” Appl. Phys. Lett. 105, 151106 (2014).
[Crossref]

Y. Kurochkin, A. S. Prasad, and A. I. Lvovsky, “Distillation of the two-mode squeezed state,” Phys. Rev. Lett. 112, 070402 (2014).
[Crossref] [PubMed]

2013 (5)

2012 (4)

Y.-X. Gong, P. Xu, J. Shi, L. Chen, X. Q. Yu, P. Xue, and S. N. Zhu, “Generation of polarization-entangled photon pairs via concurrent spontaneous parametric downconversions in a single χ(2) nonlinear photonic crystal,” Opt. Lett. 37, 4374–4376 (2012).
[Crossref] [PubMed]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single χ(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
[Crossref]

O. Černotík and J. Fiurášek, “Displacement-enhanced continuous-variable entanglement concentration,” Phys. Rev. A 86, 052339 (2012).
[Crossref]

2011 (4)

S. L. Zhang and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
[Crossref]

K. Gallo, M. Levenius, F. Laurell, and V. Pasiskevicius, “Twin-beam optical parametric generation in χ(2) nonlinear photonic crystals,” Appl. Phys. Lett. 98, 161113 (2011).
[Crossref]

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

J. Fiurášek, “Improving entanglement concentration of Gaussian states by local displacements,” Phys. Rev. A 84, 012335 (2011).
[Crossref]

2010 (1)

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).
[Crossref]

2009 (1)

2008 (2)

2007 (4)

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[Crossref] [PubMed]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

X.-B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep. 448, 1–111 (2007).
[Crossref]

A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quantum Electron. 39, 361–375 (2007).
[Crossref]

2006 (1)

2005 (3)

M. B. Plenio, “Logarithmic negativity: a full entanglement monotone that is not convex,” Phys. Rev. Lett. 95, 090503 (2005).
[Crossref] [PubMed]

J. P. Torres, G. Molina-Terriza, and L. Torner, “The spatial shape of entangled photon states generated in non-collinear, walking parametric downconversion,” J. Opt. B Quantum Semicl. Opt. 7, 235–239 (2005).
[Crossref]

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

2004 (3)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[Crossref] [PubMed]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[Crossref] [PubMed]

2003 (1)

J. Fiurášek, L. Mišta, and R. Filip, “Entanglement concentration of continuous-variable quantum states,” Phys. Rev. A 67, 022304 (2003).
[Crossref]

2002 (5)

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[Crossref] [PubMed]

J. Fiurášek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002).
[Crossref]

G. Giedke and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[Crossref]

P. T. Cochrane, T. C. Ralph, and G. J. Milburn, “Teleportation improvement by conditional measurements on the two-mode squeezed vacuum,” Phys. Rev. A 65, 062306 (2002).
[Crossref]

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[Crossref]

2001 (1)

S. Tanzilli, H. D. Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. D. Micheli, D. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[Crossref]

2000 (2)

T. Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61, 032302 (2000).
[Crossref]

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Entanglement purification of Gaussian continuous variable quantum states,” Phys. Rev. Lett. 84, 4002–4005 (2000).
[Crossref] [PubMed]

1998 (2)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[Crossref]

1996 (1)

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

1995 (1)

1992 (1)

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein–Podolsky–Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

1963 (1)

P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35, 23–39 (1963).
[Crossref]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[Crossref]

Andersen, U. L.

Anderson, M. E.

Arie, A.

E. Megidish, A. Halevy, H. S. Eisenberg, A. Ganany-Padowicz, N. Habshoosh, and A. Arie, “Compact 2D nonlinear photonic crystal source of beamlike path entangled photons,” Opt. Express 21, 6689–6696 (2013).
[Crossref] [PubMed]

A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quantum Electron. 39, 361–375 (2007).
[Crossref]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[Crossref]

Bahabad, A.

A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quantum Electron. 39, 361–375 (2007).
[Crossref]

Bai, Y. F.

Baldi, P.

S. Tanzilli, H. D. Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. D. Micheli, D. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[Crossref]

Beck, M.

Bennett, C. H.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

Berger, V.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[Crossref]

Bierlein, J. D.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[Crossref]

Boudrioua, A.

Brassard, G.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

Braunstein, S. L.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Broderick, N. G. R.

Carmichael, H. J.

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[Crossref] [PubMed]

Cerf, N. J.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[Crossref] [PubMed]

Cernotík, O.

O. Černotík and J. Fiurášek, “Displacement-enhanced continuous-variable entanglement concentration,” Phys. Rev. A 86, 052339 (2012).
[Crossref]

Chen, B.-Q.

B.-Q. Chen, C. Zhang, R.-J. Liu, and Z.-Y. Li, “Multi-direction high-efficiency second harmonic generation in ellipse structure nonlinear photonic crystals,” Appl. Phys. Lett. 105, 151106 (2014).
[Crossref]

Chen, L.

Christ, A.

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

Cirac, J. I.

G. Giedke and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[Crossref]

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Entanglement purification of Gaussian continuous variable quantum states,” Phys. Rev. Lett. 84, 4002–4005 (2000).
[Crossref] [PubMed]

Cochrane, P. T.

P. T. Cochrane, T. C. Ralph, and G. J. Milburn, “Teleportation improvement by conditional measurements on the two-mode squeezed vacuum,” Phys. Rev. A 65, 062306 (2002).
[Crossref]

Codemard, C.

Dai, M.

Dantan, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[Crossref] [PubMed]

Duan, L.-M.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Entanglement purification of Gaussian continuous variable quantum states,” Phys. Rev. Lett. 84, 4002–4005 (2000).
[Crossref] [PubMed]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[Crossref]

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Simohamed, L.-M.

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A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
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H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).
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N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
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Tittel, W.

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X.-B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep. 448, 1–111 (2007).
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J. P. Torres, G. Molina-Terriza, and L. Torner, “The spatial shape of entangled photon states generated in non-collinear, walking parametric downconversion,” J. Opt. B Quantum Semicl. Opt. 7, 235–239 (2005).
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J. P. Torres, G. Molina-Terriza, and L. Torner, “The spatial shape of entangled photon states generated in non-collinear, walking parametric downconversion,” J. Opt. B Quantum Semicl. Opt. 7, 235–239 (2005).
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A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
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Wang, X.-B.

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Wenger, J.

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H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, W. J. Yu, M. L. Zhong, G. Zhao, and S. N. Zhu, “Compact engineering of path-entangled sources from a monolithic quadratic nonlinear photonic crystal,” Phys. Rev. Lett. 111, 023603 (2013).
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J. Shi, P. Xu, M. L. Zhong, Y. X. Gong, Y. F. Bai, W. J. Yu, Q. W. Li, H. Jin, and S. N. Zhu, “Heralded generation of multipartite entanglement for one photon by using a single two-dimensional nonlinear photonic crystal,” Opt. Express 21, 7875–7881 (2013).
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S. L. Zhang and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
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H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, W. J. Yu, M. L. Zhong, G. Zhao, and S. N. Zhu, “Compact engineering of path-entangled sources from a monolithic quadratic nonlinear photonic crystal,” Phys. Rev. Lett. 111, 023603 (2013).
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Zhong, M. L.

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L. Chen, P. Xu, Y. F. Bai, X. W. Luo, M. L. Zhong, M. Dai, M. H. Lu, and S. N. Zhu, “Concurrent optical parametric down-conversion in χ(2) nonlinear photonic crystals,” Opt. Express 22, 13164–13169 (2014).
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H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, W. J. Yu, M. L. Zhong, G. Zhao, and S. N. Zhu, “Compact engineering of path-entangled sources from a monolithic quadratic nonlinear photonic crystal,” Phys. Rev. Lett. 111, 023603 (2013).
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Figures (6)

Fig. 1
Fig. 1 (a) Schematic of the 2D rectangularly poled NPC structure. (b) Reciprocal lattice of the crystal. Thin orange arrows represent reciprocal vectors of the crystal. (c) and (d) are two QPM geometries for three concurrent PDC processes. Thick blue arrows represent the pump (p) wave vector. Thick red arrows denote the signal (s), and idler (i) wave vectors. (e) Transverse pattern sketch of the parametric light in the Fourier plane.
Fig. 2
Fig. 2 PS-based distillation of the continuous variable entanglement generated from the χ (2) NPC. |0〉 represents the vacuum state. BS denotes the beam splitter.
Fig. 3
Fig. 3 (a)The distilled entanglement measured with logarithmic negativity and (b) the success probability (in logarithmic scale) of distilling the NPC-generated entanglement using the single-side PS scheme with T = 0.95.
Fig. 4
Fig. 4 (a) Entanglement of the bi-side distilled state measured with the logarithmic negativity and (b) the distillation success probability (in logarithmic scale) with parameter T = 0.95.
Fig. 5
Fig. 5 Performance of bi-side PS distillation of amplitude-damped single-mode-squeezing TMSV state. We assume that the two-outgoing modes A and B are sent to two independent amplitude-damping channels, with each transmittance efficiency η. Other parameters are chosen as :χ = 0.1, T = 0.95. All quantum states are truncated within the photon number subspace spanned by |0〉, |1〉,⋯, |6〉, whose computation convergence is sufficiently verified.
Fig. 6
Fig. 6 Comparison of the bi-side PS distillation performance between the amplitude-damped single-mode-squeezing TMSV state (circled lines) and the amplitude-damped TMSS state with single-mode squeezing operation applied after loss (dotted lines). Other parameter are chosen as χ = 0.15, T = 0.95. All quantum states are truncated within the photon number subspace spanned by |0〉, |1〉,⋯, |6〉, whose computation convergence is sufficiently verified.

Equations (18)

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G m , n = m e 1 + n e 2 , | e 1 | = 2 π Λ x , | e 2 | = 2 π Λ y ,
χ ( 2 ) ( r ) = d m , n G m , n e i G m , n r ,
G m , n = 2 R ( m Λ y ) 2 + ( n Λ x ) 2 J 1 [ 2 π R ( m Λ x ) 2 + ( n Λ y ) 2 ] ,
k s + k i + G 1 , 0 k p = 0 , ,
k s 1 + k i 1 + G 1 , 1 k p = 0 , ,
k s 2 + k i 2 + G 1 , 1 k p = 0 , ,
U ^ = exp { χ [ r ( a ^ A 2 + a ^ B 2 ) + a ^ A a ^ B ] H . c . } .
S U ^ = [ S A ( 2 r χ ) S B ( 2 r χ ) ] S A B ( χ ) ,
S A ( 2 r χ ) = S B ( 2 r χ ) = diag ( e 2 r χ , e 2 r χ ) ,
S A B ( χ ) = cosh ( χ ) I 4 + sinh ( χ ) ( 0 1 1 0 ) ( 1 0 0 1 ) ,
^ ( on ) = I | 0 0 | = n = 1 | n n | .
V A B D = ( I A S B D ( T ) ) [ ( S U ^ 1 2 I A B S U ^ T ) 1 2 I D ] ( I A S B D ( T ) ) T ,
ρ d ( 1 ) = 1 P d ( 1 ) Tr D [ ρ A B D ( I A B ^ D ( on ) ) ] ,
P d ( 1 ) ρ d ( 1 ) = ρ ( V 1 ( 1 ) ) 1 det ( V D + 1 2 I 2 ) ρ ( V 2 ( 1 ) ) ,
V A B D = ( V A B σ σ T V D ) ,
P d ( 1 ) = 1 1 det ( V D + 1 2 I 2 ) .
P d ( 2 ) ρ d ( 2 ) = j = 1 4 P j ρ ( V j ( 2 ) ) ,
S U ^ 1 2 I A B S U ^ T η ( S U ^ 1 2 I A B S U ^ T ) + 1 η 2 I A B ,

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