Abstract

The two or more degrees of freedoms (DOFs) of photon systems are very useful in hyperparallel photonic quantum computing to accomplish more quantum logic gate operations with less resource, and depress photonic dissipation noise in quantum information processing. We present some flexible and adjustable schemes for hybrid hyper-controlled-not (hyper-CNOT) gates assisted by low-Q cavities, on the two-photon systems in both the spatial-mode and the polarization DOFs. These hybrid spatial-polarization hyper-CNOT gates consume less quantum resource and are more robust against photonic dissipation noise, compared with the integration of two cascaded CNOT gates in one DOF. Besides, simultaneous counter-propagation of two photons economize extremely the operation time in the whole process of our schemes. Moreover, these quantum logic gates are more feasible for fast quantum operations in the weak-coupling region of the low-Q cavities with current experimental technology, which are much different from strong-coupling cases of the high-Q ones.

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

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Robust hyperparallel photonic quantum entangling gate with cavity QED

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Opt. Express 25(10) 10863-10873 (2017)

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2019 (4)

G. Y. Wang, B. C. Ren, F. G. Deng, and G. L. Long, “Complete analysis of hyperentangled bell states assisted with auxiliary hyperentanglement,” Opt. Express 27, 8994–9003 (2019).
[Crossref] [PubMed]

M. Wang, R. B. Wu, J. T. Lin, J. H. Zhang, Z. W. Fang, Z. F. Chai, and Y. Cheng, “Chemo-mechanical polish lithography: a pathway to low loss large scale photonic integration on lithium niobate on insulator (lnoi),” Quantum Eng. 1, e9 (2019).
[Crossref]

M. Wang, Y. Z. Wang, X. S. Xu, Y. Q. Hu, and G. L. Long, “Characterization of microresonator-geometry-deformation for cavity optomechanics,” Opt. Express 27, 63–73 (2019).
[Crossref] [PubMed]

D. E. Liu, “Sensing kondo correlations in a suspended carbon nanotube mechanical resonator with spin-orbit coupling,” Quantum Eng. 1, e10 (2019).
[Crossref]

2018 (6)

X. F. Liu, F. C. Lei, T. J. Wang, G. L. Long, and C. Wang, “Gain lifetime characterization through time-resolved stimulated emission in a whispering-gallery mode microresonator,” Nanophotonics 8, 127–134 (2018).
[Crossref]

T. Wang, X. F. Liu, Y. Q. Hu, G. Q. Qin, D. Ruan, and G. L. Long, “Rapid and high precision measurement of opto-thermal relaxation with pump-probe method,” Sci. Bull. 63, 287–292 (2018).
[Crossref]

G. Y. Wang, T. Li, Q. Ai, and F. G. Deng, “Self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom,” Opt. Express 26, 23333–23346 (2018).
[Crossref] [PubMed]

G. Y. Wang, T. Li, Q. Ai, A. Alsaedi, T. Hayat, and F. G. Deng, “Faithful entanglement purification for high-capacity quantum communication with two-photon four-qubit systems,” Phys. Rev. Appl. 10, 054058 (2018).
[Crossref]

Y. B. Sheng and L. Zhou, “Blind quantum computation with a noise channel,” Phys. Rev. A 98, 052343 (2018).
[Crossref]

T. Xin, J. S. Pedernales, E. Solano, and G. L. Long, “Entanglement measures in embedding quantum simulators with nuclear spins,” Phys. Rev. A 97, 022322 (2018).
[Crossref]

2017 (3)

Z. Yang, O. S. Magaña Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. H. Rafsanjani, G. L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light. Sci. & Appl. 6, e17013 (2017).
[Crossref]

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192 (2017).
[Crossref] [PubMed]

Y. B. Sheng and L. Zhou, “Distributed secure quantum machine learning,” Sci. Bull. 62, 1025–1029 (2017).
[Crossref]

2016 (5)

X. F. Liu, F. Lei, M. Gao, X. Yang, G. Q. Qin, and G. L. Long, “Fabrication of a microtoroidal resonator with picometer precise resonant wavelength,” Opt. Lett. 41, 3603–3606 (2016).
[Crossref] [PubMed]

T. Li and G. L. Long, “Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities,” Phys. Rev. A 94, 022343 (2016).
[Crossref]

G. Y. Wang, Q. Ai, B. C. Ren, T. Li, and F. G. Deng, “Error-detected generation and complete analysis of hyperentangled bell states for photons assisted by quantum-dot spins in double-sided optical microcavities,” Opt. Express 24, 28444–28458 (2016).
[Crossref] [PubMed]

F. F. Du, T. Li, and G. L. Long, “Refined hyperentanglement purification of two-photon systems for high-capacity quantum communication with cavity-assisted interaction,” Annals Phys. 375, 105–118 (2016).
[Crossref]

B. Hacker, S. Welte, G. Rempe, and S. Ritter, “A photon-photon quantum gate based on a single atom in an optical resonator,” Nature 536, 193 (2016).
[Crossref] [PubMed]

2015 (3)

X. H. Li and S. Ghose, “Hyperentanglement concentration for time-bin and polarization hyperentangled photons,” Phys. Rev. A 91, 062302 (2015).
[Crossref]

N. Kalb, A. Reiserer, S. Ritter, and G. Rempe, “Heralded storage of a photonic quantum bit in a single atom,” Phys. Rev. Lett. 114, 220501 (2015).
[Crossref] [PubMed]

L. Zhou and Y. B. Sheng, “Complete logic bell-state analysis assisted with photonic faraday rotation,” Phys. Rev. A 92, 042314 (2015).
[Crossref]

2014 (10)

T. Tiecke, J. D. Thompson, N. P. de Leon, L. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241 (2014).
[Crossref] [PubMed]

H. F. Wang, A. D. Zhu, and S. Zhang, “One-step implementation of a multiqubit phase gate with one control qubit and multiple target qubits in coupled cavities,” Opt. Lett. 39, 1489–1492 (2014).
[Crossref] [PubMed]

T. H. Taminiau, J. Cramer, T. van der Sar, V. V. Dobrovitski, and R. Hanson, “Universal control and error correction in multi-qubit spin registers in diamond,” Nat. nanotechnology 9, 171 (2014).
[Crossref]

S. Muralidharan, J. Kim, N. Lütkenhaus, M. D. Lukin, and L. Jiang, “Ultrafast and fault-tolerant quantum communication across long distances,” Phys. Rev. Lett. 112, 250501 (2014).
[Crossref] [PubMed]

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature 508, 237 (2014).
[Crossref] [PubMed]

T. J. Wang and C. Wang, “Universal hybrid three-qubit quantum gates assisted by a nitrogen-vacancy center coupled with a whispering-gallery-mode microresonator,” Phys. Rev. A 90, 052310 (2014).
[Crossref]

B. C. Ren, F. F. Du, and F. G. Deng, “Two-step hyperentanglement purification with the quantum-state-joining method,” Phys. Rev. A 90, 052309 (2014).
[Crossref]

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,” Sci. Reports 4, 4623 (2014).
[Crossref]

T. J. Wang, Y. Zhang, and C. Wang, “Universal hybrid hyper-controlled quantum gates assisted by quantum dots in optical double-sided microcavities,” Laser Phys. Lett. 11, 025203 (2014).
[Crossref]

E. T. Campbell, “Enhanced fault-tolerant quantum computing in d-level systems,” Phys. Rev. Lett. 113, 230501 (2014).
[Crossref] [PubMed]

2013 (5)

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics,” Phys. Rev. A 88, 012302 (2013).
[Crossref]

G. R. Feng, G. F. Xu, and G. L. Long, “Experimental realization of nonadiabatic holonomic quantum computation,” Phys. Rev. Lett. 110, 190501 (2013).
[Crossref] [PubMed]

H. R. Wei and F. G. Deng, “Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities,” Phys. Rev. A 87, 022305 (2013).
[Crossref]

C. Wang, Y. Zhang, R. Z. Jiao, and G. S. Jin, “Universal quantum controlled phase gate on photonic qubits based on nitrogen vacancy centers and microcavity resonators,” Opt. Express 21, 19252–19260 (2013).
[Crossref] [PubMed]

H. R. Wei and F. G. Deng, “Compact quantum gates on electron-spin qubits assisted by diamond nitrogen-vacancy centers inside cavities,” Phys. Rev. A 88, 042323 (2013).
[Crossref]

2012 (3)

J. M. Chow, J. M. Gambetta, A. Córcoles, S. T. Merkel, J. A. Smolin, C. Rigetti, S. Poletto, G. A. Keefe, M. B. Rothwell, and J. Rozen, “Universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits,” Phys. Rev. Lett. 109, 060501 (2012).
[Crossref] [PubMed]

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled bell state for photons assisted by quantum-dot spins in optical microcavities,” Phys. Rev. A 86, 042337 (2012).
[Crossref]

W. Munro, A. Stephens, S. Devitt, K. Harrison, and K. Nemoto, “Quantum communication without the necessity of quantum memories,” Nat. Photonics 6, 777 (2012).
[Crossref]

2010 (3)

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Esteve, and J. Reichel, “Cavity-based single atom preparation and high-fidelity hyperfine state readout,” Phys. Rev. Lett. 104, 203602 (2010).
[Crossref] [PubMed]

L. Isenhower, E. Urban, X. Zhang, A. Gill, T. Henage, T. A. Johnson, T. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-not quantum gate,” Phys. Rev. Lett. 104, 010503 (2010).
[Crossref] [PubMed]

C. Bonato, F. Haupt, S. S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “Cnot and bell-state analysis in the weak-coupling cavity qed regime,” Phys. Rev. Lett. 104, 160503 (2010).
[Crossref] [PubMed]

2009 (2)

J. H. An, M. Feng, and C. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-q cavities,” Phys. Rev. A 79, 032303 (2009).
[Crossref]

G. W. Lin, X. B. Zou, X. M. Lin, and G. C. Guo, “Robust and fast geometric quantum computation with multiqubit gates in cavity qed,” Phys. Rev. A 79, 064303 (2009).
[Crossref]

2008 (2)

B. Dayan, A. Parkins, T. Aoki, E. Ostby, K. Vahala, and H. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[Crossref] [PubMed]

Y. Liu, G. L. Long, and Y. Sun, “Analytic one-bit and cnot gate constructions of general n-qubit controlled gates,” Int. J. Quantum Inf. 6, 447–462 (2008).
[Crossref]

2007 (3)

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nat. Phys. 3, 253 (2007).
[Crossref]

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A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Reversible state transfer between light and a single trapped atom,” Phys. Rev. Lett. 98, 193601 (2007).
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2006 (2)

J. Beugnon, M. P. Jones, J. Dingjan, B. Darquié, G. Messin, A. Browaeys, and P. Grangier, “Quantum interference between two single photons emitted by independently trapped atoms,” Nature 440, 779 (2006).
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X. M. Lin, P. Xue, M. Y. Chen, Z. H. Chen, and X. H. Li, “Scalable preparation of multiple-particle entangled states via the cavity input-output process,” Phys. Rev. A 74, 052339 (2006).
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2005 (3)

X. F. Zhou, Y. S. Zhang, and G. C. Guo, “Nonlocal gate of quantum network via cavity quantum electrodynamics,” Phys. Rev. A 71, 064302 (2005).
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L. M. Duan, B. Wang, and H. Kimble, “Robust quantum gates on neutral atoms with cavity-assisted photon scattering,” Phys. Rev. A 72, 032333 (2005).
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C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
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2004 (1)

L. M. Duan and H. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
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2003 (4)

T. Yamamoto, Y. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425, 941 (2003).
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D. Zhou, B. Zeng, Z. Xu, and C. Sun, “Quantum computation based on d-level cluster state,” Phys. Rev. A 68, 062303 (2003).
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2001 (3)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” nature 409, 46 (2001).
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G. Y. Wang, T. Li, Q. Ai, A. Alsaedi, T. Hayat, and F. G. Deng, “Faithful entanglement purification for high-capacity quantum communication with two-photon four-qubit systems,” Phys. Rev. Appl. 10, 054058 (2018).
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T. Yamamoto, Y. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425, 941 (2003).
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A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Reversible state transfer between light and a single trapped atom,” Phys. Rev. Lett. 98, 193601 (2007).
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X. M. Lin, P. Xue, M. Y. Chen, Z. H. Chen, and X. H. Li, “Scalable preparation of multiple-particle entangled states via the cavity input-output process,” Phys. Rev. A 74, 052339 (2006).
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T. H. Taminiau, J. Cramer, T. van der Sar, V. V. Dobrovitski, and R. Hanson, “Universal control and error correction in multi-qubit spin registers in diamond,” Nat. nanotechnology 9, 171 (2014).
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B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics,” Phys. Rev. A 88, 012302 (2013).
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G. Y. Wang, T. Li, Q. Ai, A. Alsaedi, T. Hayat, and F. G. Deng, “Faithful entanglement purification for high-capacity quantum communication with two-photon four-qubit systems,” Phys. Rev. Appl. 10, 054058 (2018).
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Figures (4)

Fig. 1
Fig. 1 Schematic setup to implement the interaction between the atom and the single-photon pulse. The top of the low-Q cavity is perfectly reflective and the bottom is partially reflective. CPBSi (i = 1, 2) is a circularly polarizing beam splitter which transmits the photon in the right-circular polarization |R 〉 and reflects the photon in the left-circular polarization |L 〉, respectively. With CPBS1, only the L-polarized component of the single-photon pulse is reflected by the cavity. DL is the time-delay device for making the circularly polarized photon pulses R and L reach the CPBS2 simultaneously. The states |0〉 and |1〉 indicate hyperfine states of the atom in the ground states while |e 〉 is an excited state.
Fig. 2
Fig. 2 Quantum circuit for implementing the hybrid hyper-CNOT gate I assisted by an input-output process of low-Q cavities. Here Y1 and Y2 represent two types of interactions. Y1 shows the interaction between the L-polarized photon in spatial-mode |k1〉 (|k2〉, k = a, b) and the atom trapped in the cavity. For Y2, both the L and R components of the photon interact with the atom of the cavity in sequence, in which before and after the interaction, the R component will be flipped with the polarization bit-flip operation X ( σ X K P = | L K R | + | R K L | , K = A , B ). The 50:50 beam splitters (BSm, m = 1, 2, 3, 4) are used to perform the Hadamard operation on the spatial-mode DOF of the photon A (or B). DL makes the photon A (B) in spatial mode a1 (b1) and a2 (b2) simultaneously reach the second BS2 (BS4). The black (blue) arrows represent propagating directions of the photon A (B), respectively.
Fig. 3
Fig. 3 (a) and (b) represent quantum circuit for implementing hybrid hyper-CNOT gate II and III, respectively. Hn (n = 1, 2, ...) is used to perform a Hadamard operation on the polarization DOF of a photon.
Fig. 4
Fig. 4 (a) The average fidelity C1 and (b) the average efficiency η̄C1 of the hybrid hyper-CNOT gate I vs the ratio of g / κ γ with ω0 = ωc = ωp, respectively.

Equations (18)

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H = ω 0 2 σ z + ω c a a + i g ( a σ + a σ ) .
{ d a ^ ( t ) d t = [ i Δ ω c + κ 2 ] a ^ ( t ) g σ ^ ( t ) κ a ^ in ( t ) , d σ ^ ( t ) d t = [ i Δ ω 0 + γ 2 ] σ ^ ( t ) g σ ^ z ( t ) a ^ ( t ) + γ σ z ( t ) b ^ in ( t ) , a ^ o u t ( t ) = a ^ in ( t ) + κ a ^ ( t ) ,
r ( ω p ) = 1 κ [ i Δ ω 0 + γ 2 ] [ i Δ ω 0 + γ 2 ] [ i Δ ω c + κ 2 ] + g 2 .
r 0 ( ω p ) = 1 κ i Δ ω c + κ 2 .
r ( ω p ) = 1 + ( 2 g / κ γ ) 2 1 + ( 2 g / κ γ ) 2 , r 0 ( ω p ) = 1 .
| L | 1 r ( ω p ) | L | 1 = e i φ | r ( ω p ) | | L | 1 ω 0 = ω c = ω p κ g 2 / κ γ | L | 1 .
| L | 0 r 0 ( ω p ) | L | 0 = e i φ 0 | r 0 ( ω p ) | | L | 0 ω c = ω p | L | 0 .
| ϕ A = | ϕ A P | ϕ A S = ( sin α 1 | R + cos α 1 | L ) A ( sin α 2 | a 1 + cos α 2 | a 2 ) , | ϕ B = | ϕ B P | ϕ B S = ( sin β 1 | R + cos β 1 | L ) B ( sin β 2 | b 1 + cos β 2 | b 2 ) .
| Ψ 1 A = 1 2 [ | 1 1 ( sin α 1 | R + cos α 1 | L ) A + | 0 1 ( sin α 1 | R cos α 1 | L ) A ] ( sin α 2 | a 1 + cos α 2 | a 2 ) .
| Ψ 1 A = ( sin α 1 | R A | 1 1 + cos α 1 | L A | 0 1 ) [ sin ( α 2 + π 4 ) | a 1 + sin ( α 2 π 4 ) | a 2 ] ,
| Ψ 2 B = ( sin β 1 | R B | 1 2 + cos β 1 | L B | 0 2 ) [ sin ( β 2 + π 4 ) | b 1 + sin ( β 2 π 4 ) | b 2 ] .
| Ψ 12 A B = { sin α 1 | R A | 1 1 [ sin ( β 2 + π 4 ) | b 1 + sin ( β 2 π 4 ) | b 2 ] + cos α 1 | L A | 0 1 [ sin ( β 2 + π 4 ) | b 1 sin ( β 2 π 4 ) | b 2 ] } { sin β 1 | R B | 1 2 [ sin ( β 1 + π 4 ) | a 1 + sin ( β 1 π 4 ) | a 2 ] + cos β 1 | L B | 0 2 [ sin ( β 1 + π 4 ) | a 1 sin ( β 1 π 4 ) | a 2 ] } .
| Ψ 12 A B = 1 2 { [ sin α 1 | R A | ϕ B S + cos α 1 | L A σ X B S | ϕ B S ] | 1 1 + [ sin α 1 | R A | ϕ B S cos α 1 | L A σ X B S | ϕ B S ] | 0 1 } { [ sin β 1 | R B | ϕ A S + cos β 1 | L B σ X A S | ϕ A S ] | 1 2 + [ sin β 1 | R B | ϕ A S cos β 1 | L B σ X A S | ϕ A S ] | 0 2 } .
| Ψ 1 = [ sin α 1 | R A | ϕ B S + cos α 1 | L A σ X B S | ϕ B S ] [ sin β 1 | R B | ϕ A S + cos β 1 | L B σ X A S | ϕ A S ] .
| Ψ II = [ sin α 2 | α 1 | ϕ B P + cos α 2 | a 2 σ X B P | ϕ B P ] [ sin β 2 | b 1 | ϕ A P + cos β 2 | b 2 σ X A P | ϕ A P ] .
| Ψ III = [ sin α 1 | R A | ϕ B S + cos α 1 | L A σ X B S | ϕ B S ] [ sin α 2 | a 1 | ϕ B P + cos α 2 | a 2 σ X B P | ϕ B P ] .
| Ψ III N = [ sin α 1 | R A m = 1 N | ϕ B m S + cos α 1 | L A m = 1 N σ X B m S | ϕ B m S ] [ sin α 2 | a 1 m = 1 N | ϕ B m P + cos α 2 | a 2 m = 1 N σ X B m P | ϕ B m P ] .
F C 1 = i j { 1 , 2 } | k = 1 4 ( ξ 2 k 1 sin β j + ξ 2 k cos β j ) λ k ζ k | 2 k = 1 4 | ξ 2 k 1 sin β j + ξ 2 k cos β j ) λ k | 2 k = 1 4 | ζ k | 2 , η C 1 = i j { 1 , 2 } k = 1 4 | ξ 2 k 1 sin β j + ξ 2 k cos β j ) λ k | 2 256 ,

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