Abstract

We experimentally characterize a quantum photonic gate that is capable of converting multiqubit entangled states while acting only on two qubits. It is an important tool in large quantum networks, where it can be used for re-wiring of multipartite entangled states or for generating various entangled states required for specific tasks. The gate can be also used to generate quantum information processing resources, such as entanglement and discord. In our experimental demonstration, we characterized the conversion of a linear four-qubit cluster state into different entangled states, including GHZ and Dicke states. The high quality of the experimental results show that the gate has the potential of being a flexible component in distributed quantum photonic networks.

© 2017 Optical Society of America

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2016 (3)

C. Greganti, M.-C. Roehsner, S. Barz, T. Morimae, and P. Walther, “Demonstration of measurement-only blind quantum computing,” New J. Phys. 18, 013020 (2016).
[Crossref]

T. Tashima, M. S. Tame, Ş. K. Özdemir, F. Nori, M. Koashi, and H. Weinfurter, “Photonic multipartite entanglement conversion using nonlocal operations,” Phys. Rev. A 94, 052309 (2016).
[Crossref]

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, M. Ježek, and J. Fiurášek, “Experimental investigation of a four-qubit linear-optical quantum logic circuit,” Sci. Rep. 6, 33475 (2016).
[Crossref] [PubMed]

2014 (6)

M. Mičuda, E. Doláková, I. Straka, M. Miková, M. Dušek, J. Fiurášek, and M. Ježek, “Highly stable polarization independent Mach-Zehnder interferometer,” Rev. Sci. Instrum. 85, 083103 (2014).
[Crossref]

T. Kobayashi, R. Ikuta, Ş. K. Özdemir, M. S. Tame, T. Yamamoto, M. Koashi, and N. Imoto, “Universal gates for transforming multipartite entangled Dicke states,” New J. Phys. 16, 023005 (2014).
[Crossref]

M. S. Tame, B. A. Bell, C. Di Franco, W. J. Wadsworth, and J. G. Rarity, “Experimental realization of a one-way quantum computer algorithm solving Simon’s Problem,” Phys. Rev. Lett. 113, 200501 (2014).
[Crossref]

M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
[Crossref]

S. Pirandola, “Quantum discord as a resource for quantum cryptography,” Sci. Rep. 4, 6956 (2014).
[Crossref] [PubMed]

B. A. Bell, D. Markham, D. A. Herrera-Martí, A. Marin, W. J. Wadsworth, J. G. Rarity, and M. S. Tame, “Experimental demonstration of graph-state quantum secret sharing,” Nat. Commun. 5, 5480 (2014).
[Crossref] [PubMed]

2013 (2)

S. Perseguers, G. J. Lapeyre, D. Cavalcanti, M. Lewenstein, and A. Acin, “Distribution of entanglement in large-scale quantum networks,” Rep. Prog. Phys. 76, 096001 (2013).
[Crossref] [PubMed]

S. Barz, J. F. Fitzsimons, E. Kashefi, and P. Walther, “Experimental verification of quantum computation,” Nat. Phys. 9, 727–731 (2013).
[Crossref]

2012 (6)

S. Barz, E. Kashefi, A. Broadbent, J. F. Fitzsimons, A. Zeilinger, and P. Walther, “Demonstration of blind quantum computing,” Science 335, 303–308 (2012).
[Crossref] [PubMed]

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

S. M. Lee, H. S. Park, J. Cho, Y. Kang, J. Y. Lee, H. Kim, D. Lee, and S.-K. Choi, “Experimental realization of a four-photon seven-qubit graph state for one-way quantum computation,” Opt. Express. 20, 6915–6926 (2012).
[Crossref] [PubMed]

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
[Crossref]

B. Dakić, Y. O. Lipp, X. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, Č. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[Crossref]

2010 (1)

G. Vallone, G. Donati, N. Bruno, A. Chiuri, and P. Mataloni, “Experimental realization of the Deutsch-Jozsa algorithm with a six-qubit cluster state,” Phys. Rev. A 81, 050302(R) (2010).
[Crossref]

2009 (5)

H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest, “Measurement-based quantum computation,” Nat. Phys. 5, 19–26 (2009).
[Crossref]

R. Prevedel, G. Cronenberg, M. S. Tame, M. Paternostro, P. Walther, M. S. Kim, and A. Zeilinger, “Experimental realization of Dicke states of up to six qubits for multiparty quantum networking,” Phys. Rev. Lett. 103, 020503 (2009).
[Crossref] [PubMed]

W. Wieczorek, R. Krischek, N. Kiesel, P. Michelberger, G. Tóth, and H. Weinfurter, “Experimental entanglement of a six-photon symmetric Dicke state,” Phys. Rev. Lett. 103, 020504 (2009).
[Crossref] [PubMed]

G. Chiribella, G. M. D’Ariano, and P. Perinotti, “Theoretical framework for quantum networks,” Phys. Rev. A 80, 022339 (2009).
[Crossref]

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

2008 (1)

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[Crossref] [PubMed]

2007 (4)

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

N. Kiesel, C. Schmid, G. Tóth, E. Solano, and H. Weinfurter, “Experimental observation of four-photon entangled Dicke state with high fidelity,” Phys. Rev. Lett. 98, 063604 (2007).
[Crossref] [PubMed]

R. Prevedel, P. Walther, F. Tiefenbacher, P. Böhi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
[Crossref] [PubMed]

M. S. Tame, R. Prevedel, M. Paternostro, P. Böhi, M. S. Kim, and A. Zeilinger, “Experimental realization of Deutsch’s algorithm in a one-way quantum computer,” Phys. Rev. Lett. 98, 140501 (2007).
[Crossref]

2005 (3)

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

J. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2005).
[Crossref]

Y.-A. Chen, A.-N. Zhang, Z. Zhao, X.-Q. Zhou, C.-Y. Lu, C.-Z. Peng, T. Yang, and J.-W. Pan, “Experimental quantum secret sharing and third-man quantum cryptography,” Phys. Rev. Lett. 95, 200502 (2005).
[Crossref] [PubMed]

2004 (1)

Z. Zhao, Y.-A. Chen, A.-N. Zhang, T. Yang, H. J. Briegel, and J.-W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
[Crossref] [PubMed]

2003 (1)

M. Ježek, J. Fiurášek, and Z. Hradil, “Quantum inference of states and processes,” Phys. Rev. A 68, 012305 (2003).
[Crossref]

2002 (2)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

F. Verstraete, J. Dehaene, B. De Moor, and H. Verschelde, “Four qubits can be entangled in nine different ways,” Phys. Rev. A 65, 052112 (2002).
[Crossref]

2001 (2)

W. Tittel, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum secret sharing,” Phys. Rev. A 63, 042301 (2001).
[Crossref]

A. Acin, D. Bruss, M. Lewenstein, and A. Sanpera, “Classification of mixed three-qubit states,” Phys. Rev. Lett. 87, 040401 (2001).
[Crossref] [PubMed]

2000 (1)

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[Crossref]

1986 (1)

C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. 56, 58–60 (1986).
[Crossref] [PubMed]

1975 (1)

M.-D. Choi, “Completely positive linear maps on complex matrices,” Linear Algebr. Appl. 10, 285–290 (1975).
[Crossref]

1972 (1)

A. Jamiolkowski, “Linear transformations which preserve trace and positive semidefiniteness of operators,” Rep. Math. Phys. 3, 275–278 (1972).
[Crossref]

1970 (1)

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Acin, A.

S. Perseguers, G. J. Lapeyre, D. Cavalcanti, M. Lewenstein, and A. Acin, “Distribution of entanglement in large-scale quantum networks,” Rep. Prog. Phys. 76, 096001 (2013).
[Crossref] [PubMed]

A. Acin, D. Bruss, M. Lewenstein, and A. Sanpera, “Classification of mixed three-qubit states,” Phys. Rev. Lett. 87, 040401 (2001).
[Crossref] [PubMed]

Adamson, R. B. A.

R. B. A. Adamson, B. Fortescue, H. K. Lo, and A. M. Steinberg, “Experimental implementation of a three-party quantum key distribution protocol,” IEEE Conf. Las. Elec. Opt., QMA3, 1–2 (2006).

Almeida, M. P.

M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
[Crossref]

Aspelmeyer, M.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Assad, S. M.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[Crossref]

Barz, S.

C. Greganti, M.-C. Roehsner, S. Barz, T. Morimae, and P. Walther, “Demonstration of measurement-only blind quantum computing,” New J. Phys. 18, 013020 (2016).
[Crossref]

S. Barz, J. F. Fitzsimons, E. Kashefi, and P. Walther, “Experimental verification of quantum computation,” Nat. Phys. 9, 727–731 (2013).
[Crossref]

S. Barz, E. Kashefi, A. Broadbent, J. F. Fitzsimons, A. Zeilinger, and P. Walther, “Demonstration of blind quantum computing,” Science 335, 303–308 (2012).
[Crossref] [PubMed]

B. Dakić, Y. O. Lipp, X. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, Č. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

Bell, B. A.

B. A. Bell, D. Markham, D. A. Herrera-Martí, A. Marin, W. J. Wadsworth, J. G. Rarity, and M. S. Tame, “Experimental demonstration of graph-state quantum secret sharing,” Nat. Commun. 5, 5480 (2014).
[Crossref] [PubMed]

M. S. Tame, B. A. Bell, C. Di Franco, W. J. Wadsworth, and J. G. Rarity, “Experimental realization of a one-way quantum computer algorithm solving Simon’s Problem,” Phys. Rev. Lett. 113, 200501 (2014).
[Crossref]

Böhi, P.

R. Prevedel, P. Walther, F. Tiefenbacher, P. Böhi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
[Crossref] [PubMed]

M. S. Tame, R. Prevedel, M. Paternostro, P. Böhi, M. S. Kim, and A. Zeilinger, “Experimental realization of Deutsch’s algorithm in a one-way quantum computer,” Phys. Rev. Lett. 98, 140501 (2007).
[Crossref]

Briegel, H. J.

H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest, “Measurement-based quantum computation,” Nat. Phys. 5, 19–26 (2009).
[Crossref]

Z. Zhao, Y.-A. Chen, A.-N. Zhang, T. Yang, H. J. Briegel, and J.-W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
[Crossref] [PubMed]

Briegel, H.-J.

M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Van den Nest, and H.-J. Briegel, “Entanglement in Graph States and its Applications,” in Proc. Inter. Sch. Phys. “Enrico Fermi” on “Quantum Computers, Algorithms and Chaos”, G. Casati, D. L. Shepelyansky, P. Zoller, and G. Benenti, eds. IOS Press (2006).

Broadbent, A.

S. Barz, E. Kashefi, A. Broadbent, J. F. Fitzsimons, A. Zeilinger, and P. Walther, “Demonstration of blind quantum computing,” Science 335, 303–308 (2012).
[Crossref] [PubMed]

Brodutch, A.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
[Crossref]

Broome, M. A.

M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
[Crossref]

Browne, D. E.

H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest, “Measurement-based quantum computation,” Nat. Phys. 5, 19–26 (2009).
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Brukner, C.

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Figures (4)

Fig. 1
Fig. 1

The non-local conversion gate using linear optics. The gate takes two photons as inputs, one in each input mode, and performs a non-local operation when the photons exit from different output ports. PBS - polarizing beam splitter, and HWP - half-wave plate.

Fig. 2
Fig. 2

Experimental setup for the charaterization of the non-local conversion gate. QWP - quarter-wave plate, HWP - half-wave plate, PBS - polarizing beam splitter, GP - glass plate, DB - detection block, and APD - avalanche photodiode. The dotted boxes represent preparation stages for encoding different inputs. The dashed box represents the analysis stages (DB) for characterizing the output states of the gate.

Fig. 3
Fig. 3

Reconstructed process matrices χ of the conversion gate using the Jamiolkowski-Choi representation. The 16 × 16 matrices are written in the polarization basis of the input and output Hilbert spaces ({|0〉, |1〉} ↔ {|H〉, |V〉}) and correspond to the gate operations given in Table 1. They are arranged in columns: (a) Cluster state, (b) GHZ state, (c) Dicke state, and (d) two Bell states. The theoretical process matrix χth is depicted in the top row of each column followed by the real and imaginary part of the reconstructed process matrix in the middle and bottom row, respectively. Note that the theoretical process matrix has only real values.

Fig. 4
Fig. 4

Density matrix of the linear cluster state. (a) Ideal theoretical matrix ρth = |C4〉 〈C4|, (b) the real part of the experimental matrix ρ, (c) the imaginary part of the experimental matrix ρ. Note that the ideal theoretical density matrix has only real values.

Tables (3)

Tables Icon

Table 1 Non-local conversion gate angle settings, its success probabilities ps, and the maximal theoretical success probabilities ps,max for converting a linear cluster state to GHZ, Dicke and two Bell states. Each kind of conversion can be realized by several settings. The angle θ± is found from the relation sin ( 2 θ ± ) = [ ( 5 ± 5 ) / 10 ] 1 / 2.

Tables Icon

Table 2 Purity and process fidelity of the non-local conversion gate, including one standard deviation related to the last significant digit (represented by the number in brackets). The values were obtained by numerical simulation based on the obtained experimental results.

Tables Icon

Table 3 Numerically simulated fidelity of output states converted from a realistic |C4〉 〈C4| state.

Equations (5)

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G ( θ 1 , θ 2 ) = ( α 1 β 1 ) | H H out H H | in + ( α 2 β 2 ) | V V out V V | in + μ 1 | H V out H V | in μ 2 | H V out V H | in + μ 1 | V H out V H | in μ 2 | V H out H V | in ,
| C 4 = 1 2 ( | H H H H + | H H V V + | V V H H | V V V V )
G ( θ 1 , θ 2 ) | C 4 = 1 2 [ ( α 1 β 1 ) | H H H H ( α 2 β 2 ) | V V V V + μ 1 | H H V V + μ 1 | V V H H μ 2 | H V H V μ 2 | V H V H ] .
ρ out = Tr in [ ( ρ in T 𝕀 out ) χ ] Tr [ ( ρ in T 𝕀 out ) χ ] ,
F χ = Tr [ χ χ t h ] Tr [ χ t h ] Tr [ χ ] ,