Limitations of teleporting a qubit via a two-mode squeezed state
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摘要
Recently, a teleportation scheme using a two-mode squeezed state to teleport a photonic qubit, so called a"hybrid" approach, has been suggested and experimentally demonstrated as a candidate to overcome the limitations of all-optical quantum information processing. We find, however, that there exists the upper bound of fidelity when teleporting a photonic qubit via a two-mode squeezed channel under a lossy environment.The increase of photon loss decreases this bound, and teleportation better than this limit is impossible even when the squeezing degree of the teleportation channel becomes infinity. Our result indicates that the hybrid scheme can be valid for fault-tolerant quantum computing only when the photon loss rate can be suppressed under a certain limit.
Recently, a teleportation scheme using a two-mode squeezed state to teleport a photonic qubit, so called a"hybrid" approach, has been suggested and experimentally demonstrated as a candidate to overcome the limitations of all-optical quantum information processing. We find, however, that there exists the upper bound of fidelity when teleporting a photonic qubit via a two-mode squeezed channel under a lossy environment.The increase of photon loss decreases this bound, and teleportation better than this limit is impossible even when the squeezing degree of the teleportation channel becomes infinity. Our result indicates that the hybrid scheme can be valid for fault-tolerant quantum computing only when the photon loss rate can be suppressed under a certain limit.
Recently, a teleportation scheme using a two-mode squeezed state to teleport a photonic qubit, so called a"hybrid" approach, has been suggested and experimentally demonstrated as a candidate to overcome the limitations of all-optical quantum information processing. We find, however, that there exists the upper bound of fidelity when teleporting a photonic qubit via a two-mode squeezed channel under a lossy environment.The increase of photon loss decreases this bound, and teleportation better than this limit is impossible even when the squeezing degree of the teleportation channel becomes infinity. Our result indicates that the hybrid scheme can be valid for fault-tolerant quantum computing only when the photon loss rate can be suppressed under a certain limit.
引文
1.C.H.Bennett,G.Brassard,C.Crépeau,R.Jozsa,A.Peres,and W.K.Wootters,“Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,”Phys.Rev.Lett.70,1895-1899(1993).
2.E.Knill,R.Laflamme,and G.J.Milburn,“A scheme for efficient quantum computation with linear optics,”Nature 409,46-52(2001).
3.D.Gottesman and I.L.Chuang,“Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,”Nature 402,390-393(1999).
4.D.Bouwmeester,J.-W.Pan,K.Mattle,M.Eibl,H.Weinfurter,and A.Zeilinger,“Experimental quantum teleportation,”Nature 390,575-579(1997).
5.N.Lütkenhaus,J.Calsamiglia,and K.-A.Suominen,“Bell measurements for teleportation,”Phys.Rev.A 59,3295-3300(1999).
6.T.C.Ralph and G.J.Pryde,“Optical quantum computation,”in Progress in Optics(Elsevier,2010),Vol.54,pp.209-269.
7.Y.Li,P.C.Humphreys,G.J.Mendoza,and S.C.Benjamin,“Resource costs for fault-tolerant linear optical quantum computing,”Phys.Rev.X 5,041007(2015).
8.W.P.Grice,“Arbitrarily complete Bell-state measurement using only linear optical elements,”Phys.Rev.A 84,042331(2011).
9.F.Ewert and P.van Loock,“3/4-efficient bell measurement with passive linear optics and unentangled ancillae,”Phys.Rev.Lett.113,140403(2014).
10.S.-W.Lee,K.Park,T.C.Ralph,and H.Jeong,“Nearly deterministic Bell measurement for multiphoton qubits and its application to quantum information processing,”Phys.Rev.Lett.114,113603(2015).
11.H.A.Zaidi and P.van Loock,“Beating the one-half limit of ancilla-free linear optics Bell measurements,”Phys.Rev.Lett.110,260501(2013).
12.S.L.Braunstein and H.J.Kimble,“Teleportation of continuous quantum variables,”Phys.Rev.Lett.80,869-872(1998).
13.L.Vaidman,“Teleportation of quantum states,”Phys.Rev.A 49,1473-1476(1994).
14.S.Lloyd and S.Braunstein,“Quantum computation over continuous variables,”Phys.Rev.Lett.82,1784-1787(1999).
15.N.C.Menicucci,P.van Loock,M.Gu,C.Weedbrook,T.C.Ralph,and M.A.Nielsen,“Universal quantum computation with continuousvariable cluster states,”Phys.Rev.Lett.97,110501(2006).
16.A.Furusawa,J.L.S?rensen,S.L.Braunstein,C.A.Fuchs,H.J.Kimble,and E.S.Polzik,“Unconditional quantum teleportation,”Science 282,706-709(1998).
17.R.Polkinghorne and T.Ralph,“Continuous variable entanglement swapping,”Phys.Rev.Lett.83,2095-2099(1999).
18.T.Ralph,“Interferometric tests of teleportation,”Phys.Rev.A 65,012319(2001).
19.S.Takeda,T.Mizuta,M.Fuwa,P.van Loock,and A.Furusawa,“Deterministic quantum teleportation of photonic quantum bits by a hybrid technique,”Nature 500,315-318(2013).
20.N.C.Menicucci,“Fault-tolerant measurement-based quantum computing with continuous-variable cluster states,”Phys.Rev.Lett.112,120504(2014).
21.H.Jeong,J.Lee,and M.S.Kim,“Dynamics of nonlocality for a twomode squeezed state in a thermal environment,”Phys.Rev.A 61,052101(2000).
22.C.-W.Lee and H.Jeong,“Quantification of macroscopic quantum superpositions within phase space,”Phys.Rev.Lett.106,220401(2011).
23.S.Takeda,T.Mizuta,M.Fuwa,H.Yonezawa,P.van Loock,and A.Furusawa,“Gain tuning for continuous-variable quantum teleportation of discrete-variable states,”Phys.Rev.A 88,042327(2013).
24.H.F.Hofmann,T.Ide,T.Kobayashi,and A.Furusawa,“Fidelity and information in the quantum teleportation of continuous variables,”Phys.Rev.A 62,062304(2000).
25.A.Einstein,B.Podolsky,and N.Rosen,“Can quantum-mechanical description of physical reality be considered complete?”Phys.Rev.47,777-780(1935).
26.T.Ide,H.F.Hofmann,A.Furusawa,and T.Kobayashi,“Gain tuning and fidelity in continuous-variable quantum teleportation,”Phys.Rev.A 65,062303(2002).
27.K.?yczkowski,P.Horodecki,A.Sanpera,and M.Lewenstein,“Volume of the set of separable states,”Phys.Rev.A 58,883-892(1998).
28.G.Adesso,A.Serafini,and F.Illuminati,“Extremal entanglement and mixedness in continuous variable systems,”Phys.Rev.A 70,022318(2004).
29.G.Vidal and R.F.Werner,“Computable measure of entanglement,”Phys.Rev.A 65,032314(2002).
30.K.Audenaert,M.Plenio,and J.Eisert,“Entanglement cost under positive-partial-transpose-preserving operations,”Phys.Rev.Lett.90,027901(2003).
31.C.M.Dawson,H.L.Haselgrove,and M.A.Nielsen,“Noise thresholds for optical quantum computers,”Phys.Rev.Lett.96,020501(2006).
32.A.Lund,T.Ralph,and H.Haselgrove,“Fault-tolerant linear optical quantum computing with small-amplitude coherent states,”Phys.Rev.Lett.100,030503(2008).
33.D.A.Herrera-Marti,A.G.Fowler,D.Jennings,and T.Rudolph,“Photonic implementation for the topological cluster-state quantum computer,”Phys.Rev.A 82,032332(2010).
34.S.-W.Lee and H.Jeong,“Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits,”Phys.Rev.A 87,022326(2013).
35.A.Sch?nbeck,F.Thies,and R.Schnabel,“13 dB squeezed vacuum states at 1550 nm from 12 mW external pump power at 775 nm,”Opt.Lett.43,110-113(2018).
2.E.Knill,R.Laflamme,and G.J.Milburn,“A scheme for efficient quantum computation with linear optics,”Nature 409,46-52(2001).
3.D.Gottesman and I.L.Chuang,“Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,”Nature 402,390-393(1999).
4.D.Bouwmeester,J.-W.Pan,K.Mattle,M.Eibl,H.Weinfurter,and A.Zeilinger,“Experimental quantum teleportation,”Nature 390,575-579(1997).
5.N.Lütkenhaus,J.Calsamiglia,and K.-A.Suominen,“Bell measurements for teleportation,”Phys.Rev.A 59,3295-3300(1999).
6.T.C.Ralph and G.J.Pryde,“Optical quantum computation,”in Progress in Optics(Elsevier,2010),Vol.54,pp.209-269.
7.Y.Li,P.C.Humphreys,G.J.Mendoza,and S.C.Benjamin,“Resource costs for fault-tolerant linear optical quantum computing,”Phys.Rev.X 5,041007(2015).
8.W.P.Grice,“Arbitrarily complete Bell-state measurement using only linear optical elements,”Phys.Rev.A 84,042331(2011).
9.F.Ewert and P.van Loock,“3/4-efficient bell measurement with passive linear optics and unentangled ancillae,”Phys.Rev.Lett.113,140403(2014).
10.S.-W.Lee,K.Park,T.C.Ralph,and H.Jeong,“Nearly deterministic Bell measurement for multiphoton qubits and its application to quantum information processing,”Phys.Rev.Lett.114,113603(2015).
11.H.A.Zaidi and P.van Loock,“Beating the one-half limit of ancilla-free linear optics Bell measurements,”Phys.Rev.Lett.110,260501(2013).
12.S.L.Braunstein and H.J.Kimble,“Teleportation of continuous quantum variables,”Phys.Rev.Lett.80,869-872(1998).
13.L.Vaidman,“Teleportation of quantum states,”Phys.Rev.A 49,1473-1476(1994).
14.S.Lloyd and S.Braunstein,“Quantum computation over continuous variables,”Phys.Rev.Lett.82,1784-1787(1999).
15.N.C.Menicucci,P.van Loock,M.Gu,C.Weedbrook,T.C.Ralph,and M.A.Nielsen,“Universal quantum computation with continuousvariable cluster states,”Phys.Rev.Lett.97,110501(2006).
16.A.Furusawa,J.L.S?rensen,S.L.Braunstein,C.A.Fuchs,H.J.Kimble,and E.S.Polzik,“Unconditional quantum teleportation,”Science 282,706-709(1998).
17.R.Polkinghorne and T.Ralph,“Continuous variable entanglement swapping,”Phys.Rev.Lett.83,2095-2099(1999).
18.T.Ralph,“Interferometric tests of teleportation,”Phys.Rev.A 65,012319(2001).
19.S.Takeda,T.Mizuta,M.Fuwa,P.van Loock,and A.Furusawa,“Deterministic quantum teleportation of photonic quantum bits by a hybrid technique,”Nature 500,315-318(2013).
20.N.C.Menicucci,“Fault-tolerant measurement-based quantum computing with continuous-variable cluster states,”Phys.Rev.Lett.112,120504(2014).
21.H.Jeong,J.Lee,and M.S.Kim,“Dynamics of nonlocality for a twomode squeezed state in a thermal environment,”Phys.Rev.A 61,052101(2000).
22.C.-W.Lee and H.Jeong,“Quantification of macroscopic quantum superpositions within phase space,”Phys.Rev.Lett.106,220401(2011).
23.S.Takeda,T.Mizuta,M.Fuwa,H.Yonezawa,P.van Loock,and A.Furusawa,“Gain tuning for continuous-variable quantum teleportation of discrete-variable states,”Phys.Rev.A 88,042327(2013).
24.H.F.Hofmann,T.Ide,T.Kobayashi,and A.Furusawa,“Fidelity and information in the quantum teleportation of continuous variables,”Phys.Rev.A 62,062304(2000).
25.A.Einstein,B.Podolsky,and N.Rosen,“Can quantum-mechanical description of physical reality be considered complete?”Phys.Rev.47,777-780(1935).
26.T.Ide,H.F.Hofmann,A.Furusawa,and T.Kobayashi,“Gain tuning and fidelity in continuous-variable quantum teleportation,”Phys.Rev.A 65,062303(2002).
27.K.?yczkowski,P.Horodecki,A.Sanpera,and M.Lewenstein,“Volume of the set of separable states,”Phys.Rev.A 58,883-892(1998).
28.G.Adesso,A.Serafini,and F.Illuminati,“Extremal entanglement and mixedness in continuous variable systems,”Phys.Rev.A 70,022318(2004).
29.G.Vidal and R.F.Werner,“Computable measure of entanglement,”Phys.Rev.A 65,032314(2002).
30.K.Audenaert,M.Plenio,and J.Eisert,“Entanglement cost under positive-partial-transpose-preserving operations,”Phys.Rev.Lett.90,027901(2003).
31.C.M.Dawson,H.L.Haselgrove,and M.A.Nielsen,“Noise thresholds for optical quantum computers,”Phys.Rev.Lett.96,020501(2006).
32.A.Lund,T.Ralph,and H.Haselgrove,“Fault-tolerant linear optical quantum computing with small-amplitude coherent states,”Phys.Rev.Lett.100,030503(2008).
33.D.A.Herrera-Marti,A.G.Fowler,D.Jennings,and T.Rudolph,“Photonic implementation for the topological cluster-state quantum computer,”Phys.Rev.A 82,032332(2010).
34.S.-W.Lee and H.Jeong,“Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits,”Phys.Rev.A 87,022326(2013).
35.A.Sch?nbeck,F.Thies,and R.Schnabel,“13 dB squeezed vacuum states at 1550 nm from 12 mW external pump power at 775 nm,”Opt.Lett.43,110-113(2018).