SUPPLEMENTARY INFORMATION

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1 DOI: /NPHOTON Suppementary Information: Quantum teeportation using a ight emitting diode J. Nisson 1, R. M. Stevenson 1*, K. H. A. Chan 1,, J. Skiba-Szymanska 1, M. Luamarini 1, M. B. Ward 1, A. J. Bennett 1, C. L. Sater 1,, I. Farrer, D. A. Rithie and A. J. Shieds 1. 1 Toshiba Researh Europe Limited, 08 Siene Park, Miton Road, Cambridge CB4 0GZ, United Kingdom. Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom. *Correspondene emai address: mark.stevenson@r.toshiba.o.uk. 1. Teeportation of ogia states Figure S1a shows measured g (3) orresponding to a H poarized ontro photon, and H poarized detetion by Bob s APD P. Eah of the three features passing through the origin an be attributed to orreations between a speifi pair of simutaneousy deteted photons. The vertiay extending dip aong τ 1 =0 orresponds to oinident detetion of photons by SSPD H and SSPD V, and represents suppression of the probabiity of photons traveing the same arm of the Mah Zehnder interferometer due to the anti-bunhed nature of the photon soure. The horizonta feature aong τ =0 orresponds to oinident photon detetion by SSPD H and APD P, and is dependent on the poarization orreation between the entanged ania and target photons. Simiary, the diagona feature at τ 1 =τ orresponds to oinident photon detetion by SSPD V and APD P, and again depends on the poarization orreation between ania and target photons, exept the deteted ania poarization is orthogona. In figure S1a, the horizontay extending peak demonstrates orreated detetion of H a ania with H t target photons, and the diagonay NATURE PHOTONICS Mamian Pubishers Limited. A rights reserved.

2 DOI: /NPHOTON extending dip demonstrates suppressed detetion probabiity of a V a ania with H t target photons, as expeted from the idea entanged input state H H V V. a t a t Figure S1b shows g (3) measurements with detetion of a V poarized photon by APD Q, measured at the same time as those in figure S1a. This time, orreation between V a and V t are indiated by the diagona feature, and suppressed orreation between H a and V t by the horizonta feature, as expeted. For quantum teeportation, the important region of the g (3) pots is the intersetion of the features at τ 1 ~τ ~0. Here, the diagona feature dominates, and the horizonta feature is suppressed. This indiates teeportation of an H ontro state onto a V t target state, as expeted. Figures S1 and S1d show auated g (3) orreations orresponding to the experimenta resuts shown in S1a and S1b respetivey. The auations are based on jitter free two-photon statistis empiriay determined from independent XX-XX and X-XX g () measurements, as we as additiona broadening orresponding to the detetor resoution of our experiments. Exeent quaitative and quantitative agreement an be observed, as auations eary reprodue the three main features passing through the origin, and the dominant behaviour at the origin.. Additiona observed orreations In figure, the extra horizonta feature aong.5ns and the extra diagona feature aong.5ns are both due to orreation between the ontro photon and the X photon that Bob 1 reeives before Aie ompetes her joint measurement. These eary X photons are we separated from the ones that atuay arry the teeported state, and their poarizations depend on Y, the state of the ontro photons before the input state preparation proess, whih has no partiuar NATURE PHOTONICS Mamian Pubishers Limited. A rights reserved.

3 DOI: /NPHOTON expeted vaue due to the unknown poarisation evoution within the fibre system. In modeing the data for figure, Y is hosen to reprodue the extra features, whih, as one woud expet, (3) have no notieabe effet on the g near the origin. 1, 3. Physia onstraint on a assia teeporter In our experiment, Aie prepares 6 different qubits, equay spaed in the Poinaré sphere, desribed by the foowing statistia mixture: 6 in (1 / 6) n1 n n, where the n 's are defined as: 1 H, V, 3,4 H V /, H iv 5,6 /. The set of states reevant for a omparison with a assia teeportation protoo is determined by the ast optimization performed in the experiment. As the teeportation optis are in the same onfiguration for a 6 input states, the ensembe to be onsidered oinides with the one prepared by Aie. Given that, a assia teeportation protoo is defined by the foowing proedure [11]. Aie sends out one of the above states, n. A user, aed Charie, measures the state as best as he an. This means that he uses rank-1 POVM operators for his measurement, desribed by the foowing non-orthogona partition of the unity: L I 1. The states are not neessariy orthonorma and ompose an overompete set. When Charie reeives n, he ompares it to, thus obtaining a resut with probabiity P n. With this information, he prepares the pure state, whih he thinks is the osest to the one sent out by Aie, and sends it over to Bob. Hene, the state prepared by Charie is desribed by the mixture NATURE PHOTONICS Mamian Pubishers Limited. A rights reserved.

4 DOI: /NPHOTON L out P 1. The distane between Aie's initia state and the fina state reeived by Bob is then quantified by the fideity of the assia teeportation: F L 1 1 n n n. In the foowing, we provide an upper bound to F, i.e. we ook for the maximum fideity ahievabe by a assia teeporter deaing with the 6 states of our experiment. Let's onsider the normaized state /, with, and define the quantity T 6 n1 n n. Then the assia fideity an be rewritten as 1 L F 1 T. 6 An upper bound to the assia fideity is obtained by simpy maximizing the quantity T. To do so, we hoose a pair of generi states in the Poinaré sphere to represent the states and i i of T : os( / ) H e sin( / ) V, os( / ) H e sin( / ) V. It is straightforward to auate the orresponding upper bound to T : T 3 os os sin sin os( ) 3 os os sin sin 3 os max T. We have obtained that the maximum of T, aed T max, is onstant and does not depend on the anges at a. This is due to the high symmetry of the initia states onfiguration. From this resut, we an easiy obtain the upper bound to the assia fideity:, where we have used that the L max max L max (1/ 6) (1/ 6) ( / 6) / F T T T. L L Hibert spae's dimension of a photon is : 1 tr 1 tr I This proves that the best assia teeportation protoo an never overome an average fideity of /3 when the 6 states of our experiment are onsidered. As a onsequene, any experiment surpassing that imit, inuding ours, neessariy impies an underying quantum proess. 4 NATURE PHOTONICS Mamian Pubishers Limited. A rights reserved.

5 DOI: /NPHOTON Quantum dot harateristis In order for XX and X photons emitted in the same radiative asade to be entanged in poarisation the fine struture spitting (FSS) of the intermediate X state of the quantum dot must be ose to zero. The FSS for the dot used here was haraterized by inear poarisationdependent eetrouminesene spetrosopy 9 and found to be.0±0. µev. The X and XX emission was verified to be unpoarised within error. 5. Time deays The time of a photon detetion events are reorded in reation to the detetion of one H poarised photon by Aie (SSPD H ), thus giving our three-fod intensity orreations as a funtion of two time differenes; g (3) (τ 1, τ ) with τ 1 signifying the time differene between Aie s detetors SSPD H -SSPD V and τ the differene between SSPD H and APD P or APD Q. The absoute time sae for time differene τ is hosen so that τ =0 orresponds to maximum fideity, and thus refets the time differene between generation of a XX a and X t entanged photon pair. In pratie, detetion by Bob ours ~55 ns after detetion by Aie, set arbitrariy by an additiona fibre deay. The hosen definition of τ =0 obviousy has no effet on the measured fideity. NATURE PHOTONICS Mamian Pubishers Limited. A rights reserved.

6 DOI: /NPHOTON 6. Further error anaysis The detetor poarizations deviate sighty from their idea settings due to weaky poarizing eements in the fibre system, whih sighty eevates the measured fideity for input A, and sighty depresses fideity for input D. This agrees with our simuations that show that the effet works in opposite diretion for orthogona states, and anes out upon averaging between the two. The degree of poarization in our system is measured to be 8.4%, and its orientation is found to be simiar between experiments. We estimate that upon averaging teeportation fideity over a six input states, the deviation from the vaue attainabe with perfet detetor aignment is no more than 1%, whih we inude in our quoted errors. 6 NATURE PHOTONICS Mamian Pubishers Limited. A rights reserved.

7 DOI: /NPHOTON Figure S1 Third order intensity orreations g (3) for H poarized ontro photon. Experimentay deteted target photon poarisation of H and V is shown in a and b respetivey. and d represent auated behaviour orresponding to a and b respetivey. Stronger g (3) at τ 1 =τ =0 for deteted V poarized target photons (in b) ompared to H (in a) indiates teeportation of the H ontro state onto the V target state, as expeted. NATURE PHOTONICS Mamian Pubishers Limited. A rights reserved.