REPORTS process tomography of the teleportation protocol. Quantum Teleportation Between The measured average teleportation fidelity of 90% T 2% [90(2)%] over a set of mutually un- Distant Matter Qubits biased basis states, which is well above the 2/3 fidelity threshold that could be achieved classi- cally, unequivocally demonstrates the quantum S. Olmschenk,1* D. N. Matsukevich,1 P. Maunz,1 D. Hayes,1 L.-M. Duan,2 C. Monroe1 nature of the process (14, 15). Our teleportation protocol represents the implementation of a Quantum teleportation is the faithful transfer of quantum states between systems, relying on probabilistic measurement-based gate that could the prior establishment of entanglement and using only classical communication during the be used to generate entangled states for scalable transmission. We report teleportation of quantum information between atomic quantum memories quantum computation (16, 17). + separated by about 1 meter. A quantum bit stored in a single trapped ytterbium ion (Yb )is A schematic of the experimental setup (Fig. 1) + teleported to a second Yb atom with an average fidelity of 90% over a replete set of states. shows a single Yb+ atom confined and Doppler The teleportation protocol is based on the heralded entanglement of the atoms through laser–cooled in each of two nearly identical radio- interference and detection of photons emitted from each atom and guided through optical fibers. frequency (rf) Paul traps, located in independent This scheme may be used for scalable quantum computation and quantum communication. vacuum chambers (18–21). An ion will typically remain in the trap for several weeks. The qubit defining feature of quantum physics is portation. However, a quantum memory is re- states in each atom are chosen to be the first- the inherent uncertainty of physical prop- quired at both transmitting and receiving sites order magnetic field–insensitive hyperfine “clock” 2S F m 〉 Aerties, despite the fact that we observe in order to scale this protocol to quantum net- states of the 1/2 level, j ¼ 0, F ¼ 0 and only definite states after a measurement. The works and propagate quantum information over jF ¼ 1, mF ¼ 0〉, which are separated by 12.6 conventional interpretation is that the measure- multiple nodes (10). Deterministic teleportation GHz and defined to be j0〉 and j1〉, respectively. ment process itself can irreversibly influence the between quantum memories has been demon- In this notation, F is the total angular momen- quantum system under study. The field of quan- strated with trapped atomic ions in close proximity tum of the atom, and mF is its projection along a tum information science makes use of this notion to one another, relying on the mutual Coulomb quantization axis defined by an external mag- and frames quantum mechanics in terms of the interaction (11–13). In contrast to the optical sys- netic field B. The qubit exhibits coherence times storage, processing, and communication of in- tems, these implementations feature long-lived observed to be greater than 2.5 s and thus serves formation. In particular, the back-action of mea- coherences stored in good quantum memories as an excellent quantum memory (20). surement underlies the quantum “no cloning” but lack the ability to easily transmit quantum For the teleportation protocol (Fig. 2A), the theorem, which states that it is impossible to information over long distances. states of the atomic qubits are initialized with a generate identical copies of an unknown quan- We present the implementation of a heralded 1-ms pulse of 369.5-nm light resonant with the 1 2S F 〉↔2P F 〉 tum state ( ). Nevertheless, a quantum state can teleportation protocol where the advantages from 1=2j ¼ 1 1=2 j ¼ 1 transition that op- still be transferred from one system to another both optical systems and quantum memories are tically pumps the ions to j0〉 with probability by the process of quantum teleportation (2). A combined to teleport quantum states between greater than 99% (20). We can then prepare any quantum state initially stored in system A can be two trapped ytterbium ion (Yb+) quantum bits superposition of j0〉 and j1〉 by applying a teleported to system B by using the resource of (qubits) over a distance of about 1 m. We fully resonant microwave pulse with controlled phase quantum entanglement or the quantum correla- characterized the system by performing tomog- andduration(0to16ms) directly to one of the tion between systems that do not have well- raphy on the teleported states, enabling complete trap electrodes. The quantum state to be tele- defined individual properties. Relaying the result of a destructive measurement of system A al- lows the original quantum state to be recovered at system B without ever having traversed the space between the systems. The ability to teleport quantum information is an essential ingredient for the long-distance quantum communication af- forded by quantum repeaters (3)andmaybea vital component to achieve the exponential pro- cessing speed-up promised by quantum compu- tation (4). The experimental implementation of telepor- tation has been accomplished in optical sys- tems by using down-converted photons (5, 6)and squeezed light with continuous variable entangle- ment (7). Teleportation has also been accom- plished between photons and a single atomic ensemble (8, 9). Because photons are able to carry quantum information and establish entan- glement over long distances, these experiments demonstrated the nonlocal behavior of tele- + 1 Fig. 1. The experimental setup. Two Yb ions are trapped in independent vacuum chambers. An ex- JointQuantumInstitute(JQI)andDepartmentofPhysics, B University of Maryland, College Park, MD 20742, USA. 2FOCUS ternally applied magnetic field determines a quantization axis for defining the polarization of Center and Department of Physics, University of Michigan, Ann photons emitted by each atom. Spontaneously emitted photons are collected with an objective lens, Arbor, MI 48109, USA. coupled into a single-mode fiber, and directed to interfere on a beamsplitter (BS). Polarizing beamsplitters *To whom correspondence should be addressed. E-mail: (PBSs) filter out photons resulting from s decays in the atoms. The remaining p-polarized photons are [email protected] detected by single-photon counting PMTs. 486 23 JANUARY 2009 VOL 323 SCIENCE www.sciencemag.org REPORTS ported is written to ion A by using this micro- a measured mode overlap greater than 98%. Be- light is off-resonance and almost no photons are wave pulse, which prepares ion A in the state cause of the quantum interference of the two pho- scattered. By detecting the fluorescence of the jY(t1)〉A ¼ aj0〉A þ bj1〉A. A separate micro- tons, a simultaneous detection at both output atom with a single-photon counting photomul- wave pulse prepares ion B in the definite state ports of the beamsplitter occurs only if the pho- tiplier tube (PMT), we discriminate between j0〉 − jY(t1)〉B ¼j0〉B þj1〉B, where for simplicity tons are in the state jY 〉photons ¼jnblue 〉Ajnred 〉B − and j1〉 withanerrorofabout2%(20). we neglect normalization factors and assume jnred 〉Ajnblue 〉B (24–26), which projects the ions Measuring ion A projects ion B into one of ideal state evolution throughout our discussion. into the entangled state (27): the two states: After this state preparation, each ion is excited − 2P 〈Y (t )j (jY(t )〉A⊗jY(t )〉B) ¼ to the 1/2 level with near-unit probability by 3 photons 3 3 Y t 〉 a 〉 b 〉 〉 an ultrafast laser pulse (≈1 ps) having a linear j ( 5) B ¼ j1 B þ j0 B (if measured j0 A) jY(t )〉 ¼ aj0〉Aj1〉B − bj1〉Aj0〉B (2) polarization aligned parallel to the quantization 3 ions Y(t )〉B a 1〉B − b 0〉B (if measured 1〉A) axis (p-polarized) and a central wavelength of A coincident detection of two photons is there- j 5 ¼ j j j 369.5 nm. Due to the polarization of the pulse and fore the heralding event that announces the suc- (4) atomic selection rules, the broadband pulse coher- cess of the ion-ion entangling gate operation 〉 2P F m 〉 1s% A s% As% B − s% As% B s% i A ently transfers j0 to 1=2j ¼ 1, F ¼ 0 and 2 3 ( 0 0 3 3 ), where 0 is the identity and The result of the measurement on ion is 〉 2P F m 〉 22 s% i z i j1 to 1=2j ¼ 0, F ¼ 0 (Fig. 2B) ( ). Be- 3 the -Pauli operator acting on the th qubit relayed through a classical communication chan- cause the duration of this pulse is much shorter (16). In the current setup, this entangling gate only nel and used to determine the necessary phase t ≈ 2P P ≈ : −8 p than the 8 ns natural lifetime of the 1=2 succeeds with probability gate 2 2 Â 10 ,lim- of a conditional microwave pulse applied to level, each ion spontaneously emits a single pho- ited by the efficiency of collecting and detecting ion B to recover the state initially written to ion 2S 18 A 〉 R p ton while returning to the 1=2 ground state ( ). both spontaneously emitted photons. Therefore, ; measuring j0 A requires the rotation x( ), The emitted photons at 369.5 nm can each be the previous steps (state preparation and pulsed whereas j1〉A demands Ry(p). Afterward, the state collected along a direction perpendicular to the excitation) are repeated at a rate of 40 to 75 kHz, of ion B is ideally jY(t6)〉B ¼ aj0〉B þ bj1〉B, quantization axis by objective lenses of numerical including intermittent cooling, until the gate opera- which completes the teleportation of the quan- aperture NA = 0.23 and coupled into single-mode tion is successful (every 12 min, on average).