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Quantum teleportation between light and matter
Jacob Sherson, Hanna Krauter, Rasmus K. Olsson, Brian Julsgaard, Klemens Hammerer, Ignacio Cirac, Eugene S. Polzik
TL;DR
Teleportation between light and matter, representing flying and stationary media, remained to be demonstrated, although teleportation is important for distributed quantum networks. The experiment teleports a quantum state between light and matter, representing flying and stationary media. Fidelities were 0.58±0.02 for n=20 and 0.56±0.03 for n=200; experimental fidelity is higher than the classical benchmark for n≥2.
Problem
Teleportation between light and matter, representing flying and stationary media, remained to be demonstrated, although teleportation is important for distributed quantum networks.
Source: p. 1Method
The experiment teleports a quantum state between light and matter, representing flying and stationary media.
Source: p. 1Results
Fidelities were 0.58±0.02 for n=20 and 0.56±0.03 for n=200; experimental fidelity is higher than the classical benchmark for n≥2.
Source: pp. 7, 18Takeaways & Limitations
The demonstrated transfer addresses teleportation across flying and stationary media, an important ingredient in distributed quantum networks.
Source: p. 1Successful teleportation is limited at large n by small classical-gain fluctuations, which cause uncontrolled state displacements and reduce fidelity.
Source: p. 7
Abstract
from arXiv · showhide
Quantum teleportation is an important ingredient in distributed quantum networks, and can also serve as an elementary operation in quantum computers. Teleportation was first demonstrated as a transfer of a quantum state of light onto another light beam; later developments used optical relays and demonstrated entanglement swapping for continuous variables. The teleportation of a quantum state between two single material particles (trapped ions) has now also been achieved. Here we demonstrate teleportation between objects of a different nature - light and matter, which respectively represent 'flying' and 'stationary' media. A quantum state encoded in a light pulse is teleported onto a macroscopic object (an atomic ensemble containing 10^12 caesium atoms). Deterministic teleportation is achieved for sets of coherent states with mean photon number (n) up to a few hundred. The fidelities are 0.58+-0.02 for n=20 and 0.60+-0.02 for n=5 - higher than any classical state transfer can possibly achieve. Besides being of fundamental interest, teleportation using a macroscopic atomic ensemble is relevant for the practical implementation of a quantum repeater. An important factor for the implementation of quantum networks is the teleportation distance between transmitter and receiver; this is 0.5 metres in the present experiment. As our experiment uses propagating light to achieve the entanglement of light and atoms required for teleportation, the present approach should be scalable to longer distances.
Calibration and measurement techniques.
The section describes how light measurements and noise references calibrate the teleportation measurements, including an atomic projection-noise calibration using oppositely oriented ensembles.
Calibration and measurement techniques.
- Balanced homodyne detectors measure light Stokes operators: the first pulse provides the generalized Bell measurement, while a verifying pulse enables atomic-state tomography.Lock-in amplifiers process photocurrents to extract the relevant modulation components.Source: Calibration and measurement techniques · p. 8
- Linear photocurrent-variance scaling with strong-pulse optical power verifies shot-noise-limited light measurements, which are normalized to the measured vacuum-noise level [25].The vacuum reference is measured using the x-polarization mode.Source: Calibration and measurement techniques · p. 9
- Oppositely oriented atomic ensembles cancel the interaction terms proportional to κ, enabling the transmitted light to measure the collective spin variables of the two-cell sample.A second atomic cell is inserted in the beam, and the corresponding relation for the other light Stokes component substitutes collective X for collective P.Source: Calibration and measurement techniques · p. 9
- A linear variance-versus-atom-number trend and spin polarization above 0.99 establish that the measured atomic noise is projection noise; the inferred κ agrees with theory.The κ values for different atom numbers are calculated from the graph.Source: Calibration and measurement techniques · pp. 9–10
Decoherence and losses.
Atomic-state decoherence and light-reflection losses are the main imperfections. The model predicts a fidelity above the observed value, while accounting for light loss through the calibrated κ parameter requires no additional correction.
Decoherence and losses.
- Atomic-state decoherence and light-reflection losses are identified as the main sources of imperfection.Source: Decoherence and losses · p. 10
- The model predicts a fidelity above the observed value, with the difference attributed to imperfections not included in the model.The prediction is described as comparable to the experimental results.Source: Decoherence and losses · p. 10
- Light loss (ε = 0.09) modifies κ, but the modified parameter is measured in the two-cell calibration, so no extra correction is needed.Detector electronic noise is treated as an additional vacuum contribution to the input state.Source: Decoherence and losses · p. 10
Standard deviation of the teleportation fidelity.
The section estimates the teleportation-fidelity standard deviation from noise and calibration uncertainties, reporting an overall value of approximately 0.026–0.03.
Standard deviation of the teleportation fidelity.
- For 20 ≤ n, the calculation includes δPN = 0.01 for projection noise, δSN = 0.017 for shot-noise uncertainty, δel = 0.001 for electronics noise, and δβ = 0.003 for atomic-decay uncertainty.Projection noise includes fluctuations and an error due to imperfect optical pumping.Source: Standard deviation of the… · pp. 10–11
- Other included contributions are δSNR = 0.002 for detector-response-ratio fluctuations, δfit = 0.012 for quadratic-fit uncertainty, and δg = 0.008 for gain fluctuations.For n > 20, δfit = 0.016.Source: Standard deviation of the… · p. 11
- For n > 20, the fidelity standard deviation is reported as approximately 0.026, or 0.03.The calculation uses a fit uncertainty δfit = 0.016 for n > 20.Source: Standard deviation of the… · p. 11
Projection noise measurement and determination of the coupling constant κ.
The section calibrates projection noise and the light–atom coupling κ from transmitted-probe fluctuations, with a gain correction for probe-induced spin decay. Supplementary calculations describe higher-fidelity teleportation protocols using additional scattering modes and squeezed light.
Projection noise measurement and determination of the coupling constant κ.
- κ^2 is determined from transmitted-probe variance versus atom number, using an auxiliary-probe Faraday angle and fits to the measured slope.The input-probe variance is normalized to shot noise minus unity; κ^2 at the reconstruction angle is read from the figure.Source: Projection noise measurement and… · p. 20
- Measurements from several runs over weeks show reproducible projection noise, with the probe-noise increase linear in atom number as predicted.The linear dependence is consistent with Var(y_c^out) − Var(y_c^in) ∝ κ^2 N_atoms.Source: Projection noise measurement and… · p. 20
- g=0.42 corrects the unity-gain calibration for probe-induced spin decay during the 1 ms verifying pulse, which reduces the measured spin by a factor of 0.91.The decay constant with probe light is β=0.09 s^-1.Source: Projection noise measurement and… · p. 21
Supplementary Notes
- The theoretical fidelity limit is 0.74 at κ=1 without losses or decoherence; including 10% light losses and atomic decay yields a predicted fidelity of 0.72 at the same κ.In principle, arbitrarily high fidelities can be achieved for unit gain (g=1) and small variances.Source: Projection noise measurement and… · p. 22
- F=0.80 is obtained in an improved protocol using the first three scattering modes, whose mode sums add half a unit of vacuum noise to each spin component.Optimization sets g_n=0 for n>3.Source: Projection noise measurement and… · p. 23
- In the improved teleportation protocol, the optimal input pulse with κ=3.2, 6 dB light squeezing, and the first three scattering modes yields fidelity 0.93; squeezed light can reduce remaining vacuum noise.Source: Figure 1 · p. 23, Projection noise measurement and… · p. 23