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Quantum Teleportation with Photons
Nicolas Brehm, Katrin Kröger, Natascha Hedrich
ETH Zürich
08.05.2015
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 1 / 29
Motivation
The distribution of single qubits over large distance via quantumteleportation is a key ingredient for realization of a quantum network
Quantum teleportation is a secure way to send information
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 2 / 29
Motivation
The distribution of single qubits over large distance via quantumteleportation is a key ingredient for realization of a quantum networkQuantum teleportation is a secure way to send information
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 2 / 29
Overview
1 The quantum teleportation protocol
2 Experimental realizationSetupResultsSummary
3 Long Distance TeleportationSetup
Feed-ForwardNoise Reduction
Results
4 Summary
5 References
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 3 / 29
The quantum teleportation protocol
1. Alice prepares or receives a quantum bit⇒ |ψ〉1 = α |0〉1 + β |1〉1 , where: |α|2 + |β|2 = 1
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 4 / 29
The quantum teleportation protocol
2. A pair of entangled qubits is created and sent to Alice and Bob⇒ |Ψ−〉23 = 1√
2 (|01〉23 − |10〉23)
3. Rewrite the state of the three qubits:
|ψ〉123 = (α |0〉1 + β |1〉1)⊗ 1√2
(|01〉23 − |10〉23)
=14
∑k
(|Ψk〉12 ⊗ Uk |ψ〉3) ,
where |ψ〉3 = α |0〉3 + β |1〉3, Uk is a unitary Matrix, and the |Ψk〉12are Bell states
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 5 / 29
The quantum teleportation protocol
2. A pair of entangled qubits is created and sent to Alice and Bob⇒ |Ψ−〉23 = 1√
2 (|01〉23 − |10〉23)
3. Rewrite the state of the three qubits:
|ψ〉123 = (α |0〉1 + β |1〉1)⊗ 1√2
(|01〉23 − |10〉23)
=14
∑k
(|Ψk〉12 ⊗ Uk |ψ〉3) ,
where |ψ〉3 = α |0〉3 + β |1〉3, Uk is a unitary Matrix, and the |Ψk〉12are Bell states
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 5 / 29
The quantum teleportation protocol
4. Alice performs a Bell state measurement on qubit 1 and 2:
⇒ Bob’s state is projected onto Uk |ψ〉35. Alice sends the outcome of her measurement to Bob via classical
communication channel6. Four possible outcomes:
Measurement Resulting state Bob’s Operation
|Ψ−〉12 |Ψ−〉12 ⊗ (α |0〉3 + β |1〉3) σ0|Φ−〉12 |Φ−〉12 ⊗ (β |0〉3 + α |1〉3) σ1|Φ+〉12 |Φ+〉12 ⊗ (β |0〉3 − α |1〉3) σ2|Ψ+〉12 |Ψ+〉12 ⊗ (α |0〉3 − β |1〉3) σ3
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 6 / 29
The quantum teleportation protocol
4. Alice performs a Bell state measurement on qubit 1 and 2:⇒ Bob’s state is projected onto Uk |ψ〉3
5. Alice sends the outcome of her measurement to Bob via classicalcommunication channel
6. Four possible outcomes:
Measurement Resulting state Bob’s Operation
|Ψ−〉12 |Ψ−〉12 ⊗ (α |0〉3 + β |1〉3) σ0|Φ−〉12 |Φ−〉12 ⊗ (β |0〉3 + α |1〉3) σ1|Φ+〉12 |Φ+〉12 ⊗ (β |0〉3 − α |1〉3) σ2|Ψ+〉12 |Ψ+〉12 ⊗ (α |0〉3 − β |1〉3) σ3
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 6 / 29
The quantum teleportation protocol
4. Alice performs a Bell state measurement on qubit 1 and 2:⇒ Bob’s state is projected onto Uk |ψ〉3
5. Alice sends the outcome of her measurement to Bob via classicalcommunication channel
6. Four possible outcomes:
Measurement Resulting state Bob’s Operation
|Ψ−〉12 |Ψ−〉12 ⊗ (α |0〉3 + β |1〉3) σ0|Φ−〉12 |Φ−〉12 ⊗ (β |0〉3 + α |1〉3) σ1|Φ+〉12 |Φ+〉12 ⊗ (β |0〉3 − α |1〉3) σ2|Ψ+〉12 |Ψ+〉12 ⊗ (α |0〉3 − β |1〉3) σ3
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 6 / 29
The quantum teleportation protocol
4. Alice performs a Bell state measurement on qubit 1 and 2:⇒ Bob’s state is projected onto Uk |ψ〉3
5. Alice sends the outcome of her measurement to Bob via classicalcommunication channel
6. Four possible outcomes:
Measurement Resulting state Bob’s Operation
|Ψ−〉12 |Ψ−〉12 ⊗ (α |0〉3 + β |1〉3) σ0|Φ−〉12 |Φ−〉12 ⊗ (β |0〉3 + α |1〉3) σ1|Φ+〉12 |Φ+〉12 ⊗ (β |0〉3 − α |1〉3) σ2|Ψ+〉12 |Ψ+〉12 ⊗ (α |0〉3 − β |1〉3) σ3
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 6 / 29
The quantum teleportation protocol
7. Bob performs the appropriate unitary operation on his qubit
8. Bob is now in possession of the qubit Alice wanted to send!!Note: Alice’s qubit is destroyed in the measuring process!
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 7 / 29
The quantum teleportation protocol
7. Bob performs the appropriate unitary operation on his qubit8. Bob is now in possession of the qubit Alice wanted to send!!
Note: Alice’s qubit is destroyed in the measuring process!
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 7 / 29
ExperimentSetup
Crucial steps:1. Creation of entanglement2. Realization of Bell-Measurement3. Analysis of teleported state
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 8 / 29
ExperimentSetup
1. Creation of entanglementEntangled photon pair |Ψ−〉23 created via type II-Parametric DownConversionLaser pulse is reflected at mirror and creates |Ψ−〉14
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 9 / 29
ExperimentSetup
2. Realization of Bell-MeasurementPhoton 1 and 2 superimposed at BS with detectors f1 and f2Coincidence click projects photons 1 and 2 into |Ψ−〉12Difference in arrival time ≤ 520 fs ≡ arrive „simultaneously“
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 10 / 29
ExperimentSetup
3. Analysis of teleported stateBob knows via CCC if photon 3 is in desired statePolarization is analysed with PBS with detectors d1 and d2
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 11 / 29
ExperimentTheoretical prediction
Preparation in +45◦-polarization
TP-region Coincidence d1 d2Outside 50% 50% 50%Inside 25% 0% 100%
Successful teleportation:3-fold coincidence d2-f1-f2 withabsence of 3-fold coincidence d1-f1-f2
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 12 / 29
ResultsMeasured three-fold coincidences
Polarization Visibility+45◦ 0.63± 0.02−45◦ 0.64± 0.020◦ 0.66± 0.0290◦ 0.61± 0.02Circular 0.57± 0.02
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 13 / 29
ResultsMeasured four-fold coincidences
Visibilities of the dip in the orthogonal polarization are (70± 3)%Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 14 / 29
Summary
Teleportation of a single photon achieved at fidelity of 70 %Next steps:
Show teleportation in other systemsConduct experiments on the fundamental nature of quantum mechanicsProvide links between quantum computersIncrease teleportation distance
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 15 / 29
Setup
Physical setup on La Palma (Alice) and Tenerife (Bob)Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 16 / 29
Setup
Creation of photons.Photon 1 heralded by click at (t)
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 17 / 29
Setup
Alice’s Bell state measurement.|Ψ−〉12 → clicks at t-a-d or t-b-c, |Ψ+〉12 → clicks at t-a-b or t-c-d
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 18 / 29
Setup
Bob’s measurement setupClassical and quantum channels are separated via dichoric mirror
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 19 / 29
Feed-Forward
Alice’s BSM distinguishes 2 Bell states (|Ψ+〉 and |Ψ−〉)
1. |Ψ−〉 → Bob does nothing (no feed-forward)2. |Ψ+〉 → Bob applies a π pulse (feed-forward)
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 20 / 29
Feed-Forward
Alice’s BSM distinguishes 2 Bell states (|Ψ+〉 and |Ψ−〉)
1. |Ψ−〉 → Bob does nothing (no feed-forward)
2. |Ψ+〉 → Bob applies a π pulse (feed-forward)
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 20 / 29
Feed-Forward
Alice’s BSM distinguishes 2 Bell states (|Ψ+〉 and |Ψ−〉)
1. |Ψ−〉 → Bob does nothing (no feed-forward)2. |Ψ+〉 → Bob applies a π pulse (feed-forward)
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 20 / 29
Feed-Forward
Alice’s BSM distinguishes 2 Bell states (|Ψ+〉 and |Ψ−〉)
1. |Ψ−〉 → Bob does nothing (no feed-forward)2. |Ψ+〉 → Bob applies a π pulse (feed-forward)
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 20 / 29
Noise Reduction
Problem: Fluctuations in atmosphere (rain, snow, temperature, etc.) ⇒very low signal-to-noise ratio
Solutions:High creation rates of entangled photon pairsUltra-low dark count detectors with large active areaSmall coincidence windowsClosed-loop tracking system
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 21 / 29
Noise Reduction
Problem: Fluctuations in atmosphere (rain, snow, temperature, etc.) ⇒very low signal-to-noise ratio
Solutions:High creation rates of entangled photon pairs
Ultra-low dark count detectors with large active areaSmall coincidence windowsClosed-loop tracking system
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 21 / 29
Noise Reduction
Problem: Fluctuations in atmosphere (rain, snow, temperature, etc.) ⇒very low signal-to-noise ratio
Solutions:High creation rates of entangled photon pairsUltra-low dark count detectors with large active area
Small coincidence windowsClosed-loop tracking system
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 21 / 29
Noise Reduction
Problem: Fluctuations in atmosphere (rain, snow, temperature, etc.) ⇒very low signal-to-noise ratio
Solutions:High creation rates of entangled photon pairsUltra-low dark count detectors with large active areaSmall coincidence windows
Closed-loop tracking system
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 21 / 29
Noise Reduction
Problem: Fluctuations in atmosphere (rain, snow, temperature, etc.) ⇒very low signal-to-noise ratio
Solutions:High creation rates of entangled photon pairsUltra-low dark count detectors with large active areaSmall coincidence windowsClosed-loop tracking system
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 21 / 29
ResultsDensity Matrix Representation
To test the teleportation, a known state is polarization is created(photon 1) and measured by Bob.Results shown using density matrix representations.
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 22 / 29
ResultsDensity Matrix Representation
Input state: |ψ〉 = |H〉
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 23 / 29
ResultsDensity Matrix Representation
Input state: |ψ〉 = |V 〉
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 24 / 29
ResultsDensity Matrix Representation
Input state: |ψ〉 = |P〉 = |H〉+|V 〉√2
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 25 / 29
ResultsDensity Matrix Representation
Input state: |ψ〉 = |L〉 = |H〉−i |V 〉√2
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 26 / 29
ResultsFidelities
Fidelities (〈ψideal | ρmeas |ψideal〉) are always above classical limit [3]!(feed-forward results shown in red)
Note: results for |H〉 and |V 〉 with or without feed-forward differ only byglobal phase
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 27 / 29
ResultsFidelities
Fidelities (〈ψideal | ρmeas |ψideal〉) are always above classical limit [3]!(feed-forward results shown in red)
Note: results for |H〉 and |V 〉 with or without feed-forward differ only byglobal phase
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 27 / 29
Summary
We have discussed the teleportation protocol and its originalimplementation
We have seen how it can be used to teleport information over 143 kmFirst steps to world wide quantum key distribution → quantum network
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 28 / 29
Summary
We have discussed the teleportation protocol and its originalimplementationWe have seen how it can be used to teleport information over 143 km
First steps to world wide quantum key distribution → quantum network
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 28 / 29
Summary
We have discussed the teleportation protocol and its originalimplementationWe have seen how it can be used to teleport information over 143 kmFirst steps to world wide quantum key distribution → quantum network
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 28 / 29
References
1. Dik Bouwmeester, Jian-Wei Pan, Klaus Mattle, Manfred Eibl, HaraldWeinfurter & Anton Zeilinger, Experimental quantum teleportation,Nature 390, 575 (1997).
2. Ma, Xiao-Song, et al., Quantum teleportation over 143 kilometresusing active feed-forward, Nature 489, 7415 (2012).
3. Serge Massar & Sandu Popescu, Optimal extraction of informationfrom finite quantum ensembles, Phys. Rev. Lett. 74, 1259(1995).
Nicolas Brehm, Katrin Kröger, Natascha Hedrich Photonic Quantum Teleportation 08.05.2015 29 / 29