Lecture Note 3 Quantum Dense Coding and Quantum Teleportation Jian-Wei Pan
Bell states maximally entangled states: ˆ Φ Ψ Φ x σ Dense Coding Theory: [C.. Bennett & S. J. Wiesner, Phys. Rev. Lett. 69, 88 99] ˆ ˆ Φ Ψ Φ Φ y z i σ σ
Dense Coding. Alice and Bob share an entangled photon pair in the state of Φ.. Bob chooses one of the four unitary transformation { I, σ } z, σ x, σ y on his photon. The information of which choice is bit. 3. Bob sends his photon to Alice. 4. Alice performs a joint Bell-state measurement on the photon from Bob and her photon. 5. With the measurement result, she can tell Bob s unitary transformation and achieve the bit information.
Teleportation Classical Physics Scanning and Reconstructing Quantum Physics eisenberg Uncertainty Principle Forbidden Extracting All the Information from An Unknown Quantum State
Quantum Teleportation --- Six Author Scheme A A A 0 β α Φ 0 0 0 0 ± ± ± ± φ ψ [C.. Bennett et al., Phys. Rev. Lett. 73, 380 993] Bell states maximally entangled states β α 0 0 0 0 C C AB C C AB C C AB C C AB BC A ABC β α β α β α β α Ψ Ψ Φ Φ Φ Φ Ψ
Teleportation of entanglement ----Entanglement Swapping Ψ 34 Φ Φ Ψ 4 Φ Φ Ψ 3 34 34 Φ Ψ Φ 34 34 Ψ [M. Zukowski et al., Phys. Rev. Lett. 7, 487 993]
Experimental Ingredient Entangled photon pair by Spontaneous Parametric down conversion SPDC time bin entanglement momentum entanglement polarization entanglement. Bell state analyzer photon statistics at a beamsplitter
SPDC Type I Type II
SPDC time bin entanglement Ψ short short a b long a long b [J. Brendel et al., Phys. Rev. Lett. 8, 594 999]
SPDC momentum entanglement Ψ u d d u [Z. B. Chen et al., Phys. Rev. Lett. 90, 60408 003]
SPDC polarization entanglement ± Ψ ± Φ ± ± [P. G. Kwiat et al., Phys. Rev. Lett. 75, 4337 995]
Bell state analyzer with Linear Optics Controlled-NOT gate,, Φ Ψ Ψ ± [. Weinfurter, Eruophys. Lett. 5, 559 995] [J.-W. Pan et al., Phys. Rev. A 998] ±
Bell state analyzer with Linear Optics To realize a Bell state measurement is to make the two input SPDC photons indistinguishable on the BS. The method is to make the two photons spatially and timely overlapped on the BS perfectly. owever, the timely overlap is difficult since the SPDC photon has a ultrasmall coherent time about 00fs, definitely shorter than the time resolution of state-of-the-art single photon detector. What we can do is to scan the interference fringes to make it sure that the two photons arrive at the same time. But a cw laser will No interference fringes
Bell state analyzer with Linear Optics A solution is to use Pulse laser The pulse will bring some time jitter to the SPDC photon, we insert a narrow band filter can extend the coherent time of the SPDC photon
Experimental Dense Coding 0 Φ Ψ Ψ ˆ ˆ ˆ [K. Mattle et al., Phys. Rev. Lett. 76, 4656 996]
Experimental Realizations of quantum teleportation D. Bouwmeester, et al., Nature 390, 575-579 997 photons D. Boschi, et al., Phys. Rev. Lett. 80, -5 998 photons. J-W. Pan, et al., Phys. Rev. Lett. 80, 389 3894 998 mixed state of photons. A. Frusawa, et al., Science 8, 706 999 continuous-variable M. Riebe, et al., Nature 49, 734-737 004 trapped calcium ions. M.D. Barret, et al., Nature 49, 737-739 004 trapped beryllium ions I. Marcikic, et al., Nature 4, 509-53 003 long distance R. Ursin, et al., Nature 430, 849 004 long distance Z. Zhao, et al., Nature 430, 54 004 open destination teleportation
Experimental Quantum Teleportation The setup [D. Bouwmeester et al., Nature 390, 575 997]
Experimental Quantum Teleportation The result [D. Bouwmeester et al., Nature 390, 575 997]
Experimental Entanglement Swapping The setup The result [J.-W. Pan et al., Phys. Rev. Lett. 80, 389 998]
A Two-Particle Quantum teleportation experiment b b a a Ψ β α ψ. Sharing EPR Pair. Initial State Preparation ] [ b a b a b a b a b a b a b a b a b b a a β α β α α β α β ψ Φ 3. BSM [D. Boschi et al., Phys. Rev. Lett. 80, 998]
Applications of Entanglement Swapping Quantum telephone exchange Speed up the distribution of entanglement [S. Bose et al., Phys. Rev. A 57, 8 998]
Applications of Entanglement Swapping BSM E N E3 E N E [S. Bose et al., Phys. Rev. A 57, 8 998]
Ψ β α ] [ 5 4 3 5 4 3 5 4 3 5 4 3 5 4 3 5 4 3 5 4 3 5 4 3 345 345 Ψ Ψ Φ Φ Φ Ψ Ψ β α β α β α β α Open-Destination Teleportation Sharing a secret quantum state of single particles [A. Karlsson et al., Phys. Rev. A 58, 4394 998] [R. Cleve et al., Phys. Rev. Lett. 83, 648 999]
Experimental Setup
Experimental Results [Z. Zhao et al., Nature 430, 54 004]
Teleportation of a composite system ----Scheme Initial State χ α β γ δ 34 3 4 3 4 3 4 3 4 ---horizontal polarization --- vertical polarizations Just as the single qubit teleportation, first teleport photon to photon 5 χ Φ Φ χ Φ ˆ σ ˆ ˆ 35 3 5 3 z χ Ψ σ 5 3 x χ Ψ iσ 5 3 y χ 5 And then, we teleport photon to photon 6 χ Φ Φ χ Φ ˆ σ ˆ ˆ 5 46 4 56 4 z χ Ψ σ 56 4 x χ Ψ iσ 56 4 y χ 56 Finally, we can teleport the state of photon, to photon 5,6
Teleportation of a composite system ----Setup
State Teleportation of a composite system ----Result Fidelity Fidelity with noise reduction Fidelity: - 0.86±0.03 0.60±0.03 0.97±0.03 0.7±0.03 Pure state F ini ψ ψ Tel -i 0.75±0.0 0.83±0.0 Mixed state F Tr ρ ψ ψ ini Average 0.74±0.03 0.84±0.03 Well beyond the clone limit 0.40 [A. ayashi et al., Phys. Rev. A. 7, 0335 005.] Teleported State of - is Still Entangled! Tr ρw Tr[ ρ RL 0.3 ± 0.04 < 0 RL LR [M. Barbieri, et al. Phys. Rev. Lett. 9, 790 003.] LR ]
Experimental Teleportation of a Two-Qubit Composite System Q. Zhang et al., Experimental quantum teleportation of a two-qubit composite system, Nature Physics, 678-68 006.
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