Quantum Dense coding and Quantum Teleportation
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Quantum Dense coding and Quantum Teleportation
Jian-Wei Pan
Lecture Note 3
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Bell states – maximally entangled states:
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Dense Coding
Theory:[C. H. Bennett & S. J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992)]
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Dense Coding
1. Alice and Bob share an entangled photon pair in the state of .
2. Bob chooses one of the four unitary transformation
on his photon. The information of which choice is 2 bit.
3. Bob sends his photon to Alice.
4. Alice does 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 2 bit information.
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Teleportation
Classical Physics
Scanning and Reconstructing
Quantum PhysicsHeisenberg Uncertainty Principle Forbidden Extracting All the Information from An Unknown Quantum State
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Quantum Teleportation --- “Six Author Scheme”
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[C.H. Bennett et al., Phys. Rev. Lett. 73, 3801 (1993)]
Bell states – maximally entangled states
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Teleportation of entanglement ----Entanglement Swapping
[M. Zukowski et al., Phys. Rev. Lett. 71, 4287 (1993)]
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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
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SPDC
Type I Type II
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SPDC—time bin entanglement
[J. Brendel et al., Phys. Rev. Lett. 82, 2594 (1999)]
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SPDC—momentum entanglement
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[Z. B. Chen et al., Phys. Rev. Lett. 90, 160408 (2003)]
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SPDC—polarization entanglement
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[P. G. Kwiat et al., Phys. Rev. Lett. 75, 4337 (1995)]
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Bell state analyzer with Linear Optics
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Controlled-NOT gate
[H. Weinfurter, Eruophys. Lett. 25, 559 (1995)]
[J.-W. Pan et al., Phys. Rev. A (1998)]
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Bell state analyzer with Linear Optics
• To realize a Bell state measurement,one has to make the two input SPDC photons indistinguishable on the BS. The method is to make the two photons spatially and temporally overlapped on the BS perfectly.
• However, the timing overlap is difficult since the SPDC photon has a ultrasmall coherent time about 100fs, 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
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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
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Experimental Dense Coding
[K. Mattle et al., Phys. Rev. Lett. 76, 4656 (1996)]
ˆ0
ˆ1
ˆ2
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Experimental Realizations of quantum
teleportation D. Bouwmeester, et al., Nature 390, 575-579 (1997) (photons)
D. Boschi, et al., Phys. Rev. Lett. 80, 1121-1125 (1998) (photons).
J-W. Pan, et al., Phys. Rev. Lett. 80, 3891–3894 (1998) (mixed state of photons).
A. Frusawa, et al., Science 282, 706 (1999) (continuous-variable)
M. Riebe, et al., Nature 429, 734-737 (2004) (trapped calcium ions).
M.D. Barret, et al., Nature 429, 737-739 (2004) (trapped beryllium ions)
I. Marcikic, et al., Nature 421, 509-513 (2003) (long distance)
R. Ursin, et al., Nature 430, 849 (2004) (long distance)
Z. Zhao, et al., Nature 430, 54 (2004) (open destination teleportation)
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Experimental Quantum Teleportation
[D. Bouwmeester et al., Nature 390, 575 (1997)]
The setup
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Experimental Quantum Teleportation
[D. Bouwmeester et al., Nature 390, 575 (1997)]
The result
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Experimental Entanglement Swapping
The setup The result
[J.-W. Pan et al., Phys. Rev. Lett. 80, 3891 (1998)]
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A Two-Particle Quantum teleportation experiment
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1. Sharing EPR Pair
2. Initial State Preparation
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3. BSM
[D. Boschi et al., Phys. Rev. Lett. 80, 1121 (1998)]
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Applications of Entanglement Swapping
Quantum telephone exchange Speed up the distribution of entanglement
[S. Bose et al., Phys. Rev. A 57, 822 (1998)]
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Applications of Entanglement Swapping
[S. Bose et al., Phys. Rev. A 57, 822 (1998)]
)2()1()3()( ENEENE BSM
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Open-Destination Teleportation
Sharing a secret quantum state of single particles
[A. Karlsson et al., Phys. Rev. A 58, 4394 (1998)][R. Cleve et al., Phys. Rev. Lett. 83, 648 (1999)]
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Experimental Setup
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Experimental Results
[Z. Zhao et al., Nature 430, 54 (2004)]
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Teleportation of a composite system ----Scheme
12 1 2 1 2 1 2 1 2H H H V V H V V
Initial State
Just as the single qubit teleportation, first teleport photon 1 to photon 5
And then, we teleport photon 2 to photon 6
Finally, we can teleport the state of photon 1,2 to photon 5,6
H---horizontal polarization
V--- vertical polarizations
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Teleportation of a composite system ----Setup
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Teleportation of a composite system ----Result
State FidelityFidelity with
noise reduction
HV 0.86±0.03 0.97±0.03
HV-VH 0.60±0.03 0.71±0.03
(H+V)(H-iV) 0.75±0.02 0.83±0.02
Average 0.74±0.03 0.84±0.03
Well beyond the clone limit 0.40
[A. Hayashi et al., Phys. Rev. A. 72, 032325 (2005).]
Teleported State of HV-VH is Still Entangled!
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Pure state
Mixed state
Fidelity:
[M. Barbieri, et al. Phys. Rev. Lett. 91, 227901 (2003).]
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Our dream