Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Multi-Particle Entanglement & It’s Application in Quantum Networks Jian-Wei Pan Lecture Note 5

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Polarization Entangled Photons [P. G. Kwiat et al., Phys. Rev. Lett. 75, 4337 (1995).]

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Post Selection

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan 3-Photon Initial State: Four-fold coincidence Final State:

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Bell’s Inequality and Violation of Local Realism [J. S. Bell, Physics 1, 195 (1964)] Bell’s inequality states that certain statistical correlations predicted by QM for measurements on two-particle ensembles cannotbe understood within a realistic picture based on local properties of each individual particle. LR prediction:QM prediction: An unstatisfactory feature! In the derivation of BI such a local realistic and thus classical picture can explain perfect correlations and is only in conflict with statistical prediction of quantum mechanics.

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan conflict with local realism Linear polarizatoin basiscircular polarization basis

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan conflict with local realism

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan EPR reality criterion: the individual value of any local operator is predetermined. There exists an element of local reality S ix corresponding to operator conflict with local realism All six of the elements of reality S ix and S iy have to be there, each with the values +1 and –1!

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan What outcomes are possible? Consider measurement of 45° linear polarization basis local realism Possible outcomes:

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan What outcomes are possible? quantum physics Whenever local realism predicts a specific result definitely to occur for a measurement for one of the photons based on the results for the other two, quantum physics definitely predicts the opposite result! Possible outcomes:

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Experimental Results J.-W. Pan et al., Nature (London) 403, 515 (2000)

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan An improved 3- & 4-photon source [J.-W. Pan et al., Rev. Lett. 86, 4435 (2001) ]

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Quantum secret sharing A procedure for splitting a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. [M. Hillery et al., Phys. Rev. A 59, 1829 (1999).] Third-Man Quantum Cryptography A procedure that the third man, a controller, can control whether the users, say Alice and Bob, can communicate in a secure way while he has no access whatsoever on the content of the communication between Alice and Bob. [M. Żukowski et al., Acta Phys. Pol. 93, 187 (1998).] Advanced Quantum Cryptography

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Schemes for QSS and TQC A xxx measurement

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Quantum Secret Sharing xxx, xyy, yxy, yyx xyx, yxx, xxy, xyx

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Setup [Z. Zhao et al., Phy. Rev. Lett (2003). A ultra-stable high intensity source: 2 four-fold coincidence per second! 100 times brighter! stable for a few months!

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Result for QSS From bits of raw key with a QBER of 12.9%, after security check and error reduction, Alice and Bob jointly generate bits cured key with Charlie with a QBER of 0.3%.

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Third-Man’s Control If all of them randomly select the base to measure the polarization. Any two of them can create a coding by being told the other one’s measurement result. If Charlie rejects to tell them his selection or just does not make any selection then Alice and Bob can get nothing useful for the cryptography.

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Result for TQC With the permission of Charlie, after security check and error reduction Alice can generate a bits cured key with Bob, with the same QBER. Otherwise, Without knowing Charlie's results, the only thing Alice and Bob can do is to randomly guess Charlie's results and continue the same encoding and error reduction procedure. In our experiment, after performing twice error reductions, the QBER remains %. [Y.-A. Chen et al., Phy. Rev. Lett. 95, (2005) ]

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan conflict with local realism in 4-photon case

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Violation of Local Realism [Z. Zhao et al., Phy. Rev. Lett (2003).

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan A new protocol for 3-Photon [J. G. Rarity and P. R. Tapster, Phys. Rev. A 59, R35 (1999).]

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan 5-Photon Five-fold Coincidence:

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Encoding operation for simple quantum error correction This implies that a joint Bell measurement on photons 1 and 2 would project the state of photons 3, 4 and 5 into one of the four corresponding states, which can be used for either one bit-flip error or phase-shift error correction in quantum communication.

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Quantum State Sharing & Open-destination Teleportation If we perform a +45- degree measurement on photons 4 and 5, then photon 3 is left in the state of photon 1. In a similar manner the initial state of photon 1 can also be teleported either onto photon 4 or photon 5. [A. Karlsson, et al., Phys. Rev. A 58, 4394 (1998) ]

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Further Demonstration In contrast to the original teleportation scheme, after the encoding operation the destination of teleportation is left open until we perform a polarization measurement on two of the remaining three photons. Even though photons 3, 4 and 5 are far away from each other, one can still choose which particle should act as the output where the initial state of photon 1 is transferred to. This is why we have called the encoding-decoding procedure as open-destination teleportation. It is therefore a generalization of standard teleportation, when no prior agreement on the final destination of the teleportation is necessary. It is also a generalization of Quantum State Sharing. No subset of parts is sufficient to decode the state, but the entire set is. It broadens the scope of quantum information networks allowing quantum communication between multiple nodes, while providing security against malicious parties in the network as well as node and channel failures.

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Setup for Five-photon GHZ Entanglement [Z. Zhao et al., Nature 430, 54 (2004). ]

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan CNOT operation for two- independent photons +/-? H/V?

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan ControlTargetControl’Target’ HHHV HVHH VHVH VVVV CNOT Gate [T. B. Pittman, PRA 64,062311(2001)] [S. Gasparoni et al., Phys. Rev. Lett. 93, (2004); Z. Zhao et al., Phys. Rev. Lett. 94, (2005).] A full Bell state Measurement for 100% Teleportation

Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Most recently... 6-Photon [Q. Zhang et al., In preparation for Science ]