Quantum Key Establishment Wade Trappe

Talk Overview Quantum Demo Quantum Key Establishment

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Basics of Photon Polarity and Quantum A photon’s polarization can be represented by a unit vector in two- dimensional complex vector space. Let, be a ON basis for, then a photon’s polarity can be expressed as: Polaroid filters perform a measurement with respect to a vector (state). Suppose is measured against the state then the probability that the outcome is in state is Example: measured by gives the state with probability. One of the basic principles of quantum mechanics is that measurement forces the state of the photon into the result of the measurement.

Bennett-Brassard Quantum Key Distribution Alice chooses two bases B 1 and B 2, denoted: Alice will encode a 0 with the first element of a basis, and a 1 with the second element. Procedure: –Alice randomly generates bits, and randomly chooses a basis for each bit. and polarizes a photon according to that bit’s value and which basis is chosen. –The photons are sent to Bob over an optical channel. –Bob randomly chooses a basis for each bit and measures the state using the basis states. –Bob calls Alice via a classical channel and tells her what bases he used. –They keep the bits that used the same bases and discard the other bits.

Example Alice wants to send: 0,1,1,1,0,0,1,0. She chooses B 1, B 2, B 1, B 1, B 2, B 2, B 1, B 2 and sends: Bob chooses the bases B 2, B 2, B 2, B 1, B 2, B 1, B 1, B 2. The 2nd, 4th, 5th, 7th, and 8th match, giving the measurements: These correspond to the bits 1,1,0,1,0. Alice and Bob share their list of bases used, and then may use as a key for future communication over a classical channel.

Why Quantum Crypto is Cool An eavesdropper, Eve, must perform measurements in order to observe the photon transmissions between Alice and Bob. If Eve uses the same basis as Alice, then the photons will pass onto Bob unaltered, while if she uses a different basis the photons will be altered. When Bob uses the correct basis, there will be a 25% chance that he will measure the wrong value. Example: Alice sends to Bob. –If Eve uses B1, then the photon passes through correctly. –If Eve uses B2, then the photon is equally likely to be and. –When Bob uses the correct basis, half of the measurements will be correct, while half will be incorrect. If Alice and Bob test their data for discrepancies over a conventional channel (e.g. vial parity checks), they will detect any eavesdropping.