Quantum Key Establishment

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Quantum Key Establishment

• Wade Trappe

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Talk Overview

• Quantum Demo
• Quantum Key Establishment

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Demo
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Basics of Photon Polarity and Quantum

• A photons polarization can be represented by a
  unit vector in two-dimensional complex vector
  space.
• Let , be a ON basis for ,
  then a photons 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.

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Bennett-Brassard Quantum Key Distribution

• Alice chooses two bases B1 and B2, 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 bits 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.

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Example

• Alice wants to send 0,1,1,1,0,0,1,0. She chooses
  B1, B2, B1, B1, B2 , B2, B1, B2 and sends
• Bob chooses the bases B2, B2, B2, B1, B2, B1, B1,
  B2.
• 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 11010 as a key for future
  communication over a classical channel.

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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.