Deterministic Quantum Teleportation with Atoms

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Quantum Computing, Cryptography and Teleportation
Daniel F. V. James Department of
Physics University of Toronto
University of Calgary 26 September 2008
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Thanks to...
My Group
Dr. René Stock Asma Al-Qasimi Hoda
Hossein-Nejad Max Kaznadiy Arghavan
Safavi Ardavan Darabi Felipe Corredor Faiyaz
Hasan Rebecca Nie

Collaborators Prof. Rainer Blatt
(Innsbruck) Prof. Andrew White (Queensland) Prof.
Paul Kwiat (Illinois) Prof. Emil Wolf (Rochester)
Funding Agencies
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Classical and Quantum Descriptions of Nature
Classical Dynamics mass, position, velocity
etc.
The configuration (state) of the system is
the same as the observables
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Quantum Sytems Examples
An oscillator can exist only in one of a number
of discrete quantum states and to each of these
states there corresponds a definite allowed value
of its energy (Introduction to Modern Physics
F. K. Richtmyer, E. H. Kennard and J. N. Cooper,
p.233)
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Atomic Qubits
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Entanglement
When two systems, of which we know the states,
... enter into temporary physical interaction,
... they can no longer be described in the same
way as before, viz. by endowing each of them with
a state of its own. I would not call that one
but rather the characteristic trait of quantum
mechanics, the one that enforces its entire
departure from classical lines of thought. By
the interaction the two representatives (or ?
-functions) have become entangled. -Erwin
Schrödinger, 1935
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Example qubits
State of either system is well defined
separable state
The two systems are in an entangled state
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Non-locality
A
B
Two atoms, separated by some distance, prepared
in the state
Measure A with 50 probability, you get 1,
with 50 probability you get 0 (just like tossing
a coin!)
BUT instantaneously atom B is projected into
the same state. If information cannot travel
faster than light, how does it know what state
to be in?
Perhaps outcomes of measurements is
pre-determined by some hidden variable?

Bells theorem provides a test for this
hypothesis the answer is NO (sort of!)
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Key Distribution
...00011011100....
(secret key)
Alice
Bob
Alice and Bob want to share a list of random
numbers,
Quantum key distribution why not use the
non-locality of quantum mechanics?
Actual protocols, designed to be 100 secure,
are more subtle....
ranges of over 100km and bit rates
better than 1 MHz have been demonstrated.
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QKD Prof. H.-K. Los Group at Toronto
Gaussian-Modulated Continuous-Variable QKD
Decoy State QKD
Multi-user QKD on Sagnac-Loop Interferometer
Demonstration of Quantum Hacks
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Quantum Computing Basic Ideas
Classical digital computers Each register is
either 0 or 1
Quantum Computers Each register (qubit) can
be in a superposition of two states 0? and 1?
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Quantum Memories
State of one quantum data register (qubit)
a??? b?1?
State of two qubits
a?????? b????1? ? c?1???? d?1??1?
State of three qubits
a????????? b???????1? ? c????1???? d????1??1?
e?1??????? f?1?????1?
? g?1??1???? h?1??1??1?
a, b??c, d,.. etc. are the probability amplitudes.
n qubits 2n registers
Quantum memories are BIG
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Quantum Parallelism
Operations on one qubit effect ALL of the data
in the quantum register.
Example bit flip on second qubit a??????
b????1? ? c?1???? d?1??1? ? b??????
a????1? ? d?1???? c?1??1?
Quantum computers perform complex operations on
very large registers very efficiently
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Measurement and Readout
Projective measurement of each
qubit i.e. A?0? B?1? ? ?0? (probability
P0A2) OR A?0? B?1? ? ?1? (probability
P1B2)
N qubits store 2N bits of information and process
them efficiently, BUT you can only read out N
bits to get the final answer.
Restricts types of algorithms that can be
executed on a quantum computer global
mathematical properties like periodicities.
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How to build a quantum computer
1. A quantum memory of well-characterized
qubits. 2. Ability to initialize the qubits in
their ground state. 3. Long (relative)
decoherence times. 4. Universal set of quantum
gates (e.g. arbitrary one qubit operations CNOT
with any two qubits). 5. Measurement. 6. Do it
all fast enough (say 1 nsec for a gate)
D. P. DiVinzenco, Fortschr. Phys. 48 (2000)
771-783
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QC in action Quantum Teleportation
What its NOT - matter is not dematerialized
and recreated somewhere else, like in Star Trek
Quantum wavefunction Reconstruction - the
quantum state of a particle is transferred to
another particle by means of a classical
communication and a shared correlated resource
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-Continuous Variables photon number rather than
polarization Kimble et al., Science 282, 706
(1998).

• NMR no entanglement, no projective measurement,
  no pure states
• Nielsen et al., Nature 396, 52 (1998).

• Trapped Ions first complete teleportation
• Blatt et al., Nature 429, 734 (2004)
• Wineland et al., Nature 429, 737 (2004).

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Trapped Ions ( the best Quantum Computer So Far)
Cannot trap ions electrostatically (Earnshaws
Theorem) Do it dynamically (Paul trap)
oscillating saddle potential
Effectively a harmonic well in all three
directions
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Innsbruck Ion Trap
made from four blades (a), two tips (b) and a
supporting structure (c). (from F. Schmidt-Kaler
et al., Appl. Phys. B 77, 789 (2003)).
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Phonon Modes
Ions coupled by Coulomb force ? ions
oscillations have normal modes. Lowest mode
center-of-mass (CM) Next mode is stretch
mode Number of modes in each direction
number of ions.
D.F.V. James, Appl Phys B 66, 181-190 (1998)
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Trapped Ion QC
Harmonic potential
Laser pulses can Perform Rabi flips between
and . Excite phonons of the longitudinal
vibration modes.
J. I. Cirac and P. Zoller , Phys Rev Lett 74,
4091 (1995)
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Teleportation Circuit
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Teleportation Circuit
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Teleportation Circuit
Bobs qubit stored in memory
Bobs qubit ends up identical to Charlies
Transformation
selected on the basis of Alices message
Alices classical message
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Results Fidelity of Teleportation measured for
300 trials
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Killer Ap factoring (15 3 x 5)

• WHY?
• the RSA cryptosystem
• polynomial work to encrypt/decrypt
• exponential work to break factoring
• BUT quantum factoring is only polynomial work

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Killer App Factoring
Shors Algorithm what are the factors of the
integer n?
Period Finding ? Factoring
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Classical factoring evaluate fn,x(a) for a
large number ( 2L-1 ) of values of a until you
can find r.
2L operations replaced by 1 operation
Quantum Fourier Transform and measurement gives
r.
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?
?
?
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B. P. Lanyon, T. J. Weinhold, N. K. Langford, M.
Barbieri, D. F. V. James, A. Gilchrist, and A. G.
White, Physical Review Letters 99, 250505 (2007).
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Quantum Information in Canada
LITQ Montréal
IQC Waterloo
Simon Fraser Prof. Paul Haljan
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More Information Books/Special Issues Quantum
Computation and Quantum Information Nielsen and
Chuang (Mike Ike) (Cambridge, 2000). The
Physics of Quantum Information Bouwmeester, Ekert
and Zeilinger (Springer, 2000) Information,
Science, and Technology in a Quantum World Los
Alamos Science 27 (2002) online
at http//www.fas.org/sgp/othergov/doe/lanl/pubs/
number27.htm An Introduction to Quantum
Computing Kaye, Laflamme and Mosca (Oxford,
2007) Pre-prints the latest results
http//arxiv.org
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Problems that (still) must be solved 1.
Fabrication get enough qubits in the right
place. 2. Prepare the initial quantum state. 3.
Perform gates with required accuracy. 4.
Suppress decoherence. 5. Read-out final state
reliably. 6. Do it all fast enough.