Generating%20and%20harnessing%20photonic%20entanglement

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Generating and harnessing photonic entanglement
Geoff Pryde
Quantum Technology Lab
Rohan Dalton Michael Harvey Nathan Langford Till
Weinhold Jeremy OBrien Geoff Pryde Andrew White
www.quantinfo.org
Theory Colleagues
Stephen Bartlett Aggie Branczyk Michael
Bremner Jen Dodd Andrew Doherty Alexei
Gilchrist Gerard Milburn Michael Nielsen Tim Ralph
Funding
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www.quantinfo.org
Till Weinhold
Gerard Milburn
Tim Ralph
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Generating and harnessing photonic
entanglement Talk outline

• Qubits
• CNOT gate
•  Quantum process tomography
•   Generalized quantum measurements with
  photons
• Qutrits and Qudits
• Gaussian spatial modes
• Constructing and measuringqutrits
• Use in quantum bit commitment

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3 Single qubits

? Two-qubit gates
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CSIGN gate
C
C
0
0
C
C
1
1
p
phase shift
T
T
0
0
T
T
1
1
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CSIGN gate
-1/3
1/3
1/3
Ralph, Langford, Bell White, PRA 65, 062324
(2002) Hofmann Takeuchi, PRA
66, 024308 (2002)
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CSIGN gate
-1/3
1/3
1/3
Ralph, Langford, Bell White, PRA 65, 062324
(2002) Hofmann Takeuchi, PRA
66, 024308 (2002)
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CSIGN gate
-1/3
1/3
1/3
Ralph, Langford, Bell White, PRA 65, 062324
(2002) Hofmann Takeuchi, PRA
66, 024308 (2002)
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CNOT gate
-1/3
Control out
Control in
1/3
Target in
Target out
1/3
Ralph, Langford, Bell White, PRA 65, 062324
(2002) Hofmann Takeuchi, PRA
66, 024308 (2002)
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Very stable insensitive to x-y-z translation
J. L. OBrien, G. J. Pryde, et al., Nature 426,
264 (2003)
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Measured
Ideal
Average logical fidelity Tr Mideal?Mmeas/4
94 2
OBrien, Pryde, et al., Nature 426, 264 (2003)
OBrien, Pryde, et al., PRL 93, 080502 (2004)
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CñTñin 0 -1ñ1ñ H -VñVñ
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?
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Any physical process can be written as a
completely positive map
For a CNOT
0.34
Ideal
Measured (Re)
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 Physical interpretation? Change basis
(II, IX, IY, IZ, XI, XY, XZ, YI, YX, YY, YZ, ZI,
ZX, ZY, ZZ)
CNOT
87
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 Direct measurement of process fidelity
71 measurements 93 1
Chief source of non-ideal gate operation
Gilchrist, Langford, and Nielsen,
quant-ph/0408063 OBrien, Pryde, et
al., PRL 93, 080502 (2004)
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1. Measurement outcome is correlated with the signal
   input
2. The measurement does not alter the value of the
   measured obsevable
3. Repeated measurement yields the same result -
   quantum state preparation (QSP) 

Grangier et al. Nature 396, 537
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Control?in
Control?out
CNOT
Target?out
Target?in 0?
Measure
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1/3
Non-deterministic when 1 photon is detected in
the meter output the measurement is known to have
succeeded
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 Each compares two probability distributions p
and q using the classical fidelity
F gt 85 for all input states
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1/3
?V ?
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Most advanced general measurement of a qubit
non-destructive arbitrary strength any basis
BUT non-deterministic
Pryde, OBrien, White, Bartlett Ralph PRL 92,
190402 (2004)
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a (HHgt VVgt) b ?VHgt HVgt)
V
a Vgt b Hgt
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QUTRITS
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• Polarisation qubits

What if we want to create photonic qudits?

• Gaussian spatial modes
• Infinite dimensional
• Discrete
• Orthogonal
• Can describe any paraxial beam

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Gaussian optical mode
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Gouy phase shift
Non-vortex Mode Families

Hermite-Gauss (HG)
rectangular
Ince-Gauss (IG)
elliptical
Laguerre-Gauss (LGN)
cylindrical
Vortex Mode Families (carrying orbital angular
momentum)
Laguerre-Gauss (LGV)
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Mair et al., Nature 412, 313 (2001) Vaziri et
al., PRL 89, 240401 (2002)
Langford et al., PRL 93, 053601 (2004)
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Low Spatial Frequency
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• What is the spatial mode quantum state of the
  photon pairs?

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• Uses holograms and single-mode fibres (SMFs)

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coherences
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Langford et al., quant-ph/0312072
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Communication between mistrustful parties
Basis of other protocols, e.g. quantum coin
flipping
0
29-39-5
 Alice should commit to a message and not be
able to change it.  Bob should not be able to
decode the message until Alice reveals
it.  Quantum bit-commitment with arbitrarily
good security is impossible  Qutrits offer the
best-known BC security levels, whereas qubits do
not!
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Step 1 Alice starts with our experimentally
measured two-qutrit state.
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orthogonal two-qutrit states
non-orthogonal token states
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achievable with qubits
qutrits
inaccessible to best known BC protocols
KEY POINTS

• Orthogonal two-qutrit states result in
  non-orthogonal reduced token states.
• Ideal case provides optimal security, but
  simulated case still does not!

Langford et al., quant-ph/0312072
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• Quantum process tomography of CNOT fully
  characterize the process in the 2-qubit space
  high fidelity operation ? useful for q. info
  and q. physics tests
• Generalized measurement and QND
  non-destructive arbitrary strength any basis
• Qutrit entanglement measured, characterized
  for use in communications protocols