Entanglementfree Heisenberglimited phase estimation

1
Entanglement-free Heisenberg-limited phase
estimation

• Physicists calculate phase
• In increasingly accurate ways,
• But statistics brought woe
• Until Higgins and co
• Scaling at one over N did amaze.

- Group 2
2
Phase estimation

• Used to measure distance, position, optical path
  length, etc.
• Spectroscopy
• X-ray diffraction

LIGO - Laser Interferometer Gravitational-Wave
Observatory
Fraunhofer Did great-tings
3
Standard Quantum limit (SQL)

• Standard schemes limited by shot noise
• Interference techniques using independent quantum
  systems scale as
• SQL
• Want to minimise

4
Standard interferometry
A 1gt
A
B (1,0gtab 0,1gt ab)/v2
B
B
C
cosf
C
C fgt (1,0gtab exp(i f)0,1gt ab)/v2
5
High NOON
A 1gt11gt2...1gtN
A
B (N,0gtab 0,Ngt ab)/v2
B
B
C
C
C fgt (N,0gtab exp(i N f)0,Ngt ab)/v2
Problem Very difficult to create and maintain
NOON states, even for small N
6
Phase Operator

• The goal of phase estimation is to estimate the
  phase parameter phi of such a unitary operator.

7
Binary fraction notation
8
Quantum Fourier transform

• Imprints states of qubits on phase of output
  qubits.
• e.g.
• Is unitary, therefore invertible.

9
Preparation of states

• Measurement of each output qubit gives one bit of
  
• Possible error if does not terminate after n
  bits

10
Preparation of states

• Introduce ? to influence accuracy and sensitivity
  of measurement
• Previously randomize ? to obtain uniform error.

11
Adaptive phase measurement

• Measure each bit multiple (M) times
• Improve ? after each measurement
• Heisenberg limited scaling for M 4 shown
  numerically

12
Conceptual setup
13
Experimental Setup
Processor
pq
f
QWP
PBS
QWP
SPCM
HWP
MMF
Filters
p Number of passes
M times
p 8
p 4
HWP
p 2
p 1
PBD
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Experimental Procedure
We measure the standard deviation of the phase
using
Adaptive algorithm
- M 6- M 1 (Kitaevs algorithm)
For each
Also
- Standard estimation algorithm- N number of
resources used for each of the M 6.
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Experimental Results
M 1 (Kitaev)
Standard
M 6
Heisenberg Limit
16
Conclusions

• Introduced a new algorithm for phase
  estimation.- Single photons, multiple passes,
  adaptive measurement.- First measurement with
  Heisenberg-limited scaling.

Future Outlook
- Metrology applications
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Experimental Setup (2)
- Successful measurement
- Coincidence detection reduces background
counts.
SPCM
BiBO
TiSapph
Experiment
18
Inverse QFT circuit

• Theta affects the sensitivity of the
  measurements.
• 1/sqrt(N) scaling

19
Actual implementation

• Measurement of each binary digit performed M
  times (M2 in this circuit)
• Error numerically shown to scale as 1/N

20
Talk Outline

• Introduction to phase estimation
• Adaptive phase estimation algorithms
• Experimental phase measuring scheme
• Conclusion