Finding Quantum States and Detectors The Experiment

1. Muga, Nelson, Armando Pinto, and F Ferreira. n.d. “Geometric interpretation of waveplate-Induced Polarization Transformation in Stokes Space”, Symp. on Enabling Optical Networks, 2006

Literature Cited

A Working Algorithm Conclusion

The Set Up

-Can find detector POVM’s and quantum Source-Greatest source of error is in rotation errors in the waveplates

Can we find the detector POVM’s and the Source State with no knowledge of either?

A New Form of Quantum TomographyJacob Cutshall, Tommaso McPhee, Mark Beck

Reed College Physics Department

REE

D COLLEGE

FOUNDED IN 19

11

-Quantum State Tomography

finds the state of a quantum

Source

-In Detector Tomography the

Positive Operator Value Measure

(POVM) is characterized

-We want a way of finding both

simultaneously

Theory is in green, experimental results

are in red.

A few options were discussed for automating our process.

• Simplex method allows for minimizing and maximizing through

only function evaluations

• Because we are constrained to sphere zeroing can be done by

finding path that decreases the dot product fastest

Can be an efficient tool for simultaneously characterizing the

source and detector of a quantum state.

By performing only simple unitary transformations, scientists

and engineers can now find information on quantum systems

with minimal knowledge of the source or detector.

Call our source vector p and our detector POVM w, then

we can write our expectation value as:

We Measure:

Thank You To:

Two half waveplates help account for rotation errors.

We use a Soliel-Babinet Compensator between two

quarter wave plates to perform rotations on polarization.

REE

D COLLEGE

FOUNDED IN 19

11

This project was supported in part by Galakatos Funds.

Ej = Tr ΣU jρ( ) = !w i !pj + u

¬Π

Π

Π = 1/ 2( ) 1+ u( )1+i=1

3

∑ wiσ i⎡

⎣⎢

⎤

⎦⎥

¬Π = 1/ 2( ) 1− u( )1−i=1

3

∑ wiσ i⎡

⎣⎢

⎤

⎦⎥

By performing rotations on p and w, we can find the rotation

that brings them parallel.

1. First we maximize and minimize

E to find u

2. The rotation that brings E to 0

then gives us the location of pand w

A four fold ambiguity arises because E is

0 when:!k " !w

!k " − !w

!k " !p '

!k " − !p '

-If rotations can be performed quicker with more accurate waveplates, can be very efficient

p

w