Matlab QO Functions list.xls

7/28/2019 Matlab QO Functions list.xls

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Matlab Functions

Name

Bell_witness

BucketDetector

BucketDetector_noise

BucketDetectorRoot

display_state4

entangl_of_formation

expectation_value_post_selection


2/11

fockstate

g_two_definition

GHZ_fusion_type1

GHZ_mermin

GHZ_witness

index2fockstates

KLM_gate_highn


3/11

measure_2folds_4modes

measure_2folds_4modes_unsymmetric_detectors

msrmt_ch_chsh_2side_rho

one_side_project

ptrace_high_n2

SPDDetector

SPDDetectorRoot

tensor_high_n

witness_2qb_2ch_4mode


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Scripts

simplified_KLM_gate_high_n_with_bell_test3

simulation_of_entangled_state_communications

standard_definitions_qo_toolbox

test_sources_gtwo2

testing_ptrace_high_n


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Description Inputs

extract Bell_Witness from all the combinations of

measurments for a maximaly entangled Bell-state

a_p; ps

Calculates the detector projector (detection) andunprojector (non-detection) for Fock dimension N,

efficiency effc with no dark counts for an APD (bucket)

detector

N; effc

Calculates the projector (detection) and unprojector

(non-detection) for an APD (bucket) detector with

efficiency effc, and a noise factor noise_factor, which

is defined as the dark counts divided by the time unit

in Fock dimension N

N; effc; noise_factor

Detector Projector and un-projector for efficiency

Effc, in Fock Dimension N of an APD (BucketDetector). The square root of the elements is taken

for use with density matrices and partial trace

N; effc

Displays in_state in BRA,KET notation. N is the Fock

space size, in_state can be a pure state or a density

matrix

N; in_state

Entanglement of formation of a pure state called

in_state. Nomenclature of state is

|H1,V1,H2,V2,X,X,....>.

Calculation is done by traceing over modes 2,diagonalizing the matrix and then calculation of von

Neumann entropy

in_state

choose to do post selection (ps=1) or non-

postselection (ps=0) correlation value for a given

combination of measurements (probs)

out of a complete measurement series; the indices

(indx, vector of four elements) are

positive,negative,negative,positive probabilities

probs; indx; ps


6/11

result =

fockstate(N,amplitude0,amplitude1,amplitude2,...,am

plitudeN-1) generates an arbitrary Fock state, with

dimension N, and amplitude0,

amplitude1,...,amplitudeN-1 the amplitudes for the

|0>,|1>,...,|N-1> states. This function then normalizes

the resulting ket so that the input amplitudes need

only reflect the relative amplitudes. result =

fockstate(N) generates a Fock state ket with each

state |0>, |1>,...,|N-1> having equal amplitude.

N; varargin (amplitudes)

calculates the conditional g2 function at t=0 for input

state A, based on the definition of g_two(0) = /^2 and calculate the sucess probability for

finding a photon from the input state, A, with an ideal

bucket detector. N is the dimensionality of the Fock

space

N; A

Perform the the GHZ-Gate opearations of Browne and

Rudolph, by chaining Bell-pairs with type-I fusion

State nomenclature:

in_state = |mode 1h, mode 1v, mode 2h, mode

2v,mode 3h, mode 3v, mode 4h, mode 4v>

nomenclautre of PBS: H transmitted, V reflected input

state must be a rho matrix

N; in_state; proj; un_proj

Perform mermin inequality analysis on the three

particles. Input state is in, N is the Fock spacedimesionality, detectors defined as click projector

(proj), no-click projector (unproj).

N; in; proj; un_proj

Perform GHZ state witness on three particle

entanglement. Input state is in, N is he Fock space

dimesionality, detectors defined as click projector

(proj), no-click projector (unproj); inner_norm and

outer_norm are used for post-selection purposes.

Determine the Expectation Values for the Mermin

inequality

N; in; proj; un_proj; inner_norm; outer_norm

Display the index of the states as fockstates. This

function is used in display_state4. N is the Fock space

dimension

N; max_size; index

Perform the KLM-Gate operations

State nomenclature:

in_state = |cV,tV,aux1,aux2,aux3,aux4,cH,tH> =

|mode 1, mode 2, mode 3, mode 4,mode 5, mode 6,

mode 7, mode 8>

N; in_state


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Determine the probabilities for singles (H or V) and

coincidence (HH, HV, VH, or VV) counts for two

symmetric detectors given the input state in, the Fock

dimension N, and the projector and unprojector

matrices for the detectors.

N; in; proj; unproj

Determine the probabilities for singles (H1, V1, H2, or

V2) and coincidence (HH, HV, VH, VV) counts inunsymmetric detectosrs, given the input state in and

the projector and unprojector matrices for each of the

two detectors.

N; in; proj1; unproj1; proj2; unproj2

perform the measurments for a Bell test with CH

inequaltiy and CHSH inequality. State nomenclature is:

|H1,V1,H2,V2> of the photons 1 and 2 respectively. N

is the size of the fock space per mode postselection

flag: postselection (ps=1), or no postselection (ps=0).

Detectors defined as click projector (proj1,proj2), no-

click projector (unproj1,unproj2).

N; in; proj1; unproj1; proj2; unproj2; ps

Project one side of Bell pair into an array for all

polarization directions, H,V,A,D,L,R. Fock space

dimension N, input state in, detectors defined as click

projector (proj), no-click projector (unproj)

N; in; proj; unproj

Calculates the partial trace of input state A, dimension

N. Uses normal Matlab matrices to cope with a large

number of modes

N; A

Projector for single photon sensitive detector with

efficiency effc, in. Fock-Space size N; SPD (singlephoton detector = Photon Number Resolving Detector

set for one single photon )

N; effc

Projector for single photon sensitive detector with

efficiency effc, in; Fock-Space size N. SPD (single

photon detector = Photon Number Resolving Detector

set for one single photon ). The square root of the

elements is taken for use with density matrices and

partial trace

N; effc

computes tensor product of any number of vectors or

operators. A = tensor(A1,A2,...) computes tensor

product of operators A1, A2,...

Output is no longer a QO object. Now it is a normal

sparse matrix!

A1; varargin

State nomenclature is |H1,V1,H2,V2> of the qubit 1

and 2 respectively. N is the size of the fock space per

mode; in is the input state, N is the dimensionality,

detectors defined as click projector (proj), no-click

projector (unproj

N; in; proj; unproj


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calculate interference in the switchable beam splitter

(MZ + waveplates)? calculate the cphase gate output

with a pnr-detector

Test the Signal-Noise for an entangled pair sent over

lossy channes, with background noise (e.g. detectors)

Standard definitions for quantum optics calculations

used throughout the scripts. Call this M-File within a

script after defining the Fock-space dimension, N

Testing various types of quantum sources for the G2

calculation

How to use higher order partial trace function


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Outputs

W

proj; un_proj

proj; un_proj

proj; un_proj

x

E

corr


10/11

result

g2; singl_prob

out_state

mermin_ineq

witness

state_string

out_state


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probs

probs

ch; chsh

out

rho

proj; un_proj

proj; un_proj

A

probs VisVH

Matlab QO Functions list.xls

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