Localisation-based two-photon wave-function information encoding

Files Data_16__V2.zip and Data_36__V2.zip contain the raw data from the experiment from which all the datapoints in the paper “Localisation-based two-photonwave-function information encoding” are extracted. Each file is relative to N=16 states and N=36 states encoding, meaning that each photon is encoded into one of N possible states. The files are like “Counts_34_LaP_20_Side_30_.mat” so with a structure of the type: Counts_ MESSAGE_LABEL _LaP_ POISS _Side_ MAGINDX _.mat Where the parameters are: MESSAGE_LABEL: indicates the label of the message to be sent: it is a number indicating the specific pixel of the Detector which should receive the photons. POISS : indicates the mean of the Poissonian distribution of the photons which is set by attenuating the coherent source. MAGINDX: indicates the degree of demagnification on the experimental setup. The optical fiber output tip indeed is demagnified on the Detector. If the MAGINDX is 30 then only a 4x4 array of the detector is used. If the MAGINDX is 15 then only a 6x6 array of the detector is used. The files contain several Matlab Observables. “Counts”: it is the raw data matrix. Data are organized into a SxSXNFrames matrix. S is the side (in pixels, which are actually single photon detectors organized into a square array) of the detector which could be 10 or 20. The numbers in the matrix indicate the counts obtained by the relative pixel in a given frame. In the measurements just a subset of the pixels are employed depending on the magnification on the detector. In the N=16 case just the 4X4 central area of the detector has been used an thus just this area should be considered for analysis. NFrames is the number of “trials” : the number of times we tried to sent a single message to BOB. The message, indicated by the “State_Label”, correspond to the index of the detector which should (if losses or basis error are not present) receive the photon emitted from the source and reflected by the SLM. We call data obtained in a single trials from all detectors (a matrix SxS) Frames. “Counts_AVG”: is the Frame obtained by summing all data on Counts along the 3 dimension that is summing all the trials. Imaging the Counts_AVG with the imagesc(Counts_AVG) command in Matlab highlight immediately the pixel which should receive the photons if no errors are present. “State_Label”: Indicate the label of the pixels on which the photons have been focused exploiting the SLM. “Labeling”: Is a SxS matrix reporting the labeling of all the pixels on the detector array.<br>The message sent in a given frame is obtained by extracting a single Frame (Frame= Counts(:,:,FI) ) with FI the frame index to be analyzed. Then one have to check if a single photon has been detected (a single dectector must show a single count) . In the case the Frame is empty the frame is not considered. The message sent is the extracted as the label of the pixels counting a single photon (comparing the frame with the labeling matrix) To extract P_{err}/P_{corr} we consider the number of frames containing the right label (State_Label) against the frames which (due to dark counts) contain a state different form State_Label. To estimate the efficiency of a malicious eavesdropper stealing the information W compared the rate of Mutiphoton pulses (two photons detected during the gate) with the P_{corr}.<br>