Editing Quantum Oblivious Transfer
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==Outline== | ==Outline== | ||
The demonstration of oblivious transfer protocol occurs in two phases. The preparation phase, followed by the computation phase. | |||
===Preparation phase=== | ===Preparation phase=== | ||
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The protocol is adjusted to the physical limitations of the receiver's detection apparatus. | The protocol is adjusted to the physical limitations of the receiver's detection apparatus. | ||
The receiver | The receiver tells the sender the quantum efficiency and dark count rate of his detectors. | ||
The sender | The sender then tells the intensity of the light pulses she will use, the fraction of these pulses she will expect him to | ||
detect successfully, and the bit error rate she will be willing to correct in his data to compensate for his dark counts and other noise sources. | |||
She also decides on a security parameter which she communicates to the receiver. | |||
Finally, they perform a test run to verify that the receiver indeed | Both of them agree on a linear binary error-correcting code. | ||
Finally, they perform a test run to verify that the receiver can indeed detect the pulses with the said probability and error rate. | |||
===Computation phase=== | ===Computation phase=== | ||
The sender sends a random sequence of | The sender sends a random sequence of faint pulses of the four canonical polarizations from the standard basis and the Hadamard basis. | ||
The receiver randomly decides for each pulse whether to measure it in the standard or the Hadamard basis, and records the basis and measurement | The receiver randomly decides for each pulse whether to measure it in the standard or the Hadamard basis, and records the basis and measurement result in a table. | ||
He then reports to the sender the arrival times of all pulses he received, but not the bases or the measurement results. | |||
The sender then | The sender then tells the receiver the bases she used to send each of the pulses he received. | ||
The receiver partitions his pulses into two sets: a “good” set consisting of pulses he received in the correct basis, and a “bad” set consisting of pulses he received in the | The receiver partitions his pulses into two sets: a “good” set consisting of pulses he received in the correct basis, and a “bad” set consisting of pulses he received in the wrong basis. | ||
He tells the sender the addresses of the two sets without telling which is the good and which is the bad one. | He tells the sender the addresses of the two sets without telling which is the good and which is the bad one. | ||
Now, the receiver shares with the sender a word corresponding to his good set of measurements; he shares nothing with her with respect to his bad set of measurements. | Now, the receiver shares with the sender a word corresponding to his good set of measurements; he shares nothing with her with respect to his bad set of measurements. | ||
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Using the error-correcting code, sender computes the syndromes of the words corresponding to each set, and she sends them to the receiver over an error free channel. | Using the error-correcting code, sender computes the syndromes of the words corresponding to each set, and she sends them to the receiver over an error free channel. | ||
Given this data, the receiver | Given this data, the receiver should be able to recover the original word corresponding to his good set but not that corresponding to his bad set. | ||
Furthermore, the sender computes the parity of a random subset of each set, and tells the receiver the addresses defining these random subsets, but not the resulting parities. | Furthermore, the sender computes the parity of a random subset of each set, and tells the receiver the addresses defining these random subsets, but not the resulting parities. | ||
At this point, the receiver knows one of these parities exactly, and nothing about the other parity, and he knows which parity he knows. | At this point, the receiver knows one of these parities exactly, and nothing about the other parity, and he knows which parity he knows. | ||
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* Access to an error-free classical channel. | * Access to an error-free classical channel. | ||
<br/> | |||
[[File:Quantum Oblivious Transfer.png|center|Quantum Oblivious Transfer]] | |||
==Properties== | ==Properties== | ||
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== | ==Pseudocode== | ||
===Preparation phase=== | ===Preparation phase=== | ||
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# The sender sends a random sequence of <math>2N/a</math> pulses in either of <math>\{|0\rangle, |1\rangle, |+\rangle, |-\rangle\}</math> states. | # The sender sends a random sequence of <math>2N/a</math> pulses in either of <math>\{|0\rangle, |1\rangle, |+\rangle, |-\rangle\}</math> states. | ||
# The receiver | # The receiver receives roughly <math>2N</math> pulses and randomly decides to measure each pulse in the standard or the hadamard basis and records the basis and the measurement. | ||
# He then reports to the sender the arrival times of all 2N pulses he received, but not the bases he used or his measurement results. | # He then reports to the sender the arrival times of all 2N pulses he received, but not the bases he used or his measurement results. | ||
# The sender then tells the receiver the bases she used to send each of the pulses he received. | # The sender then tells the receiver the bases she used to send each of the pulses he received. |