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Weak String Erasure: Difference between revisions
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==Outline== | ==Outline== | ||
Alice and Bob first agree on a duration <maths>Delta t</math> that should correspond to an estimation of the time needed to make any known quantum memory decoheres. The protocol can be decomposed into three parts. | Alice and Bob first agree on a duration <maths>\Delta t</math> that should correspond to an estimation of the time needed to make any known quantum memory decoheres. The protocol can be decomposed into three parts. | ||
*'''Distribution''' This step involves preparation, exchange and measurement of quantum states. Alice chooses a random basis among the X or Z bases. She then chooses at random one of the two states of this basis, prepares this state and sends it over to Bob. Upon receiving the state from Alice, Bob will choose a random basis among the X or Z bases, and measure the incoming qubit in this basis. They both record the basis they have used, Bob also records his measurement outcome, and Alice record which state she has sent. Both parties repeat this procedure n times. | *'''Distribution''' This step involves preparation, exchange and measurement of quantum states. Alice chooses a random basis among the X or Z bases. She then chooses at random one of the two states of this basis, prepares this state and sends it over to Bob. Upon receiving the state from Alice, Bob will choose a random basis among the X or Z bases, and measure the incoming qubit in this basis. They both record the basis they have used, Bob also records his measurement outcome, and Alice record which state she has sent. Both parties repeat this procedure n times. | ||
*'''Waiting time''' Both parties will wait for time <maths>Delta t</math>. This is to force a malicious party to store part his quantum state in his memory. Of course he will be limited by the size of his quantum memory. | *'''Waiting time''' Both parties will wait for time <maths>\Delta t</math>. This is to force a malicious party to store part his quantum state in his memory. Of course he will be limited by the size of his quantum memory. | ||
* '''Classical post-processing''' Alice will send to Bob, the bases she has used to prepare her states. Bob will erase all the measurement outcomes of the rounds where he measured in a different basis than Alice has prepared the state.</br> | * '''Classical post-processing''' Alice will send to Bob, the bases she has used to prepare her states. Bob will erase all the measurement outcomes of the rounds where he measured in a different basis than Alice has prepared the state.</br> | ||
The losses in the transmission happen in the distribution step when Bob measure the incoming qubit in different basis as the one Alice has chosen for the preparation. | The losses in the transmission happen in the distribution step when Bob measure the incoming qubit in different basis as the one Alice has chosen for the preparation. | ||