Alice and Bob need to share a secret perfectly random sequence of zeros and ones (a so-called secure key), but cannot meet in person. Classically this is impossible, as they can never be certain that the key was not intercepted during transmission. Quantum mechanics makes secure key generation possible!
In this simulation, you can help Alice and Bob generate a secure key using polarized photons. Alice prepares each photon polarization in one of two bases, either H/V (horizontal/vertical) or +45/-45 (at ±45 degrees from the vertical), using a polarizer oriented along one of these four directions. The vertical and -45 degree orientations are assigned a value of 1, the horizontal and +45 degree orientations a value of 0. In the simulation, the states |H〉, |V〉, |+45〉, |-45〉 refer to photon states with horizontal, vertical, +45 and -45 degree polarization respectively.
Alice sends the polarized photon to Bob, who is equipped with a polarization analyzer and a single photon detector. Bob randomly chooses one of the two bases, and orients his analyzer along one of the directions in this basis. Alice informs Bob whenever she sends a photon.
Bob either registers a photon in his detector or not, determining his bit value. For example, if Bob orients his analyzer horizontally but does not detect a photon, his bit value is 1 (vertical in the H/V basis).
Alice and Bob note independent of one another the basis (H/V or +45/-45) and bit value (0 or 1) for each particle. They know that their bit values are the same when they both happened to choose the same basis. After completing the measurements, Alice and Bob publicly share the bases used (but not the values!), and keep only those values for which their bases were the same – this is the key. Alice and Bob then exchange a small number of their values (which they then discard) to check for errors.
Your goal is to help Alice and Bob decide whether or not they have generated a secure key. How can they tell that an eavesdropper Eve has infiltrated their experiment?
Click on the virtual reality goggles that allow you to “see” the photons to start sending photons from Alice to Bob and to eavesdrop by intercepting and resending photons.Assuming no eavesdropper has intervened, what sequence of outcomes could Bob have measured? Choose one or more.
Assuming no eavesdropper has intervened, how many bits are there in Alice and Bob's shared key?
Assuming no eavesdropper has intervened, what sequence of key bits could Alice and Bob have measured (most recent key bit first)?
Alice and Bob decide to compare the bit shown to determine if Eve was intercepting. They find that they do not agree. For this bit, what basis must Eve have used for her measurement?
Alice and Bob decide to compare the bit shown to determine if Eve was intercepting. They find that they do not agree. For this bit, what value did Eve obtain in her measurement?
Alice and Bob decide to compare the bit shown to determine if Eve was intercepting. They find that they agree. For this bit, what basis must Eve have used for her measurement?
It is not possible to tell from
the information given
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