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By Ben Q. Li
This brief and concise primer takes the vantage element of theoretical physics and the harmony of physics. It units out to strip the burgeoning box of quantum info technological know-how to its fundamentals via linking it to common ideas in physics. an in depth lecture instead of a entire textbook, this quantity relies on classes added over numerous years to complicated undergraduate and starting graduate scholars, yet basically it addresses an individual with a operating wisdom of easy quantum physics. Readers will locate those lectures a so much enough access element for theoretical experiences during this box.
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Extra resources for A Short Course in Quantum Information Theory: An Approach From Theoretical Physics
Example text
They calculate the parity xk ⊕ xl of the corresponding bits and substitute their original two bits by one new bit which is the parity. By iterating this procedure the information of Eve, obtained earlier, will gradually decrease until Alice and Bob will with high probability have the identical secret keys in their hands, on which Eve (or anyone else) can not have more information than a given (small) limit. We give some hint of the information theoretical proof in Sect. 7. Alice’s raw key: Alice’s qubits to Bob: Bob’s measured quantities: Bob’s measured outcomes: Bob to Alice: distributed sift key: 1 0 0 1 0 1 |↑ x |↑ z |↑ z |↑ x |↑ z |↑ x σ ˆx σ ˆx σ ˆz σ ˆz σ ˆx σ ˆz +1 -1 +1 -1 +1 +1 * * 0 1 ...
This can be generalized even further. If we allow the polarization vector n to have lengths shorter than 1 we can describe any mixed state as well: ρˆ = ˆ Iˆ + sσ ; |s| ≤ 1 . 22) The parameter s of the state is just the expectation value of the polarization vector ˆ as q-physical quantity, in the q-state ρˆ: σ, ˆ = tr (σ ˆ ρˆ) . 24) where ω is the vector of external magnetic field provided we identify the system as the electronic spin (and its giro-magnetic factor has been “absorbed” into the scale of the magnetic field).
If Eve eavesdrops the q-channel then Alice and Bob will detect it because their sift-keys will not be identical. Surely, Eve can not discriminate two non-orthogonal states without altering the original state at the same time. , she eavesdrops the q-channel too aggressively so that she may as well make the sift-keys of Alice and Bob completely uncorrelated. In this case there is nothing else left, Alice and Bob re-start the protocol. In reality, the sift-keys of Alice and Bob may differ because of the eavesdropping by Eve and/or because of the own transmission noise of the q-channel (we ignore the noise during the classical communications of the protocol).