A Short Course In Quantum Information Theory An Approach by Lajos Diosi

By Lajos Diosi

This brief and concise primer takes the vantage element of theoretical physics and the solidarity of physics. It units out to strip the burgeoning box of quantum info technology to its fundamentals by means of linking it to common suggestions in physics. an intensive lecture instead of a accomplished textbook, this quantity relies on classes added over numerous years to complicated undergraduate and starting graduate scholars, yet basically it addresses somebody with a operating wisdom of uncomplicated quantum physics. Readers will locate those lectures a so much enough access element for theoretical stories during this box.

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If the length of the key is still big enough, then Alice and Bob moves to privacy amplification. At the price of further shortening the key, it reduces the information that may has earlier been acquired by Eve. Once again, in public classical communication, Alice and Bob single out randomly the same two locations k, l from their keys. 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.

But generally there is some, and then there can be q-correlation as well. Symbolically, we write: ρˆAB = ρˆA ⊗ ρˆB + cl. corr. + q-corr. 26). The q-correlations are absent if and only if the state of the composite q-system is separable. In other words, if it can be prepared as a statistical mixture of tensor product (uncorrelated) states8 : wλ ρˆAλ ⊗ ρˆBλ ; wλ ≥ 0; ρˆAB = λ wλ = 1 . 47) λ Then and only then there are no q-correlations but classical ones at most. In the contrary case, if ρˆAB can not be written into the above form, then the subsystems A and B are said to be in entangled composite state.

Both the classical and q-channels are public, anybody has the access to the bits or q-bits travelling through them. Yet, the resulting sift-key is protected from unnoticed eavesdropping. Eve can unnoticedly eavesdrop the classical channel but she does not obtain any useful knowledge regarding the sift-key. She must concentrate on the q-channel and intercept some of the qubits. 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.

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