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 details technology to its fundamentals by means of linking it to common ideas in physics. an intensive lecture instead of a complete textbook, this quantity is predicated on classes added over numerous years to complex undergraduate and starting graduate scholars, yet basically it addresses a person with a operating wisdom of uncomplicated quantum physics. Readers will locate those lectures a such a lot enough access element for theoretical reports during this box.

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Draw an element of it at random and suppose that we can copy and multiply it in N examples. 15) then we have N copies either of z-up or z-down states in our hands. For very large N , this method allows us to explore, with high reliability, which states the depolarized ensemble had been mixed from. In particular, the alternative x-up/down states can be excluded. This would, however, contradict to the principle that a q-ensemble is uniquely and exhaustively determined by its density matrix. In summary, the unknown q-state of a single physical system can never be implemented on the other single system so that it, too, bear the same q-state.

The Schmidt number is 1. 2 State purification An arbitrary mixed state ρˆ of a q-system can be derived by reduction from a pure state of a suitably constructed fictitious larger composite q-system. Let us form the composite system consisting of the q-system in question and a fictitious environmental q-system E 1 . 35) of the state ρˆ of the original q-system: wλ |λ λ| . 3. 6) λ where we assume that the dimension of E is not less than the dimension of the original system. 3). 5) of the original q-system: ρˆ = trE (|ψbig ψbig |) .

The cumulative influence of the four logical q-operations is the following: ˆ Tˆ(θ)H ˆ |0 = e−i(ϕ/2)−i(π/4) cos θ |0 + eiϕ sin θ |1 Tˆ( 12 π + ϕ)H 2 2 . s. 6) of a qubit. Furthermore, it can be proved that by the combinations of the operations ˆ and Tˆ(ϕ) one can perform all one-qubit unitary operations. Therefore we call the H ˆ and the Tˆ(ϕ) a set of universal one-qubit operations. This becomes important for H the theory of q-computation in Chap. 11. 2 Depolarization, re-polarization, reflection The q-measurement is the most important operation among the irreversible ones.

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