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 harmony of physics. It units out to strip the burgeoning box of quantum info technological know-how to its fundamentals by way of linking it to common recommendations in physics. an in depth lecture instead of a finished textbook, this quantity is predicated on classes brought over a number of years to complex undergraduate and starting graduate scholars, yet basically it addresses an individual with a operating wisdom of uncomplicated quantum physics. Readers will locate those lectures a such a lot sufficient access aspect for theoretical reviews during this box.

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36) And the probability distribution of the measurement outcome can be written as the squared modulus of the inner product between the new and the old state vectors: pλ = ψ| · |ϕλ ϕλ | · |ψ = | ϕλ |ψ |2 . 37) Most often, the description of the quantum measurement happens in such a way that we expand the pre-measurement pure state in terms of the eigenvectors of the physical quantity to be measured: |ψ = cλ |ϕλ . 38) λ In this representation the measurement takes place this way:     0 c1 0  .

7. The present Chapter teaches the elements of q-state manipulation and various simple instances of the q-informatic approach. 1 One-qubit operations We present the reversible logical operations on single qubits, whose combinations can represent all unitary one-qubit operations. Then we discuss the example of depolarization q-operation generated by polarization measurements. We learn the notorious polarization reflection which is not a q-operation: by classical analogy it were realizable but it turns out not to be so.

This is a genuine two-state q-system, its formalism is covariant for spatial rotations which guarantees conceptual and calculational advantage. 1 State space The generic pure state of a two-state q-system takes the following form in a certain orthogonal basis of “up” and “down” states: c↑ |↑ + c↓ |↓ ; |c↑ |2 + |c↓ |2 = 1 . 4) An obvious parametrization takes normalization and the free choice of the complex phase into the account: θ θ cos |↑ + eiϕ sin |↓ . 5) 2 2 The angular parameters θ, ϕ can be identified with the standard directional angles of a 3-dimensional real unit vector n.

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