By Ben Q. Li
This brief and concise primer takes the vantage aspect of theoretical physics and the team spirit of physics. It units out to strip the burgeoning box of quantum info technological know-how to its fundamentals by means of linking it to common innovations in physics. an in depth lecture instead of a finished textbook, this quantity relies on classes introduced over a number of years to complicated undergraduate and starting graduate scholars, yet primarily it addresses an individual with a operating wisdom of easy quantum physics. Readers will locate those lectures a such a lot sufficient access element for theoretical reviews during this box.
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Additional resources for A Short Course in Quantum Information Theory: An Approach From Theoretical Physics
Let us note that the combinations of onequbit unitary operations and projective measurements can not represent all possible one-qubit q-operations. These become available if the qubit forms an interacting composite system with an environmental q-system, cf. Chap. 8. 1 Logical operations In q-physics, coherent operations are reversible, unitary transformations. If the coherent operation is applied to an unknown q-state then the state remains invariably unknown after the operation. 17). Now we are going to consider those rotations which play a distinguished role for the logical operations on qubits.
Two arbitrarily chosen q-physical quantities are, however, not compatible in general. 11) of a given q-physical quantity, will always commute, they are compatible, hence they can be measured simultaneously, cf. Sect. 1, in projective measurements. Certain incompatible physical quantities can be measured in non-projective measurements. 12) are not compatible ˆ n may not commute. 1: we lose repeatability of the measurement. 13) simplify significantly for a pure state ρˆ = |ψ ψ|. The measurement outcome is still one of the eigenvalues Aλ .
N . 53) If Aˆ is a q-physical quantity of the elementary subsystem then, in a natural way, one can introduce its arithmetic mean, over the n subsystems, as a collective q-physical quantity: Aˆ ⊗ Iˆ⊗(n−1) + Iˆ ⊗ Aˆ ⊗ Iˆ⊗(n−2) + · · · + Iˆ⊗(n−1) ⊗ Aˆ . 54) Collective q-physical quantities are not necessarily of such simple form. Their measurement is the collective q-measurement. Contrary to the classical theory, not all collective q-measurements can be reduced to independent measurements on the n subsystems, cf.
A Short Course in Quantum Information Theory: An Approach From Theoretical Physics by Ben Q. Li