By Lajos Diosi
This brief and concise primer takes the vantage aspect of theoretical physics and the solidarity 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 suggestions in physics. an in depth lecture instead of a accomplished textbook, this quantity is predicated on classes brought over a number of years to complex undergraduate and starting graduate scholars, yet basically it addresses somebody with a operating wisdom of simple 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
Its eigenvalues are 0 and 1. Often the q-state, rather than x ˆ, is called the qubit. The generic pure state is a superposition of the basis vectors: c0 |0 + c1 |1 ≡ cx |x ; |c0 |2 + |c1 |2 = 1 . 3) x=0,1 This is why we say the qubit carries much richer information than the classical bit does, since the qubit can store the values 0 and 1 in parallel as well. It is q-logical operations, see Sects. 6, where the computational basis becomes indispensable. To explore the theoretical structure of a qubit, however, the well known physical representation is more convenient, cf.
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). 7) takes this form: i dˆ ρ ˆ ρˆ] . 23) of the polarization vector: ds =ω×s. 27) where a0 is a real number, a is a real vector. 28) in obvious notation.
G. . 26 4 Foundations of q-physics Aˆ = ˆ= Aλ Pˆλ , B ˆµ . 30) µ λ ˆ in subsequent projecLet us measure both q-physical quantities, Aˆ first and then B, tive measurements. 16): ρˆ → ˆ µ Pˆλ ρˆPˆλ Q ˆµ Pˆλ ρˆPˆλ Q → . 31) ˆ → Bµ is the secwhere pµλ is the probability that Aˆ → Aλ is the first, then B ond measurement outcome. Obviously, if we had performed the two measurements in the reversed order then the distribution of the measurement outcomes would in ˆ are not simultageneral be different.
A Short Course in Quantum Information Theory: An Approach From Theoretical Physics by Lajos Diosi