A Short Course in Quantum Information Theory: An Approach by Ben Q. Li PDF

By Ben Q. Li

ISBN-10: 1846282055

ISBN-13: 9781846282058

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 complete textbook, this quantity is predicated on classes brought over numerous years to complicated undergraduate and starting graduate scholars, yet primarily it addresses a person with a operating wisdom of easy quantum physics. Readers will locate those lectures a so much enough access aspect for theoretical stories during this box.

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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. This vanishes only when a and b are parallel vectors. Then, ˆ are simply functions of each other. 4. 13). The three q-physical quantities σ ˆn , Pˆn , Pˆ−n are functions of each other.

23): HAB = C dA ⊗ C dB = {cλl ; λ = 1, . . , dA ; l = 1, . . , dB } . 41) The pure state of the composite system is described by the normalized state vector of dimension dA dB : |ψAB = {cλl } ; |cλl |2 = 1 . 42) λ,l If the two subsystems are uncorrelated then the state vector of the composite system is a tensor product: 28 4 Foundations of q-physics |ψAB = |ψA ⊗ |ψB = {cAλ cBl } . 3): ρˆAB = {ρ(λl)(µm) }. 44) The reduced state of subsystem A is obtained by tracing the composite q-system’s state over the Hilbert space of subsystem B: ρˆA = trB ρˆAB = ρ(λl)(µl) ≡ Mˆ ρAB .

3, of our q-system by cloning it to replace the prepared state |ψ0 of another q-system with the same dimension of Hilbert space. Let us prove that the map |ψ ⊗ |ψ0 → |ψ ⊗ |ψ can not be unitary. Method: let us test whether the above transformation preserves the value of inner products. 5 Two-state q-system: qubit representations Obviously the simplest q-systems are the two-state systems. Typical realization are an atom with its ground state and one of its excited states, a photon with its two polarization states, or an electronic spin with its “up” and “down” states.

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A Short Course in Quantum Information Theory: An Approach From Theoretical Physics by Ben Q. Li

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