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 info technological know-how to its fundamentals by means of linking it to common strategies in physics. an in depth lecture instead of a accomplished textbook, this quantity is predicated on classes introduced over numerous years to complicated undergraduate and starting graduate scholars, yet primarily it addresses someone with a operating wisdom of easy quantum physics. Readers will locate those lectures a so much enough access aspect for theoretical experiences during this box.

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1007/3-540-38996-2_7 54 7 Composite q-system, pure state {cλl } = √ wλ δλl , λ, l = 1, 2, . . min{dA , dB } . 2) Observe that we have formally written the normalized non-negative amplitudes as the square-roots of a normalized probability distribution wλ whose interpretation becomes clear below. The Schmidt decomposition generalizes the diagonal expansion of hermitian matrices, cf. Sect. 4, for arbitrary, even non-quadratic matrices. The rank of the given matrix coincides with the number of the nonzero diagonal terms, called also the Schmidt number.

Universality of Hadamard and phase operations. Let us show that all 2 × 2 unitary matrices (upto a complex phase) can be constructed by the repeated applicaˆ and the phase-operation Tˆ(ϕ). Method: use Euler angles tion of the Hadamard- H of rigid body rotation kinematics. 2. Statistical error of qubit determination. Suppose Alice hands over N identically prepared qubits ρˆ to Bob but she does not tell Bob what the state ρˆ is. 2. 4 Applications of no-cloning and indistinguishability 51 the estimation errors ∆sx , ∆sy , ∆sz in function of s and the number of single state measurements.

How long time must the field be switched on? 5. Interrelated q-bit physical quantities. Write down all pairwise relationships for the matrices σ ˆn , Pˆn , Pˆ−n . 6. Mixing non-orthogonal polarizations. Suppose we mix the pure states |↑ z and |↑ x together at rate 1/3 : 2/3. Write down the polarization vector s of the resulting mixed state. , on a single qubit. Entanglement can certainly not, we shall present it on composite systems in Chap. 7. The present Chapter teaches the elements of q-state manipulation and various simple instances of the q-informatic approach.

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