By Ben Q. Li

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 technology to its fundamentals through linking it to common suggestions in physics. an intensive lecture instead of a finished textbook, this quantity relies on classes introduced over numerous years to complex undergraduate and starting graduate scholars, yet primarily it addresses someone with a operating wisdom of simple quantum physics. Readers will locate those lectures a such a lot sufficient access aspect for theoretical stories during this box.

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**Additional info for A Short Course in Quantum Information Theory: An Approach From Theoretical Physics**

**Sample text**

1 of the distribution wλ governing the structure of superposition: E (|ψAB ψAB |) = − wλ log wλ , 0 ≤ E ≤ log min{dA , dB } .

1) λ=1 l=1 where {|λ; A } and {|l; B } are certain orthogonal bases in the respective subsystems A and B. 42) where the first (Greek) one labels the basis of subsystem A while the second (Latin) index labels the basis of subsystem B. Therefore the state vector can formally be considered a matrix and we can apply the theorem of Schmidt diagonalization to it: the above two orthogonal bases can be chosen in such a way that the matrix cλl of amplitudes becomes diagonal, real, and non-negative. Taking normalization into account, we can write this theorem in the following form: Lajos Diósi: A Short Course in Quantum Information Theory, Lect.

4) l Observe that the bases and the coefficients of the Schmidt decomposition can be obtained from the eigenvectors and eigenvalues of the reduced density matrices ρˆA , ρˆB . Their spectra {wλ } and {wl } are identical, in this sense the mixednesses of ρˆA and ρˆB are identical. , the Schmidt number is 1. 2 State purification An arbitrary mixed state ρˆ of a q-system can be derived by reduction from a pure state of a suitably constructed fictitious larger composite q-system. Let us form the composite system consisting of the q-system in question and a fictitious environmental q-system E 1 .