Download A Short Course In Quantum Information Theory An Approach by Lajos Diosi PDF

By Lajos Diosi

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 technology to its fundamentals by means of linking it to common thoughts in physics. an intensive lecture instead of a entire textbook, this quantity is predicated on classes introduced over numerous years to complicated undergraduate and starting graduate scholars, yet primarily it addresses somebody with a operating wisdom of uncomplicated quantum physics. Readers will locate those lectures a so much sufficient access aspect for theoretical reports during this box.

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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 . 35) of the state ρˆ of the original q-system: wλ |λ λ| . 3. 6) λ where we assume that the dimension of E is not less than the dimension of the original system. 3). 5) of the original q-system: ρˆ = trE (|ψbig ψbig |) .

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 .

1) x=0,1 Also the primitive binary q-physical quantity x ˆ is defined in the computational basis: x |x x| = |1 1| . 2) x=0,1 This is the (singular) 2 × 2 hermitian matrix of the qubit, as q-physical quantity. 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.

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