A short course in quantum information theory an approach by Lajos Diosi

By Lajos Diosi

This brief and concise primer takes the vantage aspect of theoretical physics and the harmony of physics. It units out to strip the burgeoning box of quantum info technology to its fundamentals via linking it to common ideas in physics. an in depth lecture instead of a complete textbook, this quantity relies on classes added over a number of years to complex undergraduate and starting graduate scholars, yet basically it addresses a person with a operating wisdom of uncomplicated quantum physics. Readers will locate those lectures a such a lot sufficient access element for theoretical reviews during this box.

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5 Approximate state determination and cloning Let us calculate the average fidelity between an unknown qubit |n and its faint copy |m . Suppose Alice passes a state |n = |↑ to Bob. Bob needs a copy. 21) and he prepares his copy |m after the resulting state |↑ z or |↓ z according to the measurement outcome ±1. The average fidelity of the copy is: p↑ | ↑|↑ z |2 + p↓ | ↑|↓ z |2 . 22) Since Bob could only choose the direction z at random, the expected fidelity of the copy will be the isotropic average over all directions, that is 2/3.

5, the bank will, on average, unveil 1/3 of the forgeries while 2/3 of the forged money could be perfectly consumed. Just for this reason, as a matter of course, Alice makes more than one independent qubit-marker stick to each banknote. N qubits reduces Bob’s chances from 2/3 to (2/3)N . For Alice and the bank, a simple q-protocol may be the following. Each banknote is identified by the usual public serial number and by a private q-serialnumber. The latter is this. Each banknote contains a sequence of N independent two-state q-systems (qubits).

The expectation value of the physical quantity s parametrizes the state ρˆ: ρˆ = ˆ Iˆ + sσ ˆ ρˆ) =? 8). One must measure The three components of σ them on the given state ρˆ. , are not compatible, one must measure them in separate measurements. If the q-ensemble representing the state ρˆ consists of N elements then it is possible to consume cca. N/3 elements for the measurement of each Pauli matrix. The outcome of each measurement is 44 6 One-qubit manipulations either +1 or −1; up or down in other words.

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