Qubit, An Intuition #3 — Quantum Measurement, Full and Partial Qubits

The beauty of Quantum Mechanics for Quantum Computation, featuring IBM Quantum

Andi Sama — CIO, Sinergi Wahana Gemilang with Cahyati S. Sangaji

TL;DR; 
Quantum measurement for full and partial qubits, with examples. Quantum state. Pure state.
Please refer to the previous articles:
“Qubit, An Intuition #1 — First Baby Steps in Exploring the Quantum World” for a discussion on a single qubit as a computing unit for quantum computation.
- "Qubit, An Intuition #2 - Inner Product, Outer Product, and Tensor Product" for a discussion on two-qubits operations.

For an introductory helicopter view of the overall six articles in the series, please visit this link “Embarking on a Journey to Quantum Computing — Without Physics Degree.”

In the last two articles on the “Qubit, An Intuition” series, we have discussed the basics of a quantum bit (qubit) and two-qubits operations: inner product, outer product, as well as the tensor product. In this article, we discuss quantum measurement, the observation of quantum states that change the wave function Psi |Ψ> from a superposition state to a pure quantum state.

Qubit and Two-Qubits operations

A single quantum bit (qubit) is exciting with its nature of being in superposition. Hence |Ψ> = α|0> + β|1>. The quantum state Psi is in the linear combination of |0> and |1> with the probability of being in state |0> is |α|², and the probability of being in state|1> is |β|².

α and β are the probability amplitudes while α* and β* are the complex conjugate of α and β, respectively. It fulfills the normalization constraint, such that |α|²+|β|²=1 or α*α+β*β=1, where α, β ∈ ℂ².

An inner product is a product of two quantum states bra Psi <Ψ| and ket Phi |Φ>, producing a value. An inner product is also called an overlap, the overlap between quantum states.

An outer product is a product of two quantum states, ket Psi|Ψ> and bra Phi <Φ|, producing a matrix. The outer product is also called a projection.

A tensor product is a product of two quantum states, ket Psi|Ψ> and ket Phi |Φ>, producing a column vector with length 2ⁿ…