What are the difference between quantum state, quantum system and qubit(s)?


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Quantum state: what a quantum system is in. It can be represented by a state vector, i.e., a normalized vector $|\psi\rangle \in \mathcal{H}^{2^n}$ where $n$ is the number of qubits in the system. (The state doesn’t need to be necessarily of a system composed of two-level quantum systems such as the qubit, it can be made up of quantum systems of any level; in general the state vector will be in $\mathcal{H}^{k^n}$ for a system composed of $n$ $k$-level units). It can also be represented as a density matrix.

Quantum system: it is a physical system that obeys the laws of quantum mechanics. It is made up of several smaller systems. Specific to quantum computing, it can be the tensor product of all the qubits you’re working on. In this case, the larger system is $|\psi_0\rangle\otimes|\psi_1\rangle\otimes\cdots\otimes|\psi_n\rangle$ where each $|\psi_i\rangle$ may be itself made up of one or more qubits.

Qubit: a two-level quantum mechanical system. It is the basic unit of quantum information and an analogue of the classical bit. It’s one of the simpler quantum systems that portrays the peculiar phenomena of quantum mechanics.


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