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We can describe the state of any quantum system by a state vector in a
Hilbert space. A Hilbert space is a complex linear vector space
[18]. In the Hilbert space for a
state vector describing an *N*-state quantum system there will be *N*
perpendicular axes, which correspond to the measurable states of the
system. These are called basis states or *eigenstates*. In
general, the total state of a quantum system can be any complex linear
combination of the basis states. The Hilbert space for a single qubit
has two perpendicular axes, one corresponding to the 0 state, and the
other corresponding to the 1 state.

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Matthew Hayward Lower Query Bounds in the Quantum Oracle Model GitHub Repository