Final answer:
Another qubit |q> orthogonal to the given qubit |p> can be |q>=√8/9|0>+i/3|1>. They form an orthogonal basis in the Hilbert space, a concept closely related to the Pauli exclusion principle in quantum mechanics.
Step-by-step explanation:
The question asks for another qubit |q> that could be the orthogonal counterpart to the given qubit |p>=i/3|0>−√8/9|1> in an orthogonal basis. Since the qubits are in a two-state quantum system, the orthogonal qubit must have amplitudes that are orthogonal to |p> under the vector inner product. We can calculate |q> by setting its amplitudes to be orthogonal to those of |p>. One possible qubit that satisfies this condition could be |q>=√8/9|0>+i/3|1>, where the inner product equals 0, as required.
Orthogonal qubits are fundamental in quantum mechanics, as they form a basis for the two-dimensional Hilbert space of a qubit. This is tied to the concepts like the Pauli exclusion principle, which applies to systems of identical particles with half-integral spin, like electrons.