# Representation of a Signal and its evolution via Quantum System

I am a total beginner in the field of Quantum Mechanics. So, the question I am asking may be a silly one. So kindly give me possible answers or advice for modifications.

Recently I am learning the concept of qubit. The quantum theory tells that a $n$-qubit system is represented by a unit vector in $(\mathbb{C^2})^{\bigotimes{n}}$ with some basis set. Now, we can also express a $2^n$ dimensional complex signal as a vector at any point of time, and with suitable normalization it is nothing but a qubit.

Now, as far as I know, the evolution of a qubit is always dictated by a unitary operator, whereas, the evolution of a signal can be dictated by any arbitrary operator. So, is there any way, any sort of transformation that allows,given a signal and its evolution, to create its equivalent representation as an evolution of qubit, so that we can solve problems of signals using methods of Quantum Mechanics.

• The state of a single qubit is a unit vector in a two-dimensional, complex vector space (namely $\mathbb C^2$), so shouldn't the state of $n$ such quibits be an element of $(\mathbb C^2)^{\otimes n}$? In particular, the complex dimension of the Hilbert space should be $2^n$. – joshphysics Feb 27 '14 at 21:37
• Correct @joshphysics, I'm editing that in my question. Thanks. – Samrat Mukhopadhyay Feb 28 '14 at 9:57