quantum-state
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| Pure states are written as ket vectors $\lvert\psi\rangle = \alpha\lvert 0\rangle + \beta\lvert 1\rangle$, where $\alpha, \beta \in \CC$ and $|\alpha|^2 + |\beta|^2 = 1$. The squared magnitudes $|\alpha|^2$ and $|\beta|^2$ give the probabilities of measuring $\lvert 0\rangle$ and $\lvert 1\rangle$ respectively. When a system cannot be described by a single ket — because it is entangled with the environment or prepared as a statistical mixture — the state is instead represented by a [[density-matrix|density matrix]] $\rho$. | Pure states are written as ket vectors $\lvert\psi\rangle = \alpha\lvert 0\rangle + \beta\lvert 1\rangle$, where $\alpha, \beta \in \CC$ and $|\alpha|^2 + |\beta|^2 = 1$. The squared magnitudes $|\alpha|^2$ and $|\beta|^2$ give the probabilities of measuring $\lvert 0\rangle$ and $\lvert 1\rangle$ respectively. When a system cannot be described by a single ket — because it is entangled with the environment or prepared as a statistical mixture — the state is instead represented by a [[density-matrix|density matrix]] $\rho$. | ||
| - | The set of single-qubit pure states maps one-to-one onto the surface of the [[bloch-sphere|Bloch sphere]], where the north and south poles are $\lvert 0\rangle$ and $\lvert 1\rangle$, the equatorial $x$-axis states are $\lvert +\rangle$ and $\lvert -\rangle$, and the equatorial $y$-axis states are $\lvert +i\rangle$ and $\lvert -i\rangle$. Multi-qubit states can be entangled, meaning they cannot be written as a product of individual qubit states; the [[bell-state|Bell states]] are the canonical two-qubit entangled states. | + | The set of single-qubit pure states maps one-to-one onto the surface of the [[bloch-sphere|Bloch sphere]], where the north and south poles are $\lvert 0\rangle$ and $\lvert 1\rangle$, the equatorial $x$-axis states are $\lvert +\rangle$ and $\lvert -\rangle$, and the equatorial $y$-axis states are $\lvert +i\rangle$ and $\lvert -i\rangle$. Multi-qubit states can be entangled, meaning they cannot be written as a product of individual qubit states; the [[bell-states|Bell states]] are the canonical two-qubit entangled states. |
| - | ## List of quantum states | ||
| - | |||
| - | - [[zero-state]] | ||
| - | - [[one-state]] | ||
| - | - [[plus-state]] | ||
| - | - [[minus-state]] | ||
| - | - [[plus-i-state]] | ||
| - | - [[minus-i-state]] | ||
| - | - [[bell-state]] | ||
| - | - [[w-state]] | ||
| - | - [[ghz-state]] | ||
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