Notation

Symbol				Definition
${\mathcal {H}}\,\!$				Hilbert Space
${\mathbb {C} }\,\!$				The set of complex numbers
${\mathbb {R} }\,\!$				The set of real numbers
		Chapter 2 - Qubits and Collections of Qubits
$H\,\!$				The Hadamard gate (see Section 2.3.2, Section 5.4, Eq. 2.16, and Eq. 5.10)
$X\,\!$				The Pauli X matrix (see Table 2.1)
$Y\,\!$				The Pauli Y matrix (see Table 2.1)
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$\otimes \,\!$				The Tensor Product (see Section C.7)
		Chapter 3 - Physics of Quantum Information
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$U\,\!$				The Unitary Matrix
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${\vec {n}}\,\!$				A unit vector (see Section C.5.1)
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		Chapter 4 - Entanglement
$\lambda \,\!$				A possible hidden variable (see Section 4.3)
$L\,\!$				Local operations (see Section 4.4 and Eq. 4.11)
$L\left\vert \Phi \right\rangle$				Local transformations (see Section 4.4 and Eq. 4.12)
$\left\vert \psi _{+}\right\rangle ,\left\vert \psi _{-}\right\rangle ,$
$\left\vert \phi _{+}\right\rangle ,\left\vert \phi _{-}\right\rangle$				Bell States (see Section 4.4.1 and Eq. 4.14)
		Chapter 5 - Quantum Information
$\sigma _{i}^{2}\,\!$				The variance of an observable (see Section 5.3 and Eq. 5.4)
$H\,\!$				The Hadamard gate (see Section 2.3.2, Section 5.4, Eq. 2.16, and Eq. 5.10)
$\left\vert H\right\rangle \,\!$, $\left\vert V\right\rangle \,\!$
$\left\vert D\right\rangle \,\!$, $\left\vert -D\right\rangle \,\!$				Polarization states of photons (see Section 5.6.1, Figure 5.1, and Table 5.1)
		Chapter 6 - Noise in Quantum Systems
$\rho ^{\prime }\,\!$				A linear map (see Section 6.2 and Eqs. 6.1-6.14)