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)
$Z\,\!$				The Pauli Z matrix (see Table 2.1)
${\mathbb {I} }\,\!$				The
${\delta _{ij}}\,\!$				The Kronecker delta (see Equation C.17)
${\epsilon _{ijk}}\,\!$				Epsilon (see Equation C.8)
$\otimes \,\!$				The Tensor Product (see Section C.7)
		Chapter 3 - Physics of Quantum Information
$H\,\!$				The Hamiltonian (see Eqs. 3.1 - 3.4)
$\hbar \,\!$				H-bar (Planck's constant divided by $2\pi \,\!$)
$U\,\!$				The Unitary Matrix (see Eqs. 3.5 - 3.6)
$\rho \,\!$				The Density Matrix or Density Operator (see Appendix E - Density Operator: Extensions)
${\mbox{Tr}}\,\!$				The trace of a matrix (see Section C.3.5)
$\det(N)\,\!$				The determinant of a matrix (see Section C.3.6)
${\vec {n}}\,\!$				A unit vector (see Section C.5.1)
$\lambda _{\pm }$				Eigenvalues (see Section C.6)
$\langle {\mathcal {O}}\rangle$				The expectation value of an operator (see Eqs. 3.47 - 3.48)
		Chapter 4 - Entanglement
$\lambda \,\!$				A possible hidden variable (see Eqs. 4.4 - 4.9)
$L\,\!$				Local operations (see Eq. 4.11)
$L\left\vert \Phi \right\rangle$				Local transformations (see 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 Eq. 4.14)
${\mbox{Tr}}_{B}(\rho _{ss})\,\!$				The partial trace over one of the subsystems (particle states) of a composite system (see Eq. 4.19)
		Chapter 5 - Quantum Information
$\sigma _{i}^{2}\,\!$				The variance of an observable (see 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 Figure 5.1 and Table 5.1)
		Chapter 6 - Noise in Quantum Systems
$\rho ^{\prime }\,\!$				A linear map (see Eqs. 6.1 - 6.14)
$A\,\!$				The mapping matrix (see Eqs. 6.6 - 6.12)
$H_{S}\,\!$				The Hamiltonian for the system alone (see Eq. 6.15)
$H_{B}\,\!$				The Hamiltonian for the bath alone (see Eq. 6.15)
$S_{\gamma }\,\!$				Operator on the system (see Eq. 6.15)
$B_{\gamma }\,\!$				Operator on the bath (see Eq. 6.15)
$\rho _{S}(0)\,\!$				The initial density matrix of the (open) system (see Eq. 6.16)
$\rho _{B}(0)\,\!$				The initial density matrix of the bath (see Eq. 6.16)
		Chapter 7 - Quantum Error Correcting Codes