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)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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)
${\mathbb {I} }\,\!$				Identity operator
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\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)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L\,\!}				Local operations (see Eq. 4.11)
$L\left\vert \Phi \right\rangle$				Local transformations (see Eq. 4.12)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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)
$\left\vert H\right\rangle \,\!$, $\left\vert V\right\rangle \,\!$
$\left\vert D\right\rangle \,\!$, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left\vert -D\right\rangle\,\!}				Polarization states of photons (see Figure 5.1 and Table 5.1)
		Chapter 6 - Noise in Quantum Systems
$\rho ^{\prime }\,\!$, $\rho \,\!$				Linear mapping vectors (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)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_{B}(0)\,\!}				The initial density matrix of the bath (see Eq. 6.16)
		Chapter 7 - Quantum Error Correcting Codes
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_\alpha\,\!}				Operator element
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P\,\!}				A projector onto the code space
$C(n,t)\;\!$				The binomial coefficient (see Eq. 7.17)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m\;\!}				The number of code words (see Eq. 7.17)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{S}\,\!}				The stabilizer
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{S}\subset \mathcal{P}_n \,\!}				An abelian subgroup of the Pauli group that does not contain $-\mathbb {I} ,\pm i\mathbb {I} \,\!$
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{C}(\mathcal{S})\,\!}				A stabilizer code
$P_{1}\,\!$				Classical parity check matrix (see Eq. 7.21)
$G\,\!$				The generator matrix (see Eq. 7.22)
		Chapter 8 - Decoherence-Free/Noiseless Subsystems
$H_{S}\,\!$				Hamiltonian acting only on the system (see Eq. 8.1)
$H_{B}\,\!$				Hamiltonian acting only on the bath (see Eq. 8.1)
$H_{I}\,\!$				The interaction Hamilton (see Eqs. 8.1 and 8.2)
${\mathcal {A}}\,\!$				Denotes the "error algebra" generated by the set $\{H_{S},S_{\alpha }\}\,\!$
$S_{\alpha }\,\!$				Set of error operators acting only on the system (see Eq. 8.2)
$B_{\alpha }\,\!$				Acts only on the bath (see Eq. 8.2)
$U_{dns}\,\!$				A particular unitary transformation
$H_{cpe}\,\!$				Collective phase error Hamiltonian (see Eq. 8.3)
$Z^{(i)}\,\!$				A phase operator which acts on the $i\,\!$th qubit (see Eq. 8.3)
$S_{x}\,\!$, $S_{y}\,\!$, $S_{z}\,\!$				The three collective errors (see Eq. 8.9)
$U_{dns}\,\!$				Unitary transformation corresponding to the collection of Wigner-Clebsch-Gordan coefficients
${\mathcal {C}}^{\perp }\,\!$				The orthogonal subspace (to the code) (see Eq. 8.17)
$\Psi \,\!$				An encoded state
$\{\Lambda _{i}\}\,\!$				Basis for the noise operators
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S\in\mathcal{S} \,\!}				The stabilizer element (see Eq. 8.18)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C\,\!}				Casimir operator (see Eqs. 8.22 - 8.24)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda_\alpha \,\!}				Elements of the Lie algebra (see Eqs. 8.22 - 8.26, Eq. D.21, Section D.7.1 and Sections D.8.1 - D.8.3)
$H\,\!$				The Hamiltonian
$\mu _{ijk}\,\!$				A complete set of Hermitian matrices in terms of which any Hermitian matrix can be expanded
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_i\,\!}				Form a basis for the stabilizer of the system
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_i g_i S_i\,\!}				An arbitrary linear combination of those stabilizer elements
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_{ijk}\,\!}				A set of real numbers
$g_{i}\,\!$				Arbitrary coefficients
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{X} \,\!}				A logical Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X \,\!} operation (see Eqs. 8.28 - 8.34)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{Z} \,\!}				A logical $Z\,\!$ operation (see Eqs. 8.29 - 8.35)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{Y} \,\!}				A logical Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y \,\!} operation (see Section 8.5.2)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{ZZ}, \,\!}				A logical two-qubit entangling gate (see Eq. 8.30)