Notation

Symbol				Definition
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 H}\,\!}				Hilbert Space
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 {\mathbb{C}}\,\!}				The set of complex numbers
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 {\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)
${\mathbb {I} }\,\!$				Identity operator
${\delta _{ij}}\,\!$				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)
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}\,\!}				The trace of a matrix (see Section C.3.5)
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 \det(N)\,\!}				The determinant of a matrix (see Section C.3.6)
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 \vec{n}\,\!}				A unit vector (see Section C.5.1)
$\lambda _{\pm }$				Eigenvalues (see Section C.6)
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 \langle \mathcal{O} \rangle}				The expectation value of an operator (see Eqs. 3.47 - 3.48)
		Chapter 4 - Entanglement
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 \,\!}				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)
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\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,}
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 \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)
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 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 \left\vert H\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 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
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^\prime\,\!} , 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\,\!}				Linear mapping vectors (see Eqs. 6.1 - 6.14)
$A\,\!$				The mapping matrix (see Eqs. 6.6 - 6.12)
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 H_{S}\,\!}				The Hamiltonian for the system alone (see Eq. 6.15)
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 H_{B}\,\!}				The Hamiltonian for the bath alone (see Eq. 6.15)
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_{\gamma }\,\!}				Operator on the system (see Eq. 6.15)
$B_{\gamma }\,\!$				Operator on the bath (see Eq. 6.15)
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_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
$P\,\!$				A projector onto the code space
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(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 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 -\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 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 \{H_S,S_\alpha\}\,\!} (see Section 8.2)
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 S_\alpha\,\!}				Acts only on the system (see Section 8.2 and Eq. 8.2)
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 B_\alpha\,\!}				Acts only on the bath (see Section 8.2 and Eq. 8.2)
$U_{dns}\,\!$				A particular unitary transformation (see Section 8.2)
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 H_{cpe}\,\!}				Collective phase error Hamiltonian (see Section 8.3.1 and Eq. 8.3)
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 Z^{(i)}\,\!}				A phase operator which acts on the 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 i\,\!} th qubit (see Section 8.3.1 and Eq. 8.3)
$S_{x}\,\!$, 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_y\,\!} , 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_z\,\!}				The three collective errors (see Eq. 8.9)