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)
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)
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\,\!}				The Pauli Y matrix (see Table 2.1)
$Z\,\!$				The Pauli Z matrix (see Table 2.1)
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}}\,\!}				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 {\delta_{ij}}\,\!}				The Kronecker delta (see Equation C.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 {\epsilon_{ijk}}\,\!}				Epsilon (see Equation C.8)
$\otimes \,\!$				The Tensor Product (see Section C.7)
		Chapter 3 - Physics of Quantum Information
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 Hamiltonian
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 \hbar\,\!}				H-bar (Planck's constant divided by 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 2\pi\,\!} )
$U\,\!$				The Unitary Matrix
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\,\!}				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 Section 3.6)
		Chapter 4 - Entanglement
$\lambda \,\!$				A possible hidden variable (see Section 4.3)
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 L\,\!}				Local operations (see Section 4.4 and 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 Section 4.4 and 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 Section 4.4.1 and 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 Section 4.5.1)
		Chapter 5 - Quantum Information
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 \sigma^2_i\,\!}				The variance of an observable (see Section 5.3 and 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)
$\left\vert H\right\rangle \,\!$, 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\,\!}
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\,\!} , 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 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)
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\,\!}				The mapping matrix (see Section 6.2 and 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 Section 6.3.1 and 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 Section 6.3.1 and Eq. 6.15)
$S_{\gamma }\,\!$				Operator on the system (see Section 6.3.1 and Eq. 6.15)
$B_{\gamma }\,\!$				Operator on the bath (see Section 6.3.1 and Eq. 6.15)
$\rho _{S}(0)\,\!$				The initial density matrix of the (open) system (see Section 6.3.1 and Eq. 6.16)
$\rho _{B}(0)\,\!$				The initial density matrix of the bath (see Section 6.3.1 and Eq. 6.16)
		Chapter 7 - Quantum Error Correcting Codes