Notation

Symbol				Definition
${\mathcal {H}}\,\!$				Hilbert Space
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		Chapter 2 - Qubits and Collections of Qubits
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$X\,\!$				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
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		Chapter 3 - Physics of Quantum Information
$H\,\!$				The Hamiltonian (see Eqs. 3.1 - 3.4)
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$\rho \,\!$				The Density Matrix or Density Operator (see Appendix E - Density Operator: Extensions)
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${\vec {n}}\,\!$				A unit vector (see Section C.5.1)
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$\langle {\mathcal {O}}\rangle$				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)
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$\left\vert \phi _{+}\right\rangle ,\left\vert \phi _{-}\right\rangle$				Bell States (see Eq. 4.14)
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		Chapter 5 - Quantum Information
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$H\,\!$				The Hadamard gate (see Section 2.3.2, Section 5.4, Eq. 2.16, and Eq. 5.10)
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		Chapter 6 - Noise in Quantum Systems
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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)
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$S_{\gamma }\,\!$				Operator on the system (see Eq. 6.15)
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		Chapter 7 - Quantum Error Correcting Codes
$A_{\alpha }\,\!$				Operator element
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${\mathcal {S}}\,\!$				The stabilizer
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$P_{1}\,\!$				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 $\{H_{S},S_{\alpha }\}\,\!$(see Section 8.2)
$S_{\alpha }\,\!$				Set of error operators acting only on the system (see Section 8.2 and Eq. 8.2)
$B_{\alpha }\,\!$				Acts only on the bath (see Section 8.2 and Eq. 8.2)
$U_{dns}\,\!$				A particular unitary transformation (see Section 8.2)
$H_{cpe}\,\!$				Collective phase error Hamiltonian (see Section 8.3.1 and Eq. 8.3)
$Z^{(i)}\,\!$				A phase operator which acts on the $i\,\!$th qubit (see Section 8.3.1 and 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 (see Section 8.3.2)