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• Hilbert–Schmidt norm $\|X\|_2 = \sqrt{\mathrm{Tr}\{X^\dagger X\}}$Definition

  Sep 2026

• Entanglement fidelity $F_e(\rho,\mathcal{N}) = \langle\psi|(\mathrm{id}_R\otimes\mathcal{N})(|\psi\rangle\langle\psi|)|\psi\rangle$Definition

  Sep 2026

• Channel codes, achievable rates, capacity $C(\mathcal N)$ and $I(\mathcal N)$ (§14.10, for Theorem 14.10.1)Definition

  Sep 2026

• Conditional sample entropy and the conditionally typical set $T_\delta^{Y^n|x^n}$ (Definitions 14.6.1–14.6.2)Definition

  Sep 2026

• Joint sample entropy and the jointly typical set $T_\delta^{X^nY^n}$ (Definitions 14.5.1–14.5.3)Definition

  Sep 2026

• Typical sequences and the typical set $T_\delta^{X^n}$ (Definitions 14.2.2–14.2.3)Definition

  Sep 2026

• Conditional empirical distribution and the strong conditionally typical set (Definitions 14.9.1–14.9.2)Definition

  Sep 2026

• Strongly typical set $T_\delta^{X^n}$ and strong jointly typical set (Definitions 14.7.2, 14.8.1–14.8.2)Definition

  Sep 2026

• Types, type classes and typical types (Definitions 14.7.1, 14.7.3, 14.7.4)Definition

  Sep 2026

• Joint sample entropy and the jointly typical set $T_\delta^{X^nY^n}$ (Definitions 14.5.1–14.5.3)Definition

  Sep 2026

• Typical sequences and the typical set $T_\delta^{X^n}$ (Definitions 14.2.2–14.2.3)Definition

  Sep 2026

• Sample entropy $\overline{H}(x^n)$ (Definition 14.2.1)Definition

  Sep 2026

• Source codes, error probability and achievable compression rates (§14.4, for Theorem 14.4.1)Definition

  Sep 2026

• i.i.d. product distribution $p_{X^n}$ on sequences, set probabilities, letter counts (Ch. 14 setting)Definition

  Sep 2026

• Fidelity $F(\rho,\sigma) = \|\sqrt{\rho}\sqrt{\sigma}\|_1^2$ and root fidelity $\sqrt{F}$Definition

  Sep 2026

• Pure-state fidelity $F(\psi,\phi) = |\langle\psi|\phi\rangle|^2$Definition

  Sep 2026

• Uhlmann fidelity: $\max_U |\langle\phi^\rho| U_R \otimes I_A |\phi^\sigma\rangle|^2$ over canonical purificationsDefinition

  Sep 2026

• Classical fidelity $F(p,q) = [\sum_x \sqrt{p(x) q(x)}]^2$Definition

  Sep 2026

• Expected fidelity $F(\psi,\rho) = \langle\psi|\rho|\psi\rangle$Definition

  Sep 2026

• Separable state: $\sigma_{AB} = \sum_x p_X(x)\, |\psi_x\rangle\langle\psi_x|_A \otimes |\phi_x\rangle\langle\phi_x|_B$Definition

  Sep 2026

• Classical channel $N(y|x)$ and its action $Np$, $Nq$ (Corollary 10.7.2)Definition

  Sep 2026

• Couplings and maximal couplings of two random variables (Definitions 10.7.2–10.7.3)Definition

  Sep 2026

• Markov chain $X\to Y\to Z$ of three random variables (§10.7.2)Definition

  Sep 2026

• Classical trace distance $\|p-q\|_1$ (Definition 10.7.1)Definition

  Sep 2026

• Diamond-norm distance $\|\mathcal{N} - \mathcal{M}\|_\diamond$ between quantum channels (and $\mathrm{id}_R \otimes \mathcal{N}$)Definition

  Sep 2026

• Joint entropy $H(X,Y)$ (Definition 10.3.1)Definition

  Sep 2026

• Conditional mutual information $I(X;Y|Z)$ (Definition 10.6.1)Definition

  Sep 2026

• Mutual information $I(X;Y)$ (Definition 10.4.1)Definition

  Sep 2026

• Trace distance $\|M - N\|_1$Definition

  Sep 2026

• Partial trace $\mathrm{Tr}_B\{X_{AB}\}$ and $\mathrm{Tr}_A\{X_{AB}\}$Definition

  Sep 2026

• Trace norm (Schatten 1-norm) $\|M\|_1 = \mathrm{Tr}\{|M|\}$Definition

  Sep 2026

• Density operator: $\rho \ge 0$ and $\mathrm{Tr}\{\rho\} = 1$Definition

  Sep 2026

• Quantum channel in Choi–Kraus form: $\mathcal{N}(X) = \sum_l V_l X V_l^\dagger$, $\sum_l V_l^\dagger V_l = I$Definition

  Sep 2026

• Relative entropy $D(p\|q)$ (Definitions 10.5.1–10.5.2)Definition

  Sep 2026

• Conditional entropy $H(X|Y)$ (Definition 10.2.1)Definition

  Sep 2026

• Binary entropy function $h_2(p)$ (Definition 10.1.2)Definition

  Sep 2026

• Entropy $H(X)$ of a random variable (Definition 10.1.1)Definition

  Sep 2026

• Probability distribution on a finite alphabet (and marginals, reindexing, independence)Definition

  Sep 2026