Physics of quantum information — the study of the information-theoretic properties of quantum systems and the protocols that exploit them. Foundations: pure vs mixed states represented by density operators ρ (trace 1, positive…
quantum-information-physics
Density operator ρ: tr ρ = 1, ρ ≽ 0; pure ⇔ ρ² = ρ ⇔ tr ρ² = 1
Density operator ρ on a finite-dimensional Hilbert space H encodes the complete quantum-statistical state of the system: ρ is Hermitian (ρ†…
Bell states {|Φ±⟩, |Ψ±⟩}: maximally-entangled 2-qubit basis
The four Bell (Einstein-Podolsky-Rosen-Bohm) states are a maximally-entangled orthonormal basis for 2-qubit Hilbert space C² ⊗ C²: |Φ^±⟩ =…
CHSH operator C = AB + AB' + A'B − A'B': LHV ≤ 2, QM ≤ 2√2
Clauser-Horne-Shimony-Holt 1969 operator C = A⊗B + A⊗B' + A'⊗B − A'⊗B' on a bipartite quantum system, where A, A' are Alice-side dichotomic…
CHSH: LHV bound 2, Tsirelson 2√2, gap (2√2)²−2² = 4
Sympy-exact symbolic witness of the CHSH classical-vs-quantum bound gap. Step 1 — classical: on dichotomic ±1 observables the quantity C =…
No-cloning: ⟨φ|ψ⟩ = √2/2 forbids perfect copy; BH fidelity 5/6, shortfall 1/6
Sympy-exact symbolic witness of the Wootters-Zurek 1982 / Dieks 1982 no-cloning theorem + the Bužek-Hillery 1996 universal cloner bound. …
Bell singlet |Ψ⁻⟩: concurrence 1, ρ_A = 𝟙/2, S(ρ_A) = log 2
Sympy-exact matrix verification of the Bell singlet's maximal entanglement via the Wootters 1998 concurrence C = |⟨Ψ|Ψ̃⟩| with |Ψ̃⟩ = (σ_y…