Quantum Information.

No measurement strategy, however clever, can extract more classical (readable) information out of a quantum ensemble than its Holevo quantity χ — a hard ceiling on quantum communication capacity that sits below the naive per-qubit rate one might expect.

The Margolus–Levitin theorem sets a fundamental speed limit on how fast any physical process, including computation, can occur: an isolated quantum system needs at least τ ≥ πℏ/[2(E−E₀)] to evolve into a fully distinguishable (orthogonal) state.

The no-cloning theorem is one of quantum mechanics' foundational impossibility results: unlike classical information, an arbitrary unknown quantum state cannot be copied — a direct consequence of the linearity of quantum evolution, and the basis for quantum cryptography's security guarantees.

Exact two-way-assisted secret-key capacity of a pure-loss bosonic channel without repeaters.

Parameter bound for an [[n,k,d]] quantum error-correcting code.

Sphere-packing parameter bound for nondegenerate binary quantum codes.

Unassisted quantum capacity of a qubit erasure channel with erasure probability p.

The general unassisted quantum capacity is open; the hashing coherent-information lower bound and dimensional upper bound form a verified interval.

A finite-dimensional code detecting arbitrary single-subsystem errors cannot have a universal transversal encoded gate set.

Squared concurrence shared by one qubit with two others obeys the CKW monogamy inequality.

Linearity forbids universally deleting one copy of an unknown state while retaining the other.

Ideal entangled N-probe estimation can scale no better than inverse total coherent resource number.

Independent-probe phase estimation exhibits inverse-square-root resource scaling.

Asymptotic existence lower bound for families of binary stabilizer quantum codes.

A set of mixed quantum states can be broadcast exactly if and only if the states commute.

Deterministic exact teleportation of one arbitrary qubit consumes one ebit and two classical bits.

A noiseless qubit channel assisted by one shared ebit transmits two classical bits per use.

Maximum CHSH correlator allowed by quantum mechanics.

Maximum CHSH correlator in local hidden-variable theories.

A historically proposed energy-limited information-processing rate whose universality depends on physical modeling assumptions.

Minimum orthogonalization time from energy uncertainty.