Quantum Information Reference

This collection helps identify a formula, convention, protocol, or performance quantity before using it in a calculation. Each entry states the assumptions that make the lookup valid and links to the page that explains the subject. The collection covers established definitions and representative constructions; changing experimental records belong to Research.

Enter this chapter

Choose a reference for your calculation, then check the assumptions in the second column.

Lookup	Check before using the result
Glossary	A physical carrier, logical encoding, and algorithmic register are different objects.
Gate Library	Basis order, rotation sign, and global phase.
Circuit Identities	Control direction and whether equality is exact or only up to phase.
Common Quantum States	Normalization, subsystem split, and finite-energy approximation.
Entanglement Measures Table	Pure versus mixed states and operational regime.
Channel and Noise Model Table	Parameter convention, computational subspace, and time interval.
Algorithm Index	Input access, output type, precision, and total cost.
Complexity Class Glossary	Decision versus promise problem and uniform resource bounds.
Error-Correcting Code Table	Error model, distance, checks, and recovery circuit.
Protocol Index	Initial entanglement, classical communication, and trust assumptions.
Hardware Metrics Table	Definition, units, experimental context, and uncertainty.
Benchmark Index	Quantity being estimated, noise assumptions, and limits of the conclusion.
Reading Lists	Background and a concrete learning outcome.

From lookup to calculation

A formula becomes useful only after its symbols have been tied to the physical task. For example, an error parameter called $p$ might mean the probability of a nonidentity Pauli or the weight of replacement by the maximally mixed state. These conventions give different numerical values for the same channel. Likewise, a state fidelity may be defined with or without a square. Record the equation, not only the name.

For a circuit calculation, first use the gate library to fix tensor order and phase, then use the circuit identities to simplify it, and finally evaluate the output against a known state. For an experimental comparison, pair the hardware metrics table with the benchmark index: the former defines a quantity, while the latter explains what measurement supports it.

For partial traces and subsystem structure, start with Composite Systems and Entanglement. For measurement outcomes, state changes, and environmental noise, use Measurement and Open Quantum Systems. Return to the linked explanations when you need to derive a formula or decide whether its assumptions fit your problem.

References

• Nielsen, Michael A., and Isaac L. Chuang, Quantum Computation and Quantum Information, 10th anniversary edition, Cambridge University Press, 2010, doi:10.1017/CBO9780511976667 — standard terminology and the circuit, communication, and error-correction framework.
• Watrous, John, The Theory of Quantum Information, Cambridge University Press, 2018, author manuscript and errata — precise finite-dimensional definitions and operational qualifications.