Quantum Singleton bound

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

Specification version 1Published 2010-12-091 evidence records

About this problem

The question, scope, and sources behind this Registry record.

Formal question

Bound logical qubits k and distance d for an n-qubit quantum code.

Scope & constraints

code: [[n,k,d]] quantum code
errors: arbitrary errors on fewer than d positions
alphabet: qubits

Primary sources

Quantum Computation and Quantum Information — Quantum Singleton bound >= Chapters 2, 6, 10 and 12

What we know

Current frontiers derived from accepted Claims.

KNOWN LOWER BOUNDKNOWN UPPER BOUND

n-k >= 2(d-1)

OPEN FRONTIER

Unknown

Lower boundGap: UnknownUpper bound

Claims

Assertions tied to evidence, attribution, and review.

2026

CLM-QUANT-003312-1>= n-k >= 2(d-1)LOWER BOUNDThe cited theorem establishes n-k >= 2(d-1) under the recorded assumptions.Source: Quantum Computation and Quantum Information — Quantum Singleton bound >= ↗

PROVEN

Timeline

The frontier as it changed over time.

How this frontier is derived

Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.

—No breakthrough events recorded yetEvents appear here when an accepted Claim tightens a bound or closes the frontier.