The rapid adoption of Large Language Model (LLM) applications in multi-agent architectures has exposed fundamental challenges in how contextual information is represented, persisted, and exchanged across intelligent systems. Current approaches rely predominantly on natural language representations that introduce semantic redundancy, token inefficiency, and non-deterministic state reconstruction. This paper presents the Quantized Context Protocol (QCP), a formal specification for representing operational context in a compact, machine-readable, and semantically stable form. Unlike conventional summarization or compaction techniques, QCP operates as a semantic compression protocol that preserves meaning, causality, and operational intent while systematically eliminating linguistic redundancy. We introduce a three-layer architecture (QCP-PRETTY, QCP-CANONICAL, QCP-COMPACT) enabling interoperability across human-readable, normative, and token-efficient representations. The protocol defines a minimal vocabulary of semantic primitives (invariants, causal relations, decisions, and pending actions) with formal translation rules for bidirectional conversion between natural language and quantized context units. Preliminary experimental observations suggest compression ratios exceeding 3:1 with semantic preservation metrics above 90%, enabling efficient context handoff in multi-agent systems. QCP represents a shift from treating context as prose toward treating context as structured, operational data, complementing existing protocols like MCP and A2A by addressing the representation layer they do not specify.