As agentic artificial intelligence systems scale across globally distributed and long lived infrastructures, secure and policy compliant communication becomes a fundamental systems challenge. This challenge grows more serious in the quantum era, where the cryptographic assumptions built into today's AI deployments may not remain valid over their operational lifetime. Here, we introduce quantum secure by construction, or QSC, as a design paradigm that treats quantum secure communication as a core architectural property of agentic AI systems rather than an upgrade added later. We realize QSC through a runtime adaptive security model that combines post quantum cryptography, quantum random number generation, and quantum key distribution to secure interactions among autonomous agents operating across heterogeneous cloud, edge, and inter organizational environments. The approach is cryptographically pluggable and guided by policy, allowing the system to adjust its security posture according to infrastructure availability, regulatory constraints, and performance needs. QSC contributes a governance aware orchestration layer that selects and combines link specific cryptographic protections across the full agent lifecycle, including session bootstrap, inter agent coordination, tool invocation, and memory access. Through system level analysis and empirical evaluation, we examine the trade offs between classical and quantum secure mechanisms and show that QSC can reduce the operational complexity and cost of introducing quantum security into deployed agentic AI systems. These results position QSC as a foundational paradigm for post quantum agentic intelligence and establish a principled pathway for designing globally interoperable, resilient, and future ready intelligent systems.