Prim-Lex Quantum Finance: A Five-Prim-Fire, Eight-Dimensional Coherence and Nine-Nexus Framework for Quantum Technology Risk Assessment, Investment Decision-Making and Capital Allocation
Quantum technologies are rapidly moving from laboratory research toward industrialization, commercialization, and capital formation, while introducing new sources of financial risk associated with technological uncertainty, cybersecurity and post-quantum cryptography (PQC) migration, regulatory change, supply-chain resilience, and investment timing. In 2024, the U.S. National Institute of Standards and Technology (NIST) finalized and published three foundational PQC standards, FIPS 203, FIPS 204, and FIPS 205. In 2025, the Bank for International Settlements (BIS) advanced Project Leap to test quantum-safe cryptography in financial infrastructure, while the OECD published its A Quantum Technologies Policy Primer. In 2026, the Hong Kong Monetary Authority (HKMA) introduced the first Quantum Preparedness Index (QPI), with an initial sector-level score of 2.3 out of 10, indicating that quantum preparedness in the banking sector remains at an early stage. These developments highlight a growing need to integrate technological, cybersecurity, institutional, and financial-risk perspectives within a coherent decision architecture. This paper develops a Prim-Lex Quantum Finance framework based on Prim-Lex Theory (Economic Climatology), integrating five Prim-Fires, eight-dimensional coherence, and Nine-Nexus guidance. The Five Prim-Fires comprise Technological-Capability Prim-Fire, Security-Resilience Prim-Fire, Institutional-Governance Prim-Fire, Industrial-Commercial Prim-Fire, and Earth-System Intelligence-Coherence Prim-Fire. The Prim-Lex Eight-Dimensional Quantum Finance State Space (PL-8D-QF) characterizes quantum-technology investment projects across eight dimensions: Technological Capability; Security and Quantum Readiness; Policy and Regulatory Alignment; Technology Maturity and Lifecycle; Ex-ante Financial Viability; Supply-Chain and Systemic Resilience; Temporal Synchronization and Transition Readiness; and Information Quality and Transparency. Building on this state space, the paper introduces the Quantum Investment Coherence Index (QICI), which combines a weighted geometric aggregation of eight-dimensional state strengths with a Kuramoto-based coherence measure derived from dynamic phase information extracted using the Hilbert transform. The central testable proposition is that multidimensional coherence contains incremental predictive information about financial risk beyond the information contained in dimension strengths alone. The framework further specifies a quantitative transmission mechanism from QICI to Probability of Default (PD), Expected Loss (EL), risk-adjusted returns, and financing costs or credit spreads, while distinguishing the Quantum Sovereignty Index (QSI) for national strategic assessment from QICI for project- and investment-level decision-making. The paper formulates 12 testable hypotheses and develops an empirical validation design incorporating panel data, predictive modeling, data-driven critical phase-threshold identification, block bootstrap procedures, out-of-sample validation, and falsification or placebo tests. The critical phase threshold is not imposed ex ante as a universal constant, such as , but is identified from predictive performance in the data; is retained only as a falsifiable theoretical benchmark. The framework then links QICI to risk pricing, investment timing, capital allocation, risk mitigation, and exit decisions, thereby establishing a decision chain from quantum-technology state assessment to financial-risk pricing and capital allocation. The paper seeks to extend the assessment of quantum technologies from technological evaluation to financial evaluation and from compliance-oriented assessment to risk-sensitive allocation optimization. It provides a quantifiable, testable, programmable, and auditable analytical framework for quantum-technology investment, institutional quantum preparedness, post-quantum cryptography migration, and emerging quantum-climate-finance research.
Quantum technologies are rapidly moving from laboratory research toward industrialization, commercialization, and capital formation, while introducing new sources of financial risk associated with technological uncertainty, cybersecurity and post-quantum cryptography (PQC) migration, regulatory change, supply-chain resilience, and investment timing. In 2024, the U.S. National Institute of Standards and Technology (NIST) finalized and published three foundational PQC standards, FIPS 203, FIPS 204, and FIPS 205. In 2025, the Bank for International Settlements (BIS) advanced Project Leap to test quantum-safe cryptography in financial infrastructure, while the OECD published its A Quantum Technologies Policy Primer. In 2026, the Hong Kong Monetary Authority (HKMA) introduced the first Quantum Preparedness Index (QPI), with an initial sector-level score of 2.3 out of 10, indicating that quantum preparedness in the banking sector remains at an early stage. These developments highlight a growing need to integrate technological, cybersecurity, institutional, and financial-risk perspectives within a coherent decision architecture. This paper develops a Prim-Lex Quantum Finance framework based on Prim-Lex Theory (Economic Climatology), integrating five Prim-Fires, eight-dimensional coherence, and Nine-Nexus guidance. The Five Prim-Fires comprise Technological-Capability Prim-Fire, Security-Resilience Prim-Fire, Institutional-Governance Prim-Fire, Industrial-Commercial Prim-Fire, and Earth-System Intelligence-Coherence Prim-Fire. The Prim-Lex Eight-Dimensional Quantum Finance State Space (PL-8D-QF) characterizes quantum-technology investment projects across eight dimensions: Technological Capability; Security and Quantum Readiness; Policy and Regulatory Alignment; Technology Maturity and Lifecycle; Ex-ante Financial Viability; Supply-Chain and Systemic Resilience; Temporal Synchronization and Transition Readiness; and Information Quality and Transparency. Building on this state space, the paper introduces the Quantum Investment Coherence Index (QICI), which combines a weighted geometric aggregation of eight-dimensional state strengths with a Kuramoto-based coherence measure derived from dynamic phase information extracted using the Hilbert transform. The central testable proposition is that multidimensional coherence contains incremental predictive information about financial risk beyond the information contained in dimension strengths alone. The framework further specifies a quantitative transmission mechanism from QICI to Probability of Default (PD), Expected Loss (EL), risk-adjusted returns, and financing costs or credit spreads, while distinguishing the Quantum Sovereignty Index (QSI) for national strategic assessment from QICI for project- and investment-level decision-making. The paper formulates 12 testable hypotheses and develops an empirical validation design incorporating panel data, predictive modeling, data-driven critical phase-threshold identification, block bootstrap procedures, out-of-sample validation, and falsification or placebo tests. The critical phase threshold is not imposed ex ante as a universal constant, such as , but is identified from predictive performance in the data; is retained only as a falsifiable theoretical benchmark. The framework then links QICI to risk pricing, investment timing, capital allocation, risk mitigation, and exit decisions, thereby establishing a decision chain from quantum-technology state assessment to financial-risk pricing and capital allocation. The paper seeks to extend the assessment of quantum technologies from technological evaluation to financial evaluation and from compliance-oriented assessment to risk-sensitive allocation optimization. It provides a quantifiable, testable, programmable, and auditable analytical framework for quantum-technology investment, institutional quantum preparedness, post-quantum cryptography migration, and emerging quantum-climate-finance research.
On May 28, 2026, the OECD Council adopted the Recommendation of the Council on Quantum Technologies (OECD/LEGAL/0508), the world's first intergovernmental standard for quantum technologies, marking the official transition of quantum technology governance from "academic discussion" to "institutional construction". At the same time, Academician Pan Jianwei of the Chinese Academy of Sciences warned at the 2026 Future Science Forum that excessive capital enthusiasm and conceptual hype in the quantum information industry are rampant, calling for the establishment of a national-level technology evaluation mechanism and industry access standards. The disruptive impact of quantum computing on existing encryption systems, the geopolitical implications of quantum communication, and the military applications of quantum sensing have made quantum technology a new frontier in great power competition. Based on the eight-dimensional framework of Prim-Lex Theory (Economic Climatology), this paper introduces, for the first time, quantum technology governance into the mathematical expression of a complexified unified field. From Prim-Unity·Prim-Fire (quantum computing energy consumption and qubit coherence time) to Eight Trigrams·Eight Information (entropy governance of quantum information networks), it constructs a quantitative assessment system for quantum technology governance dimension by dimension. Using three empirical anchors——the US-China-Europe quantum competition, post-quantum cryptography (PQC) standardization and migration, and the quantum-safe encryption standards debate——this paper demonstrates the application pathway of the eight-dimensional framework in identifying "phase differences" and "critical windows" in quantum governance, providing a quantifiable, programmable, and auditable mathematical language and governance tool for the transition of global quantum technology from "technological competition" to "sustainable governance."
Abstract: This study develops a public policy evaluation framework for quantum-safe cyber-defence in financial infrastructure, with emphasis on post-quantum cryptography, quantum communications and the governance of critical-sector resilience. The research addresses a strategic problem now facing central banks, payment operators, market infrastructures, commercial banks, fintech platforms and regulators: the public-key cryptographic foundations used for authentication, key establishment and digital trust will become exposed if a cryptographically relevant quantum computer emerges before high-value financial systems complete migration. The paper treats quantum risk not as a narrow algorithm replacement problem, but as a multi-layered policy challenge involving standards, operational continuity, procurement, vendor coordination, legal accountability, cyber-insurance, institutional capability and cross-border interoperability. The framework is grounded in real public evidence from standards bodies, cyber agencies and financial-system reports, including NIST post-quantum standards, NIST migration guidance, NCSC system-owner guidance, NSA post-quantum resources, BIS financial-system quantum-readiness work, BIS Project Leap and national quantum strategy evidence (NIST, 2023; NIST, 2024; BIS, 2025; OECD, 2025). The methodological contribution is a structured evaluation model that links cryptographic exposure, data longevity, systemic criticality, migration complexity and mitigation maturity into a risk-priority index. The results identify wholesale settlement, central counterparty clearing, securities settlement, cross-border financial messaging, certificate trust anchors and key-management services as the most urgent layers for cryptographic inventory, hybrid testing and staged transition. The analysis finds that post-quantum cryptography is the practical near-term route to scalable resilience, while quantum key distribution remains appropriate only for carefully bounded pilots unless cost, authentication and infrastructure dependencies are resolved. The paper concludes that quantum-safe financial infrastructure requires an integrated policy architecture built around cryptographic agility, real-time asset discovery, supervisory milestones, interoperable implementation testing, mathematically auditable decision rules and coordinated public-private transition governance. Keywords: post-quantum cryptography; quantum-safe finance; cyber-defence; financial infrastructure; public policy evaluation; quantum communications; critical infrastructure resilience; cryptographic agility; ML-KEM; ML-DSA; quantum readiness; payment systems
Abstract: This study develops a unified approach to quantum-safe security in accounting and finance by linking concept analysis, a design framework, and implementation guidance to measurable risk reduction. Concept analysis distinguishes confidentiality lifetimes, “harvest-now-decrypt-later” exposure, and cryptographic dependence across ledgers, payments, reporting pipelines, and audit trails. Building on this, a layered framework is articulated comprising (i) threat taxonomy and impact surfaces for financial workflows; (ii) standards alignment with post-quantum cryptography (PQC) suites and crypto-agility policies; (iii) key- and certificate-lifecycle orchestration using HSM-backed services; and (iv) controls for ledger integrity, non-repudiation, and regulatory evidence. The core problem addressed is the absence of end-to-end, standards-compatible designs that deliver quantum resilience without disrupting performance, interoperability, or compliance. Methodology integrates formal threat modeling, standards mapping, and reference-architecture synthesis with scenario evaluation in representative financial processes (inter-system reconciliation, e-signature workflows, and archival protection). Results show that phased PQC migration with automated key rotation and dual-stack validation reduces exposure windows, preserves auditability, and maintains throughput within target bounds for typical batch and near-real-time workloads. Impact arises from procurement-ready patterns, crypto-agile runbooks, and assurance artifacts that support regulatory review and external audit. The implications include actionable migration roadmaps for institutions, improved durability of financial records against future cryptanalytic advances, and clearer accountability through evidence bundles that connect controls to quantifiable risk reduction. Keywords: quantum-safe cryptography, post-quantum cryptography (PQC), financial systems security, accounting information systems, harvest-now decrypt-later, crypto-agility, key management and HSM, digital signatures and non-repudiation, ledger integrity, regulatory compliance, audit evidence, zero-trust architecture, certificate lifecycle, risk assessment and migration planning
The advent of Quantum Technology (QT) and its application in Quantum Computing (QC) marks the next major technological frontier following Artificial Intelligence, by prompting significant investment from governments and global corporations, particularly from the financial sector. The immense data processing capabilities of QC are poised to revolutionize finance, offering new avenues for optimizing complex financial transactions and enhancing fraud detection systems. However, such technological leap simultaneously introduces a critical and urgent risk to global cybersecurity and, by extension, the stability of the financial markets. Specifically, such computational power inherent in advanced quantum systems fundamentally compromises the cryptographic algorithms which are currently used in electronic financial transactions, which may cause instability and thereby pose substantial risk across the financial ecosystem. Major countries are taking proactive actions to address such risk by initiating policy transitions toward quantum security and considering adopting Post-Quantum Cryptography (PQC). These jurisdictions are actively preparing a shift in their digital infrastructure to mitigate the inevitable risk of a “Store Now, Decrypt Later” attack. In stark contrast, domestic discussions and policy preparations for this critical security transition remain relatively inactive in South Korea. Such regulatory and policy gap highlights an urgent need to adopt preemptive action to safeguard the nation’s financial integrity. Given the circumstances, this paper, therefore, examines the current legal and regulatory framework in South Korea related to cryptographic systems in electronic finance, identifies specific legislative deficiencies, and proposes concrete measures to overcome such risks. To effectively manage the rapid technological shifts characteristic of the Fourth Industrial Revolution, this paper will focus how South Korea should align with international trends by prioritizing a regulatory approach centered on soft law and non-binding guidelines, rather than imposing rigid, strict legal regulations. Furthermore, the paper will emphasize the importance of adopting a purposive (teleological) interpretation of existing and future laws to ensure regulatory frameworks remain agile and relevant in the face of continuous technological evolution. Based on such legislative and interpretive foundations, the paper aims to stress the necessity for South Korea to actively engage with major international stakeholders and foreign countries as such international cooperation is crucial not only for collectively strengthening global financial cybersecurity but also for reducing the risk of regulatory fragmentation in a complex and interconnected quantum security landscape.
Abstract Quantum computing is rapidly advancing from a theoretical possibility to a transformative force in financial systems. With its high-dimensional computational capacity, quantum technology is promising for enhancing risk modelling, fraud detection and transaction efficiency. However, it also seriously threatens cryptographic security, regulatory coherence and systemic stability. This paper critically analyses the risks introduced by cryptographically relevant quantum computers and assesses the readiness of legal and institutional frameworks to respond. Focusing on the UK financial regulatory environment, the study proposes a quantum-safe integration roadmap grounded in post-quantum cryptography, adaptive regulatory models and sector-wide governance strategies. The paper argues for anticipatory regulation that embeds enforceable standards and strategic collaboration across public and private stakeholders through an interdisciplinary approach combining legal analysis and financial risk modelling. The UK’s leadership in quantum policy positions it to shape international norms in secure quantum adoption. Finally, the paper offers an analytical framework to ensure that quantum innovation reinforces rather than destabilises data integrity, financial resilience and public trust.
Quantum computing is advancing rapidly and is expected to reshape the cybersecurity foundations of the financial sector. Modern financial systems rely heavily on classical public-key cryptography such as Rivest-Shamir-Adleman (RSA) and elliptic-curve cryptography (ECC), which are vulnerable to quantum algorithms capable of breaking current encryption schemes. As these technologies mature, financial institutions face growing pressure to transition toward quantum-resistant security frameworks that can preserve the confidentiality and integrity of financial data. This paper reviews the role of quantum cryptography in finance and describes how governments, regulators, and financial institutions are preparing for the transition to quantum-resilient security systems. Drawing on academic literature, institutional reports, and organizational case studies, the analysis explores the technical, regulatory, and economic factors shaping the adoption of post-quantum security measures across global financial networks. Particular attention is given to hybrid security strategies that combine post-quantum cryptography (PQC) with quantum key distribution (QKD), which are emerging as practical solutions for strengthening communication security while maintaining operational performance. The findings highlight substantial disparities in national and institutional readiness, with higher-income countries and large financial organizations leading pilot programs and infrastructure investments while lower-capacity systems remain dependent on legacy encryption. These differences create uneven levels of protection across interconnected financial networks and increase the risk of systemic vulnerability. The paper concludes that coordinated standards, phased implementation strategies, and sustained investment in technical capacity will be essential for maintaining secure and stable financial systems in the quantum era.