We briefly review the correspondence principle proposed in our previous paper, which claims that if we regard a matrix element defined in terms of the future state at time $T_B$ and the past state at time $T_A$ as an expectation value in the complex action theory whose path runs over not only past but also future, the expectation value at the present time $t$ of a future-included theory for large $T_B-t$ and large $t-T_A$ corresponds to that of a future-not-included theory with a proper inner product for large $t-T_A$ . This correspondence principle suggests that the future-included theory is not excluded phenomenologically.We briefly review the correspondence principle proposed in our previous paper, which claims that if we regard a matrix element defined in terms of the future state at time $T_B$ and the past state at time $T_A$ as an expectation value in the complex action theory whose path runs over not only past but also future, the expectation value at the present time $t$ of a future-included theory for large $T_B-t$ and large $t-T_A$ corresponds to that of a future-not-included theory with a proper inner product for large $t-T_A$. This correspondence principle suggests that the future-included theory is not excluded phenomenologically.

arXiv:1211.7269Nov 30, 20124 citations

An Information-Geometric Reconstruction of Quantum Theory, II: The Correspondence Rules of Quantum Theory

Philip Goyal

In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism within the framework of information geometry. In this paper, we formulate a correspondence principle, the Average-Value Correspondence Principle, that allows relations between measurement results which are known to hold in a classical model of a system to be systematically taken over into the quantum model of the system. Using this principle, we derive the explicit form of the temporal evolution operator (thereby completing the derivation of the abstract quantum formalism begun in Paper I), and derive many of the correspondence rules (such as operator rules, commutation relations, and Dirac's Poisson bracket rule) that are needed to apply the abstract quantum formalism to model particular physical systems.In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism within the framework of information geometry. In this paper, we formulate a correspondence principle, the Average-Value Correspondence Principle, that allows relations between measurement results which are known to hold in a classical model of a system to be systematically taken over into the quantum model of the system. Using this principle, we derive the explicit form of the temporal evolution operator (thereby completing the derivation of the abstract quantum formalism begun in Paper I), and derive many of the correspondence rules (such as operator rules, commutation relations, and Dirac's Poisson bracket rule) that are needed to apply the abstract quantum formalism to model particular physical systems.

arXiv:0805.2765May 19, 20081 citation

History and Meaning of the Quantum Correspondence Principle

Insok Ko

철학논총Jan 1, 20030 citations

History-Recoverability Post-Quantum Security (HR-PQS)

Trinity Labo

This paper introduces History-Recoverability Post-Quantum Security (HR-PQS), a lightweight theoretical framework for post-quantum security based on the principle of unrecoverable history. Rather than treating the quantum threat as merely a problem of replacing vulnerable cryptographic algorithms, HR-PQS reformulates post-quantum security as a question of whether future quantum-capable adversaries can reconstruct meaningful past histories from stored ciphertexts, keys, logs, backups, certificates, metadata, and operational residues. The central claim is that post-quantum cryptography is necessary but not sufficient. Even when quantum-resistant algorithms are deployed, long-lived information may remain vulnerable through archived ciphertexts, residual key material, metadata leakage, certificate chains, traffic patterns, and backup recovery paths. HR-PQS therefore shifts the security objective from simple decryption failure to semantic history-unrecoverability. The framework unifies existing security practices such as post-quantum cryptography, perfect forward secrecy, ratcheting, secure key erasure, re-encryption, envelope encryption, metadata hiding, and cryptographic agility under a single operational principle: history pruning. In this view, key rotation is not merely a lifecycle procedure, but a mechanism for cutting future reconstruction paths from past encrypted histories. Mathematically, HR-PQS models a future quantum adversary as a relational observer with access to quantum computation, classical computation, internal information, stored ciphertexts, backups, and metadata. Security is defined through a history-recoverability functional combining mutual information leakage, semantic recovery advantage, collapse risk, and operational cost. The paper further introduces a semantic recovery game and a history-recoverability distance for measuring whether an adversary can reconstruct useful domain-specific features of past information, such as financial transaction graphs, medical diagnosis patterns, communication networks, or enterprise activity timelines. The theory is inspired by TrinityLabo's Recoverable Reality Principle and Relational Recoverable Reality Principle, but reverses their role for cryptographic security: in physical theory, good compression should remain recoverable; in security theory, attacker-side reconstruction must remain impossible. HR-PQS is not proposed as a new cryptographic primitive or replacement protocol. Instead, it is a lightweight upper-level theory for organizing existing and emerging post-quantum security practices around the deeper requirement of protecting the past from future reconstruction. In short: not merely quantum-resistant encryption, but unrecoverable history.This paper introduces History-Recoverability Post-Quantum Security (HR-PQS), a lightweight theoretical framework for post-quantum security based on the principle of unrecoverable history. Rather than treating the quantum threat as merely a problem of replacing vulnerable cryptographic algorithms, HR-PQS reformulates post-quantum security as a question of whether future quantum-capable adversaries can reconstruct meaningful past histories from stored ciphertexts, keys, logs, backups, certificates, metadata, and operational residues. The central claim is that post-quantum cryptography is necessary but not sufficient. Even when quantum-resistant algorithms are deployed, long-lived information may remain vulnerable through archived ciphertexts, residual key material, metadata leakage, certificate chains, traffic patterns, and backup recovery paths. HR-PQS therefore shifts the security objective from simple decryption failure to semantic history-unrecoverability. The framework unifies existing security practices such as post-quantum cryptography, perfect forward secrecy, ratcheting, secure key erasure, re-encryption, envelope encryption, metadata hiding, and cryptographic agility under a single operational principle: history pruning. In this view, key rotation is not merely a lifecycle procedure, but a mechanism for cutting future reconstruction paths from past encrypted histories. Mathematically, HR-PQS models a future quantum adversary as a relational observer with access to quantum computation, classical computation, internal information, stored ciphertexts, backups, and metadata. Security is defined through a history-recoverability functional combining mutual information leakage, semantic recovery advantage, collapse risk, and operational cost. The paper further introduces a semantic recovery game and a history-recoverability distance for measuring whether an adversary can reconstruct useful domain-specific features of past information, such as financial transaction graphs, medical diagnosis patterns, communication networks, or enterprise activity timelines. The theory is inspired by TrinityLabo's Recoverable Reality Principle and Relational Recoverable Reality Principle, but reverses their role for cryptographic security: in physical theory, good compression should remain recoverable; in security theory, attacker-side reconstruction must remain impossible. HR-PQS is not proposed as a new cryptographic primitive or replacement protocol. Instead, it is a lightweight upper-level theory for organizing existing and emerging post-quantum security practices around the deeper requirement of protecting the past from future reconstruction. In short: not merely quantum-resistant encryption, but unrecoverable history.

May 10, 20260 citations

We briefly review the correspondence principle proposed in our previous paper, which claims that if we regard a matrix element defined in terms of the future state at time

T_B

and the past state at time

T_A

as an expectation value in the complex action theory whose path runs over not only past but also future, the expectation value at the present time

t

of a future-included theory for large

T_B-t

and large

t-T_A

corresponds to that of a future-not-included theory with a proper inner product for large

t-T_A

. This correspondence principle suggests that the future-included theory is not excluded phenomenologically.