[Paper Review] The Transactional Nature of Quantum Information

Subhash Kak|arXiv (Cornell University)|Jul 14, 2009

Quantum Mechanics and Applications9 references3 citations

TL;DR

This paper proposes a transactional interpretation of quantum information, arguing that information is inherently relational and only meaningful when a sender's choice is communicated to a receiver. Unlike von Neumann entropy, the proposed measure assigns non-zero information to unknown pure quantum states, enabling potentially infinite information extraction through repeated measurements, thus redefining quantum information as a dynamic, relational transaction rather than a static property.

ABSTRACT

Information, in its communications sense, is a transactional property. If the received signals communicate choices made by the sender of the signals, then information has been transmitter by the sender to the receiver. Given this reality, the potential information in an unknown pure quantum state should be non-zero. We examine transactional quantum information, which unlike von Neumann entropy, depends on the mutuality of the relationship between the sender and the receiver, associating information with an unknown pure state. The information that can be obtained from a pure state in repeated experiments is potentially infinite.

Motivation & Objective

• To redefine quantum information not as a static property but as a transactional process between sender and receiver.
• To challenge the conventional use of von Neumann entropy as the sole measure of quantum information.
• To demonstrate that unknown pure quantum states can carry non-zero, potentially infinite information when measured repeatedly.
• To establish a foundation for quantum information theory based on mutual correlation between sender and receiver.
• To provide a conceptual framework where information arises only through the completion of a quantum measurement transaction.

Proposed method

• Proposes a transactional model of quantum information where information is transmitted only when a sender's choice is communicated to a receiver via a quantum state.
• Defines information as a relational property dependent on the mutual interaction between sender and receiver, not intrinsic to the state alone.
• Argues that the potential information in a pure state is non-zero and can be accessed through repeated experimental preparations and measurements.
• Uses the concept of 'transaction' from the transactional interpretation of quantum mechanics to frame information exchange as a handshake between emitter and absorber.
• Rejects von Neumann entropy as inadequate for capturing the full information potential of pure states.
• Introduces a new information measure that depends on the mutual correlation between sender and receiver, emphasizing the role of choice and confirmation in information transfer.

Experimental results

Research questions

• RQ1 Can quantum information be meaningfully defined without a receiver or a completed measurement transaction?
• RQ2 Why does von Neumann entropy assign zero information to a pure state, despite its potential for repeated, reproducible measurement outcomes?
• RQ3 What is the information content of an unknown pure quantum state when it is repeatedly prepared and measured?
• RQ4 How does the relational nature of information in quantum mechanics differ from classical information theory?
• RQ5 Can the concept of a quantum transaction fully account for the emergence of information in quantum systems?

Key findings

• The information content of an unknown pure quantum state is non-zero and potentially infinite when measured repeatedly.
• The transactional interpretation provides a more complete account of quantum information than von Neumann entropy, which fails to capture the relational nature of information.
• Information in quantum mechanics is not a property of the state alone but emerges from the interaction between sender and receiver.
• The potential for infinite information extraction from a single pure state arises from the repeatability of quantum measurements and the confirmation of choices.
• The paper establishes that quantum information is fundamentally transactional—requiring both emission and reception to be meaningful.
• The framework redefines quantum information as a dynamic, relational process rather than a static, state-dependent quantity.