Extending Shannon's Ideas: The Evolution of Information in Quantum Mechanics

In summary, the conversation discusses the extension of Shannon's classical information to quantum mechanics and how information evolves through measurements. It is stated that obtaining information requires work, which is equivalent to the entropy of the projected information. The concept of a "bit" of information and its corresponding entropy is also mentioned. The conversation then goes on to discuss the relationship between information and communication, as well as the role of measurement in obtaining information. The informational approach to understanding quantum mechanics is also mentioned, with the idea that all information is a result of communication or computation. Lastly, the conversation touches on the field of Quantum Information Theory and its connection to classical information theory.
  • #1
sirchasm
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I've been trying to extend Shannon's ideas of classical information to QM, and the way information (as events that we measure) evolves, as it were.
Obviously to get information, you have to do work, which is (at least) equivalent to the entropy of the information that's projected, or determined.
For a 'bit' of information this entropy is = [tex] k_B ln(2) [/tex]. Which effectively is the separation of a pure state from a mixed state, in entropy-per-bit terms.

Information in the Shannon model is a result of communication, so surely it's ok to say the mixed state evolves to a pure state, the same way a signal translates or is communicated? In fact it's ok to say a measurement is a computation, or a projection of information (in some dimension)?
So QM systems compute this result, when we 'do the work' of getting the "comms channel" to transmit something in our direction?

This is the informational approach - everything that constitutes information is the result of a communication/computation. Is this pseudoscientific?
 
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  • #2
Well correlations can be viewed in a Information Theoretic way as an exploitable communications resource. The field of treating Quantum Correlations as generalizations of Classical Information channels is known as Quantum Information Theory.

A good resource is Stephen Barnett's Quantum Information. The introductory chapter is even a nice crash course on Classical Information Theory.
 
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1. What is Shannon's Theory of Communication?

Shannon's Theory of Communication, also known as Shannon's Information Theory, is a mathematical theory that explains how information can be quantified, stored, and transmitted accurately and efficiently. It was introduced by Claude Shannon in 1948 and is considered the foundation of modern information theory.

2. How does quantum mechanics relate to Shannon's Theory?

Quantum mechanics is a branch of physics that studies the behavior of matter and energy at a very small scale, such as atoms and subatomic particles. Shannon's Theory of Communication has been extended to quantum mechanics to explain how information is processed and transmitted in quantum systems, such as quantum computers and quantum communication channels.

3. What are some key differences between classical and quantum information?

Classical information, as described by Shannon's Theory, is discrete and can only take on two values (0 or 1). On the other hand, quantum information can exist in multiple states simultaneously, known as superposition, and can also be entangled with other quantum particles. This allows for more complex and powerful information processing in quantum systems.

4. How does the concept of entropy apply to quantum information?

In Shannon's Theory, entropy is a measure of uncertainty or randomness in a system. In quantum information, entropy plays a similar role but is extended to include the uncertainty in the quantum state of a system. This is known as von Neumann entropy and is used to quantify the amount of information that can be extracted from a quantum system.

5. What are some practical applications of extending Shannon's Theory to quantum mechanics?

One potential application is in quantum cryptography, where quantum information is used to create unbreakable codes for secure communication. Another application is in quantum computing, where quantum information is used to perform complex calculations and solve problems that are currently intractable for classical computers. Additionally, understanding the evolution of information in quantum mechanics can help us better understand the behavior of complex quantum systems and potentially lead to new technologies and advancements in various fields.

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