Heisenberg modelと相転移I

Masuo Suzuki

Sion Nicolas Ledbetter

We construct a classical code, called a Heisenberg code, which is not uniquely decipherable in order to mimic the quantum behavior of uncertainty. We classify this code according to two properties and determine the possible codeword lengths for a Heisenberg code. We suggest a possible example of a physical system which utilizes Heisenberg codes. We define a channel for Heisenberg codes, called a Heisenberg channel, which is a composite of a sender state and a receiver state which are matrices of probability amplitudes. We demonstrate that Heisenberg channels have partial trace properties similar to density matrices for quantum states. Next, we show that certain Heisenberg channels can be associated to the correlations between different partite systems of a quantum states, and define Heisenberg states and Heisenberg density matrices which are sender states and Heisenberg channels with complex entries, respectively. We prove that a Heisenberg state exists for any quantum state and that a Heisenberg density matrix relating to an n-qubit quantum state is itself a density matrix for a (2n − 1)-qubit quantum state.

Masuo Suzuki

Guji Tian

In this article we discuss the relation between Heisenberg's inequality and logarithmic Heisenberg's (entropy) inequality for ambiguity function. After building up a Heisenberg's inequality, we obtain a connection of variance with entropy by variational method. Using classical Taylor's expansion, we prove that the equality in Heisenberg's inequality holds if and only if the entropy of 2k - 1 order is equal to (2k - 1}!.

Akihide Oguchi

Guido Bacciagaluppi, Elise Crull

This chapter introduces in more comprehensive fashion than elsewhere in the literature the interesting role of Heisenberg in the EPR debate. Although we have already published an analysis of Heisenberg’s posthumously published draft response to EPR, only now are we able to situate this excellent primary source in its fullest context, by contributing a chapter describing, for example, Heisenberg’s thinking prior to EPR about interacting systems and hidden variables, the crucial role of Grete Hermann for Heisenberg’s thinking about separability, completeness and observational context, and describing the correspondence between Heisenberg and Bohr discussing Heisenberg’s manuscript.