Posted on

Simulation of quantum entangled states by classical probabilistic models

A new preprint:

We propose a classical probabilistic plasma-like model of bipartite quantum states, including entangled states. In a finite-dimensional approximation, a bipartite density operator can be written as a finite signed sum of product-state projectors,

ρ=∑kqk|ak,bk⟩⟨ak,bk|,\rho=\sum_k q_k |a_k,b_k\rangle\langle a_k,b_k|,

where an entangled state necessarily requires negative coefficients in every such decomposition. By linearity and factorization of the Wigner transform on product states, the corresponding bipartite Wigner function has the form

W(𝐱1,𝐩1,𝐱2,𝐩2)=∑k=1KqkW1k(𝐱1,𝐩1)W2k(𝐱2,𝐩2).W(\mathbf{x}_1,\mathbf{p}_1,\mathbf{x}_2,\mathbf{p}_2) =\sum_{k=1}^{K}q_kW_{1k}(\mathbf{x}_1,\mathbf{p}_1)W_{2k}(\mathbf{x}_2,\mathbf{p}_2).

Building on an earlier plasma-like model of one-particle Wigner functions in terms of classical particles and antiparticles, we interpret |qk||q_k| as the expected value of the number of copies of the k-th plasma pair in a realization of the ensemble, while the sign of qkq_k distinguishes particle- and antiparticle-type contributions. Negative quasiprobabilities therefore enter the construction at two distinct levels: through possible negativity of the one-particle Wigner functions and through negative coefficients in the product-state decomposition associated with entanglement. Averaging over the ensemble of plasma copies reproduces the bipartite Wigner function and therefore the corresponding quantum state.

Posted on

A chapter in a new book

A book including my chapter has been published.

The book: Quantum Mechanics: A Century Later. In Celebration of Heisenberg’s Seminal 1925 Paper. Edited by: Tuck Choy. World Scientific, 2026, 399 p.

The chapter: Andrey Akhmeteli, Minimalist versions of the Maxwell-Dirac electrodynamics and other quantum gauge theories, pp. 357-377.

Posted on

A new result

I added an important result in the new version of my preprint: after the spinor field is eliminated from the Maxwell-Dirac electrodynamics, the resulting equations describe independent evolution of the electromagnetic field, in other words, a Cauchy problem can be formulated in terms of the electromagnetic field alone.

Posted on

On the possibility of differential algebraic elimination of the spinor field from the Maxwell-Dirac electrodynamics

A new preprint:

We investigate whether the spinor field can be eliminated from the Maxwell-Dirac equations by differential algebraic methods. A generic truncated power series solution is constructed, the prolonged system of the Maxwell-Dirac electrodynamics is linearized about the solution, and the ranks of the associated coefficient matrices are computed. The results indicate that, generically, the spinor components are uniquely determined by the electromagnetic field and its derivatives. This strongly suggests that differential-algebraic elimination of the spinor field is possible.