2011/05/31 by Joan A. Vaccaro, J. A. Vaccaro
Computer Science · Mathematics · Physics and Astronomy · #Asymmetry #Classical mechanics #Duality (order theory) #Geometry #Global symmetry #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum optics and atomic interactions #Rotational symmetry #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #Symmetry number #Symmetry operation #Theoretical physics #quant-ph
paper · pdf · doi:10.1098/rspa.2011.0271
published as Proc. R. Soc. A 468, 1065-1084 (2012) · 20 pages, 3 figures
openalex publication_date 2011/12/07 · arxiv created 2012/03/20 · arxiv updated 2012/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Symmetry plays a central role in many areas of modern physics. Here, we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry, whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by , where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus a more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators.