Observing Dirac’s Classical Phase Space Analog to the Quantum State

2013/09/30 by Jeff S. Lundeen, C. Bamber, Charles Bamber · 3 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Dirac (video compression format) #Mathematical physics #Measure (data warehouse) #Open quantum system #Phase space #Physics #Probability amplitude #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum operation #Quantum state #quant-ph

paper · pdf · doi:10.1103/physrevlett.112.070405

published as Physical Review Letters, 112, 070405 (2014) · 9 pages, 4 figures, Supplementary Material

arxiv created 2013/11/29 · openalex publication_date 2014/02/19 · arxiv updated 2014/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In 1945, Dirac attempted to develop a “formal probability” distribution to describe quantum operators in terms of two noncommuting variables, such as position x and momentum p [Rev. Mod. Phys. 17, 195 (1945)]. The resulting quasiprobability distribution is a complete representation of the quantum state and can be observed directly in experiments. We measure Dirac’s distribution for the quantum state of the transverse degree of freedom of a photon by weakly measuring transverse x so as to not randomize the subsequent p measurement. Furthermore, we show that the distribution has the classical-like feature that it transforms (e.g., propagates) according to Bayes’ law.

Citations

• Localized States for Elementary Systems
• Complex weak values in quantum measurement
• Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. II. Quantum Mechanics in Phase Space
• Non-negative subtheories and quasiprobability representations of qubits
• Direct Probing of Quantum Phase Space by Photon Counting
• Experimental realization of the quantum box problem
• Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase
• On the principles of elementary quantum mechanics
• Image rotation, Wigner rotation, and the fractional Fourier transform
• Testing Quantum Nonlocality in Phase Space
• Equivalence of Semiclassical and Quantum Mechanical Descriptions of Statistical Light Beams
• Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
• Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer
• Phase space tomography of classical and nonclassical vibrational states of atoms in an optical lattice
• No extension of quantum theory can have improved predictive power
• Einstein, incompleteness, and the epistemic view of quantum states
• Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. I. Mapping Theorems and Ordering of Functions of Noncommuting Operators
• Coherent and Incoherent States of the Radiation Field
• On the Quantum Correction For Thermodynamic Equilibrium

Cited by

• What dynamics can be expected for mixed states in two-slit experiments?
• Estimation of temporal separation of slow light pulses in atomic vapors by weak measurement
• Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance