Extracting joint weak values from two-dimensional spatial displacements

Abstract

The joint weak value is a counterfactual quantity related to quantum correlations and quantum dynamics, which can be retrieved via weak measurements, as initiated by Aharonov and colleagues. In this Rapid Communication, we provide a full analytical extension of the method described by Puentes et al. [Phys. Rev. Lett. 109, 040401 (2012)], to extract the joint weak values of single-particle operators from two-dimensional spatial displacements of Laguerre-Gauss probe states, for the case of azimuthal index |l|>1. This method has a statistical advantage over previous ones since information about the conjugate observable, i.e., the momentum displacement of the probe, is not required. Moreover, we demonstrate that under certain conditions, the joint weak value can be extracted directly from spatial displacements without any additional data processing.

4 pages, no figures

References in corpus (22)

• Entanglement of Orbital Angular Momentum States of Photons
• Measurement of conditional phase shifts for quantum logic
• Direct Measurement of the Quantum Wavefunction
• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Experimental violation of a Bell's inequality in time with weak measurement
• Complex weak values in quantum measurement
• Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
• Violation of the Leggett-Garg inequality with weak measurements of photons
• Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values
• Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
• Experimental Violation of Two-Party Leggett-Garg Inequalities with Semi-weak Measurements
• The analogy between optical beam shifts and quantum weak measurements
• Sequential weak measurement
• Weak Measurements Beyond the Aharonov-Albert-Vaidman Formalism
• Extracting joint weak values with local, single-particle measurements
• Violation of Leggett-Garg inequalities in quantum measurements with variable resolution and back-action
• Generalized shifts and weak values for polarization components of reflected light beams
• Strange Weak Values
• Weak measurements with orbital angular momentum pointer states
• Helical mode conversion using conical reflector
• Observation of geometric phases in quantum erasers
• Weak interference in the high-signal regime

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• Post-selected von Neumann measurement with Hermite-Gaussian and Laguerre-Gaussian pointer states
• Experimental Realization of Sequential Weak Measurements of Arbitrary Non-commuting Pauli Observables
• Coupling-Deformed Pointer Observables and Weak Values
• A framework for measuring weak values without weak interactions and its diagrammatic representation
• How a single particle modifies the physical reality of two distant others simultaneously: a quantum nonlocality and weak value study
• Protective Measurement -- a new quantum measurement paradigm: detailed description of the first realisation
• Quantification of Concurrence via Weak Measurement
• Disembodiment of arbitrary number of properties in quantum Cheshire cat experiment
• Joint weak value for all order coupling using continuous variable and qubit probe
• Interferometric weak value of polarization observable and differential Jones matrix algebra
• Manifestation of pointer state correlations in complex weak values of quantum observables
• The real and imaginary parts of a weak value appearing as back-actions via a post-selection