Memory effects in a sequence of measurements of non-commuting observables

Abstract

We use continuous, stochastic quantum trajectories within a framework of quantum state diffusion (QSD) to describe alternating measurements of two non-commuting observables. Projective measurement of an observable completely destroys memory of the outcome of a previous measurement of the conjugate observable. In contrast, measurement under QSD is not projective and it is possible to vary the rate at which information about previous measurement outcomes is lost by changing the strength of measurement. We apply our methods to a spin 1/2 system and a spin 1 system undergoing alternating measurements of the $S_z$ and $S_x$ spin observables. Performing strong $S_z$ measurements and weak $S_x$ measurements on the spin 1 system, we demonstrate return to the same eigenstate of $S_z$ to a degree beyond that expected from projective measurements and the Born rule. Such a memory effect appears to be greater for return to the $\pm 1$ eigenstates than the $0$ eigenstate. Furthermore, the spin 1 system follows a measurement cascade process where an initial superposition of the three eigenstates of the observable evolves into a superposition of just two, before finally collapsing into a single eigenstate, giving rise to a distinctive pattern of evolution of the spin components.

References in corpus (48)

• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• The Uncertainty Principle in the Presence of Quantum Memory
• Direct Measurement of the Quantum Wavefunction
• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
• Observing single quantum trajectories of a superconducting qubit
• 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
• To catch and reverse a quantum jump mid-flight
• Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
• Direct measurement of general quantum states using weak measurement
• Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect
• Violation of the Leggett-Garg inequality with weak measurements of photons
• Experimental investigation of the uncertainty principle in the presence of quantum memory
• Weak values and the Leggett-Garg inequality in solid-state qubits
• Undoing a weak quantum measurement of a solid-state qubit
• Uncollapsing of a quantum state in a superconducting phase qubit
• Quantum Trajectories and Quantum Measurement Theory
• Direct Measurement of a 27-Dimensional Orbital-Angular-Momentum State Vector
• Experimental Violation of Two-Party Leggett-Garg Inequalities with Semi-weak Measurements
• Realization of All-or-nothing-type Kochen-Specker Experiment with Single Photons
• Dynamics of simultaneously measured non-commuting observables
• Direct measurement of the density matrix of a quantum system
• A feasible "Kochen-Specker" experiment with single particles
• Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations
• Randomness in Quantum Mechanics: Philosophy, Physics and Technology
• Sequential weak measurement
• Qubit models of weak continuous measurements
• Violation of Leggett-Garg inequalities in quantum measurements with variable resolution and back-action
• Measuring incompatible observables of a single photon
• Continuous quantum measurement with independent detector cross-correlations
• Experiment Investigating the Connection between Weak Values and Contextuality
• Stochastic path integral formalism for continuous quantum measurement
• Qubit state monitoring by measurement of three complementary observables
• Realization of a quantum random generator certified with the Kochen-Specker theorem
• Sequential measurements of non-commuting observables with quantum controlled interactions
• Experimental Realization of Sequential Weak Measurements of Arbitrary Non-commuting Pauli Observables
• Simultaneous continuous measurement of non-commuting observables: quantum state correlations
• Testing super-deterministic hidden variables theories
• Probing quantumness with joint continuous measurements of non-commuting qubit observables
• Observation of non-classical correlations in sequential measurements of photon polarization
• Simultaneous weak measurement of non-commuting observables
• Kraus representation for density operator of arbitrary open qubit system
• Bacon-Shor code with continuous measurement of non-commuting operators
• Assessment of weak-coupling approximations on a driven two-level system under dissipation
• A Scheme for Performing Strong and Weak Sequential Measurements of Non-commuting Observables
• Stochastic quantum trajectories demonstrate the Quantum Zeno Effect in open spin 1/2, spin 1 and spin 3/2 systems
• Stochastic entropy production for continuous measurements of an open quantum system
• Process Tomography for Systems in a Thermal State

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