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Geometrical aspects of weak measurements and quantum erasers

Tamate, S., Kobayashi, H., Nakanishi, T., Sugiyama, K., Kitano, M.

Published Jan 1, 2009• 28 citations
OpenAlex

Abstract

We investigate the mechanism of weak measurement by using an interferometric framework. In order to appropriately elucidate the interference effect that occurs in weak measurement, we introduce an interferometer for particles with internal degrees of freedom. It serves as a framework common to quantum eraser and weak measurement. We demonstrate that the geometric phase, particularly the Pancharatnam phase, results from the post-selection of the internal state, and thereby the interference pattern is changed. It is revealed that the extraordinary displacement of the probe wavepackets in weak measurement is achieved owing to the Pancharatnam phase associated with post-selection.

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We investigate the mechanism of weak measurement by using an interferometric framework. In order to appropriately elucidate the interference effect that occurs in weak measurement, we introduce an interferometer for particles with internal degrees of freedom. It serves as a framework common to quantum eraser and weak measurement. We demonstrate that the geometric phase, particularly the Pancharatnam phase, results from the post-selection of the internal state, and thereby the interference pattern is changed. It is revealed that the extraordinary displacement of the probe wavepackets in weak measurement is achieved owing to the Pancharatnam phase associated with post-selection.
We investigate the mechanism of weak measurement by using an interferometric framework. In order to appropriately elucidate the interference effect that occurs in weak measurement, we introduce an interferometer for particles with internal degrees of freedom. It serves as a framework common to quantum eraser and weak measurement. We demonstrate that the geometric phase, particularly the Pancharatnam phase, results from the post-selection of the internal state, and thereby the interference pattern is changed. It is revealed that the extraordinary displacement of the probe wavepackets in weak measurement is achieved owing to the Pancharatnam phase associated with post-selection. A correction was made to equation (15) on 30 September 2009
We investigate the mechanism of weak measurement by using an interferometric framework. In order to appropriately elucidate the interference effect that occurs in weak measurement, we introduce an interferometer for particles with internal degrees of freedom. We demonstrate that the geometric phase, particularly the Pancharatnam phase, results from the post‐selection of the internal state, and thereby the interference pattern is changed. It is revealed that the extraordinary displacement of the probe wavepackets in weak measurement is achieved by utilizing the Pancharatnam phase.
The quantum eraser variant of the double-slit experiment, and its 'delayed choice' sub-variant, are considered from the perspective of weak value and weak measurement theory (which is briefly reintroduced here). The interference fringes that appear when measuring certain spin states, which can then be 'erased' when measuring other spin states, are shown to be anomalous weak values that depend on particular post-selection choices. By framing the choice of spin measurement as a weak value of a certain weak measurement, it is then made clear what physical claims can and cannot be made about what occurs in the quantum eraser experiment. Specifically, claims about the choice of spin-state `retrocausally' influencing the choice of slit(s) for the particles to travel through are discredited, and a simple framework is presented for understanding how the fringes arise and why they can be 'erased'.
We present a procedure to completely determine the complex modular values of arbitrary observables of pre- and postselected ensembles, which works experimentally for all measurement strengths and all postselected states. This procedure allows us to discuss the physics of modular and weak values in interferometric experiments involving a qubit meter. We determine both the modulus and the argument of the modular value for any measurement strength in a single step, by simultaneously controlling the visibility and the phase in a quantum eraser interference experiment. Modular and weak values are closely related. Using entangled qubits for the probed and meter systems, we show that the phase of the modular and weak values has a topological origin. This phase is completely defined by the intrinsic physical properties of the probed system and its time evolution. The physical significance of this phase can thus be used to evaluate the quantumness of weak values.
It is widely assumed that the quantum fluctuations of the meter readout in a weak measurement make it impossible to identify the contributions originating from the individual values of the physical property observed in the measurement. Here, we show that a careful analysis of the quantum dynamics of the meter system allows us to identify a universal relation between quantum interference in the post-selection probability, and quantum interference in the statistics of the meter readout. The analysis reveals that quantum interference modifies the readout distribution of the meter in two ways, a diffusion term that identifies the appropriate operator ordering in the post-selected variance of the observed system property, and a wavefunction-dependent update of the initial meter statistics based on the effect of back action on the post-selection probability. Our results show that the statistical patterns described by meter interference provide important details about the physics of post-selection in weak measurements, allowing us to exclude the possibility of statistical artefacts in the experimental observation of weak values.
We introduce a simple experiment involving a double-slit interferometer by which one can learn basic concepts of quantum interference such as which-path marking, quantum erasers, and geometric phases. Each of them exhibits seemingly mysterious phenomena in quantum physics. In our experiment, we use the double-slit interference of visible light with the polarization as an internal state to demonstrate the disappearance of fringes by which-path marking, recovery of interference using quantum erasers, and the rapid shifting of the fringe pattern induced by the geometric phase. We also present a simple theoretical analysis of an interferometer with an internal state.