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arXiv:2006.12436 · Quantum Information Processing

Weak measurements, non-classicality and negative probability

Sooryansh Asthana, V. Ravishankar

Published Oct 1, 2021• 2 citations
arXivHTMLPDF
DOI
10.1007/s11128-021-03289-5

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We examine weak measurements of arbitrary observables where the object is prepared in a mixed state and on which measurements with imperfect detectors are made. The weak value of an observable can be expressed as a conditional expectation value over an infinite class of different generalized Kirkwood quasiprobability distributions. ``Strange'' weak values for which the real part exceeds the eigenvalue spectrum of the observable can only be found if the Terletsky-Margenau-Hill distribution is negative or, equivalently, if the real part of the weak value of the density operator is negative. We find that a classical model of a weak measurement exists whenever the Terletsky-Margenau-Hill representation of the observable equals the classical representation of the observable and the Terletsky-Margenau-Hill distribution is non-negative. Strange weak values alone are not sufficient to obtain a contradiction with classical models. We propose feasible weak measurements of photon number of the radiation field. Negative weak values of energy contradict all classical stochastic models, whereas negative weak values of photon number contradict all classical stochastic models where the energy is bounded from below by the zero-point energy. We examine coherent states in particular and find negative weak values with probabilities of 16% for kinetic energy (or squared field quadrature), 8% for harmonic oscillator energy, and 50% for photon number. These experiments are robust against detector inefficiency and thermal noise.
We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. Using the idea of weak measurement, we study Hardy's gedanken experiment and show how the negative probabilities emerge in weak measurement. By calculating the information gain of the measuring device about which path the particles pass through, we show that the negative probabilities only emerge for cases when the information gain is little due to very weak coupling between the measuring device and the particles. When the coupling strength increases, we can unambiguously determine whether a particle passes through a given path every time, hence the average shifts always represent true probabilities, and the strange negatives probabilities disappear.
Abstract The weak measurement (WM) and quantum measurement reversal (QMR) are crucial in protecting the collapse of quantum states. The idea of WM and QMR has recently been used to protect and enhance quantum correlations and universal quantum teleportation (UQT) protocols. Here, we study the quantum correlations, maximal fidelity, and fidelity deviation of the two-qubit negative quantum states developed using discrete Wigner functions with(without) WM and QMR. To take into account the effect of a noisy environment, we evolve the states via non-Markovian amplitude damping and random telegraph noise quantum channels. To benchmark the performance of negative quantum states, we calculate their success probability. We compare our results with the two-qubit maximally entangled Bell state. Interestingly, we observe that some negative quantum states perform better with WM and QMR than the Bell state for different cases under evolution via noisy quantum channels.