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We consider the time delay of massive, non-relativistic, one-dimensional particles due to a tunneling potential. In this setting the well-known Hartman effect asserts that often the sub-ensemble of particles going through the tunnel seems to cross the tunnel region instantaneously. An obstacle to the utilization of this effect for getting faster signals is the exponential damping by the tunnel, so there seems to be a trade-off between speedup and intensity. In this paper we prove that this trade-off is never in favor of faster signals: the probability for a signal to reach its destination before some deadline is always reduced by the tunnel, for arbitrary incoming states, arbitrary positive and compactly supported tunnel potentials, and arbitrary detectors. More specifically, we show this for several different ways to define ``the same incoming state and the same detector when comparing the settings with and without tunnel potential. The arrival time measurements are expressed in the time-covariant approach, but we also allow the detection to be a localization measurement at a later time.
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The transit times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Considering two identical particles symmetrically impinging on a one-dimensional barrier, we demonstrate that the phase time and the dwell time give connected results where, however, the exact position of the scattered particles is explicitly determined by the phase time (group delay). For the antisymmetrized wave function configuration, an unusual effect of {em accelerated} transmission is clearly identified in a simultaneous tunneling of two identical fermions.
The stationary phase method is often employed for computing tunneling {em phase} times of analytically-continuous {em gaussian} or infinite-bandwidth step pulses which collide with a potential barrier. The indiscriminate utilization of this method without considering the barrier boundary effects leads to some misconceptions in the interpretation of the phase times. After reexamining the above barrier diffusion problem where we notice the wave packet collision necessarily leads to the possibility of multiple reflected and transmitted wave packets, we study the phase times for tunneling/reflecting particles in a framework where an idea of multiple wave packet decomposition is recovered. To partially overcome the analytical incongruities which rise up when tunneling phase time expressions are obtained, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and a one dimensional squared potential barrier where the scattered wave packets can be recomposed by summing the amplitudes of simultaneously reflected and transmitted waves.
We characterize the operational capabilities of quantum channels which can neither create nor detect quantum coherence vis-`a-vis efficiently manipulating coherence as a resource. We study the class of dephasing-covariant operations (DIO), unable to detect the coherence of any input state, as well as introduce an operationally-motivated class of channels $rho$-DIO which is tailored to a specific input state. We first show that pure-state transformations under DIO are completely governed by majorization, establishing necessary and sufficient conditions for such transformations and adding to the list of operational paradigms where majorization plays a central role. We then show that $rho$-DIO are strictly more powerful: although they cannot detect the coherence of the input state $rho$, the operations $rho$-DIO can distill more coherence than DIO. However, the advantage disappears in the task of coherence dilution as well as generally in the asymptotic limit, where both sets of operations achieve the same rates in all transformations.
The general and explicit relation between the phase time and the dwell time for quantum tunneling of a relativistically propagating particle is investigated and quantified. In analogy with previously obtained non-relativistic results, it is shown that the group delay can be described in terms of the dwell time and a self-interference delay. Lessons concerning the phenomenology of the relativistic tunneling are drawn.
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. It can be shown quantum kernels exist that, subject to computational hardness assumptions, can not be computed classically. It is an important challenge to find quantum kernels that provide an advantage in the classification of real world data. Here we introduce a class of quantum kernels that are related to covariant quantum measurements and can be used for data that has a group structure. The kernel is defined in terms of a single fiducial state that can be optimized by using a technique called kernel alignment. Quantum kernel alignment optimizes the kernel family to minimize the upper bound on the generalisation error for a given data set. We apply this general method to a specific learning problem we refer to as labeling cosets with error and implement the learning algorithm on $27$ qubits of a superconducting processor.
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