Optimal non-invasive measurement of Full Counting Statistics by a single qubit

Abstract

The complete characterisation of the charge transport in a mesoscopic device is provided by the Full Counting Statistics (FCS) $P_t(m)$, describing the amount of charge $Q=me$ transmitted during the time $t$. Although numerous systems have been theoretically characterized by their FCS, the experimental measurement of the distribution function $P_t(m)$ or its moments $⟨Q^n⟩$ are rare and often plagued by strong back-action. Here, we present a strategy for the measurement of the FCS, more specifically its characteristic function $\chi (\lambda )$ and moments $⟨Q^n⟩$, by a qubit with a set of different couplings ${\lambda }_j$, $j=1,\dots ,k,\dots k+p$, $k=\lceil n/2\rceil$, $p\ge 0$, to the mesoscopic conductor. The scheme involves multiple readings of Ramsey sequences at the different coupling strengths ${\lambda }_j$ and we find the optimal distribution for these couplings ${\lambda }_j$ as well as the optimal distribution $N_j$ of $N=\sum N_j$ measurements among the different couplings ${\lambda }_j$. We determine the precision scaling for the moments $⟨Q^n⟩$ with the number $N$ of invested resources and show that the standard quantum limit can be approached when many additional couplings $p\gg 1$ are included in the measurement scheme.

8 pages, 1 figure, Accepted for publication in PRB

References in corpus (6)

• Scattering matrix approach to the description of quantum electron transport
• Wave-packet Formalism of Full Counting Statistics
• Wide-band detection of the third moment of shot noise by a hysteretic Josephson junction
• Fluctuation theorem for heat transport probed by a thermal electrode
• Measurement of high order current correlators
• Fluctuation of heat current in Josephson junctions

Cited by in corpus (5)

• Quantum metrology with a transmon qutrit
• Quasi-probability distributions for observables in dynamic systems
• Dynamical Scheme for Interferometric Measurements of Full-Counting Statistics
• Short time dynamics of molecular junctions after projective measurement
• Coherent interaction-free detection of noise