Weak measurement of qubit oscillations with strong response detectors: Violation of the fundamental bound imposed on linear detectors

Abstract

Qubit measurement by mesoscopic charge detectors has received great interest in the community of mesoscopic transport and solid-state quantum computation, and some controversial issues still remain unresolved. In this work, we revisit the continuous weak measurement of a solid-state qubit by single electron transistors ͑SETs͒ in nonlinear-response regime. For two SET models typically used in the literature, we find that the signal-to-noise ratio can violate the universal upper bound "4," which is imposed quantum mechanically on linear-response detectors. This different result can be understood by means of the cross correlation of the detector currents by viewing the two junctions of the single SET as two detectors. Possible limitation of the potential-scattering approach to this result is also discussed.

Quantum Efficiency of Charge Qubit Measurements Using a Single Electron Transistor

“…This feature contradicts our intuition that an asymmetric SET is like a point-contact (PC) detector, by noting that an ideal PC detector has unit quantum efficiency which is independent of the response strength. We also notice that this conclusion differs from some statements in Ref.[18], but agrees well with the fact that the signal-to-noise ratio is considerably affected by the response strength [19,23].For the strong response detector model (II), we now demonstrate that the quantum limit can be achieved. The respective τ m , Γ d and η are plotted in the right column of Fig 2. The solid-line in the upper panel plots the simple result τ m = 1/Γ L + 1/Γ R from the waiting-time analysis, while the dotted-line shows the result from the wave-packet analysis as a comparison.…”

“…Moreover, it is believed that the SET detector holds promising applications in solid-state quantum computation [11,12], whose measurement properties have been therefore received considerable attention in the past years [13][14][15][16][17][18][19]. While in the higher-order cotunneling regime the measurement can reach the quantum limit (η = 1) in principle [15,16], it was found that the quantum efficiency of the SET detector is rather poor in the weak response and sequential tunneling regime [12][13][14].More recently, however, it was found that the signalto-noise ratio in the power spectrum of qubit oscillation measurements using the SET, another important figure of merit, can reach and even exceed the ideal value of quantum limited linear-response detectors [19], i.e., the Korotkov-Averin bound [20]. To achieve such a result, the necessary conditions for the SET detector are an asymmetric tunnel coupling with the leads and a strong-response to the qubit.…”

“…For the qubit, its Hamiltonian reads H qu = j=a,b E j |j j| + Ω(|a b| + H.c.). For the SET, in this work we consider two models [19], as schematically shown in Fig. 1.…”

“…In this notation |0(1)a(b) means that the SET dot is empty (occupied) and the qubit is in state |a(b) . Explicitly, for model (I) we have [19] 3 while for model (II) it readṡIn these equations, ρ (nR) means that the state is conditioned on the number of electrons tunneled through the right junction of the SET, which is more explicitly labeled here by "n R ", instead of "n" in Eq. (1).…”

Qubit detection with a T-shaped double quantum dot detector

“…For instance, a quantum point contact (QPC) has been widely investigated, with special attention paid to the nontrivial correlation between the QPC and qubit [4][5][6][7][8][9][10][11][12][13][14]. Alternatively, a single electron transistor (SET) was shown to have advantages over QPC in many respects, such as high sensitivity, wide circuit bandwidth, and low noise [15][16][17][18][19][20][21]. In particular, single-shot measurement has recently been realized based on SET detectors, in which the information of the qubit is uniquely determined in simply one run [22][23][24][25].…”