Limits of the time-multiplexed photon-counting method

Regina Kruse, Johannes Tiedau, Tim J. Bartley, Sonja Barkhofen, and Christine Silberhorn

Phys. Rev. A 95, 023815 – Published 8 February 2017

Abstract

The progress in building large quantum states and networks requires sophisticated detection techniques to verify the desired operation. To achieve this aim, a cost- and resource-efficient detection method is the time multiplexing of photonic states. This design is assumed to be efficiently scalable; however, it is restricted by inevitable losses and limited detection efficiencies. Here, we investigate the scalability of time-multiplexed detectors under the effects of fiber dispersion and losses. We use the distinguishability of Fock states up to $n = 20$ after passing the time-multiplexed detector as our figure of merit and find that, for realistic setup efficiencies of $η = 0.85$ , the optimal size for time-multiplexed detectors is 256 bins.

Received 14 November 2016

DOI:https://doi.org/10.1103/PhysRevA.95.023815

Physics Subject Headings (PhySH)

Optical fibers Photon statistics

Photon counting

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Regina Kruse^*, Johannes Tiedau, Tim J. Bartley, Sonja Barkhofen, and Christine Silberhorn

Applied Physics, University of Paderborn, Warburger Straße 100, 33098 Paderborn, Germany

^*regina.kruse@upb.de

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Issue

Vol. 95, Iss. 2 — February 2017

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Images

Figure 1
Schematic of a time-multiplexed detection network.
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Figure 2
Maximum number of bins as limited by fiber dispersion. In (a) we consider the maximum time bin number depending on the repetition rate $R_{Rep}$ and the input pulse duration. We find that even for low repetition rates and long pulse duration the number of time bins is bound by $\approx 2.5 \times 10^{5}$ bins. In (b) we cut (a) at fixed input pulse lengths (long-dashed pink line: $250 fs$ , dotted orange line: $1 ps$ , short-dashed green line: $5 ps$ , and solid black line: $9 ps$ ). For short pulse durations the decrease in the repetition rate is compensated by the increased fiber dispersion, keeping the overall number of time bins constant. For long pulses the dispersion is less pronounced, and decreasing the repetition rate helps to increase the bin number.
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Figure 3
Overlap of the click statistics between different Fock states after passing a TMD. In (a) we consider the different contributions to the final overlap separately for the example $〈 15 | 20 〉$ . For small bin numbers, the overlap is governed by the convolution matrix (dashed line, black pluses); for high bin numbers it is governed by the losses (dotted line, blue pluses). The minimum of the curve that considers both effects (solid line, red pluses) gives the optimal parameters for minimal overlap, marked in gray. In (b)–(d), we extract the optimal bin number and overlap (curves in the insets) for different detection and setup efficiencies $η$ . The additional losses deteriorate the click statistics quite severely, such that for realistic setup and detection efficiencies ( $η = 0.8$ ) it holds no advantage to implement TMDs larger than 256 bins. The faint lines hold no physical meaning and are provided as a guide to the eye.
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Figure 4
For different, but fixed, Fock state inputs $| n 〉$ , we calculate the overlap to the adjacent $\pm 10$ Fock states in the click statistics after passing TMDs of different size. The width of the overlap curve gives a measure with which precision a Fock state can be measured and is therefore a criterion for the resolution of the measurement method. Even for very small input Fock states $[n = 5$ in (a)] large TMDs ( $2^{10}$ bins in green, dotted line) do not perfectly resolve the input state. For larger states [e.g., $n = 50$ in (d)], the resolution goes down drastically. From this we conclude that TMDs are not sufficient to verify large quantum states directly. The faint lines in the plots hold no physical meaning and are provided as a guide to the eye.
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