Zero Error In Science

[Terpsícore Deckelman]

Azero error in measurements refers to a constant error that affects all readings of an instrument equally.

In more detail, zero error is a type of systematic error that occurs when an instrument does not read zero when the quantity to be measured is zero. This error is significant because it can lead to inaccuracies in all measurements taken with that instrument, regardless of the actual value being measured. It is a constant error, meaning it does not change based on the quantity being measured.

For example, if a micrometer screw gauge has a zero error of +0.02mm, this means that when the jaws of the gauge are completely closed (i.e., when it should read 0mm), it instead reads +0.02mm. This error will then be present in all measurements taken with this gauge, leading to a consistent overestimation of the actual values.

Zero error can be positive or negative. A positive zero error indicates that the instrument reads a value greater than the actual value when it should read zero, while a negative zero error indicates that the instrument reads a value less than the actual value when it should read zero.

It's important to identify and correct for zero error to ensure the accuracy of measurements. This can often be done by calibrating the instrument, or by subtracting the zero error from all measurements taken with the instrument. For instance, in the micrometer screw gauge example above, if a measurement reads 5.02mm, the corrected measurement would be 5.00mm (5.02mm - 0.02mm).

Understanding zero error is crucial in physics experiments, as it helps students to ensure the reliability and accuracy of their results. It also teaches them the importance of careful and precise measurement, and the need to account for potential sources of error in their work. In this context, familiarising oneself with the use of instruments in physics is invaluable for accurate data collection. Moreover, recognising systematic errors alongside zero errors, and differentiating these from absolute and relative uncertainties, provides a comprehensive understanding of the challenges in physical measurement and the strategies for overcoming them.

IB Physics Tutor Summary: Zero error is when a measuring device doesn't show zero when it should, causing all measurements to be slightly off. This error, which can be either too high or too low, affects all readings and must be corrected to get accurate results. Recognising and adjusting for zero error is vital for precise measurements in experiments, ensuring reliability and accuracy in your findings.

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Single-photon avalanche diodes (SPADs) are the most widespread commercial solution for single-photon counting in quantum key distribution applications. However, the secondary photon emission that arises from the avalanche of charge carriers that occurs during the detection of a photon may be exploited by an eavesdropper to gain information without inducing errors in the transmission key. In this paper, we characterize such backflash light in gated InGaAs/InP SPADs and discuss its spectral and temporal characterization for different detector models and different operating parameters. We qualitatively bound the maximum information leakage due to backflash light and propose solutions for preventing such leakage.

Quantum key distribution (QKD) is a method for sharing secret cryptographic keys between two parties (Alice and Bob) with an unprecedented level of security1, 2, 3, 4, 5, 6, 7. This level of security is ensured by the laws of quantum mechanics and does not depend on the technological resources available to an eavesdropper (Eve), provided that the QKD implementation does not deviate from the theoretical model. However, the security of a practical system (just as for any other cryptographic system) strongly depends on its device implementation. Any deviation of a QKD device from the theoretical model can be exploited as a side channel or back door 8, 9, 10.

In 2010, two zero-error attacks on commercial QKD systems were reported that exploited defects in quantum signal encoding8 and detection9. Shortly after, a plethora of quantum hacking attacks were implemented using existing technologies to exploit device imperfections in a number of QKD designs (with different protocols, modules and systems)10, 11, 12, 13, 14, 15, 16. To guarantee security, each practical implementation must be carefully analyzed and tested for its robustness against zero-error attacks.

Single-photon avalanche diodes (SPADs) are the most widespread commercial solution for single-photon detection in practical QKD implementations17, 18, 19, 20, 21, 22, 23, 24, 25, 26. They can also be the most vulnerable components because they are optically exposed to Eve through the open quantum channel. Eve can inject strong light to take control of these detectors, thereby compromising the security of an entire QKD system. Alternatively, Eve can also passively measure any backflash light arising from avalanching carriers27 to learn the detected bit value (Figure 1). Backflashes have been shown to exist in both InGaAs/InP and Si SPADs27, 28, 29, 30. However, these demonstrations are limited to free-space detectors, and no experiments have been performed on fiber-pigtailed SPADs, which are the detectors of choice in all existing commercial QKD systems because of their practicality.

Representation of an eavesdropper attack exploiting backflash light. Alice sends the photons of the key to Bob; when the photons are detected by Bob using a SPAD, a flash of light, the backflash, is emitted back to the channel. Eve can use a circulator to intercept this spot of light to acquire information about the detector that has clicked.

Here, we present the first characterization of backflash light in fiber-pigtailed InGaAs SPADs from various manufacturers. We construct a reconfigurable optical time-domain reflectometer (OTDR) operating at the single-photon level31, 32, 33, 34, 35 with exceptional sensitivity. This OTDR enables unambiguous identification of detector backflashes from conventional light back reflections and provides a practical way to bound the information leakage, i.e., a fundamental step toward QKD security. Furthermore, we show that information can be leaked through backflashes when two detectors produce temporally distinguishable secondary emissions.

Each type of DUT has a unique, identifiable temporal profile, which reveals the type of detector and its manufacturer. We confirmed this finding by testing four additional devices of the DUT1 type and two of the DUT2 type. Such identifiable backflash profiles can be exploited by Eve to launch attacks tailored to a specific detector type.

Here, we evaluate the maximum possible information leakage PL due to backflash light for QKD systems implemented with detectors of either the DUT1 type or the DUT2 type. We consider a poorly designed QKD system that allows complete temporal discrimination of backflashes between different detectors. PL is estimated starting from the ratio between the number of detected backflashes, NB, and the corresponding total number of valid counts, NP, of the DUT. NB refers only to backflash events, i.e., after background subtraction. We consider the worst-case scenario in which Eve has ideal equipment, i.e., equipment that is lossless and with an ideal (unit) photon detection efficiency. Thus PL is evaluated as

where corrections for losses and inefficiencies of the OTDR system are applied, i.e., for the detection efficiency of the OTDR detector, ηdet, and for the losses in the optical channel connecting the DUT and the OTDR detector due to the circulator and the fiber connections, ηch. To be conservative, we slightly overestimate these losses and inefficiencies by assuming ηchηdet=0.05 based on their approximate evaluations. We obtain an information leakage PL of 9.8% for DUT1 and a PL of 6% for DUT2. These results suggest that the information that Eve can obtain by observing backflash light is not negligible and that countermeasures must be put in place.

For QKD applications, superconducting-nanowire single-photon detectors are an excellent option. Indeed, in addition to their high detection efficiency, their low dark count rate, and their short recovery time45, 46, 47, it is expected that they should not produce any backflash light (and thus should not allow any related information leakage). Unfortunately, they require cryogenic temperatures for operation, and because of the high cost of cryogenic equipment, they currently appear unsuitable for the practical deployment of QKD systems in the real world.

In a complete analysis of the security of a realistic QKD system design, other sources of information leakage must be considered in addition to backflashes. Eve can obtain information about the key by, for example, measuring the spatial, spectral or temporal properties of the transmitted qubits, exploiting the detector dependence of the signal basis and channel losses, or manipulating the detectors9, 48, 49. Once information leakage has been reduced as much as possible with dedicated hardware-based countermeasures, the residual information leakage can be overcome by applying privacy amplification protocols49, 50, 51, 52.

IPD, AT and ZY conceived the idea of the experiment, which was discussed and designed with input from all authors. AM, IPD and GB realized the experimental setup and collected the data in the INRIM Quantum Optics Labs, coordinated by MG. All authors discussed the results and contributed to the writing of the paper.

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