Is high-dimensional photonic entanglement robust to noise?

Abstract

High-dimensional entangled states are of significant interest in quantum science as they increase the information content per photon and can remain entangled in the presence of significant noise. The authors develop the analytical theory and show experimentally that the noise tolerance of high-dimensional entanglement can be significantly increased by a modest increase in the size of the Hilbert space. For example, doubling the size of a Hilbert space with a local dimension of d = 300 leads to a reduction in the threshold detector efficiencies required for entanglement certification by two orders of magnitude. This work is developed in the context of spatial entanglement in the few-photon limit, but it can easily be translated to photonic states entangled in different degrees of freedom. The authors also demonstrate that knowledge of a single parameter, the signal-to-noise ratio, precisely links measures of entanglement to a range of experimental parameters quantifying noise in a quantum communication system, enabling accurate predictions of its performance. This work serves to answer a simple question: “Is high-dimensional photonic entanglement robust to noise?” Here, the authors show that the answer is more nuanced than a simple “yes” or “no” and involves a complex interplay between the noise characteristics of the state, channel, and detection system.

Measuring dimensionality and purity of high-dimensional entangled states

“…As a form of validation of these results, we estimate values from other techniques, with the comparison given in Table 1 . If the dimension and noise are known or assumed, then it is possible to calculate the purity following , where Q is the quantum contrast and K the dimension 20 . Likewise, if the state is assumed to be pure and not mixed, and background subtraction is done to remove noise, then the spiral spectrum can be used to get an upper bound on the dimension.…”

“…valid for prime or prime power dimensions) and, finally, the high-dimensional Bell tests can fail the fair sampling condition 16 , 17 . A further limitation in the present state of the art is that certain dimensionality measurements consider only pure states 9 , 18 , yet noise mechanisms always introduce some degree of the mixture to the system 19 , which has a detrimental effect on the accuracy of measured dimensions due to the reduced purity 20 . Yet, knowing the purity and dimension of the state is crucial for fundamental tests of quantum mechanics as well as for quantum information processing protocols, setting the required violation of inequalities in the former, and the information capacity of the state, the allowed error bounds in secure communication systems and the requirement for entanglement distillation in the latter.…”

Engineering Entangled Photons for Transmission in Ring-Core Optical Fibers

“…which is a 6 × 6 maximally entangled state. Higher-dimensional states can provide higher key transmission rates in quantum key distribution [6][7][8][9][10][11], as well as increased resilience to noise [12] and other applications [13,27,28]. These are just a few simple examples of how the dimension and entanglement of the twophoton state can be controlled by manipulating the PV pump beam and post-selection capabilities of the ring-core fiber.…”

“…In the quantum regime, SDM technology has attractive features. The multiple spatial modes are a straightforward way to increase the dimension of quantum systems, which has several advantages in quantum key distribution (QKD) [6][7][8][9][10][11], and have shown to be more resistant to some types of noise [12]. Additional applications can be found in a recent review [13].…”

High-Dimensional Pixel Entanglement: Efficient Generation and Certification

“…While many initial demonstrations have relied on entanglement between qubits, recent advances in technology and theory now allow us to fully exploit high-dimensional quantum systems. In particular, the large dimensionality offered by photonic quantum systems has provided the means for quantum communication with record capacities [7,8], noise-resistant entanglement distribution [9,10], robust loophole-free tests of local realism [11,12], and scalable methods for quantum computation [13].…”