Imprecision Plateaus in Quantum Steering

Abstract

In 1935, Schrödinger noted that if one of two entangled particles is subjected to a suitable measurement, it appears as if the state of the other particle is instantaneously influenced at a distance. This phenomenon, which Schrödinger referred to as quantum steering, exhibits properties favorable for quantum information theory. Therefore, much research has been put into developing criteria to detect quantum steering. In particular, to detect if an unknown state is so-called steerable, one must characterize the state by performing suitable measurements on it. Since quantum measurements cannot be implemented exactly, new steering criteria that take into account the lack of perfect measurement control have been developed in the last few years. However, the ability of these criteria to detect steering typically deteriorates rapidly as small measurement imprecisions are permitted in the analysis. In sharp contrast, a very different steering criterion was recently found through numerical analysis. Interestingly, this criterion suggests the existence of an "imprecision plateau", i.e., a limited regime in which imprecise measurements do not appear to influence the criterion's ability to detect quantum steering.

The aim of this project is to explore this observation. In particular, this is done in a framework in which the experimenter can estimate how well the lab's measurements approximate the intended measurements. We start by analytically proving the existence of the described "imprecision plateau" for the Elegant Bell Inequality (EBI) steering scenario. Thereafter, we show that this phenomenon is not unique to the EBI scenario, but occurs in other steering scenarios as well. Finally, we investigate how numerical optimization methods that bound the set of quantum correlations from the interior and the exterior can be used to study the imprecision plateau in more complex settings.

Popular Abstract

In this project, we find that it is possible to construct simple criteria used to detect quantum entanglement that remains constant under measurement errors up to a certain threshold of imprecision.

Quantum information science is an emerging research field that plays an important role in the development of new innovative technologies, including quantum computers, quantum communication, and quantum sensors. The success of quantum technology lies in its ability to harness fundamental quantum properties that have no classical counterparts. One of these quantum resources is a counterintuitive phenomenon known as quantum entanglement. If two particles are entangled, they are connected in such a way that the state of one of the particles directly relates to the state of the other particle, regardless of the distance between them. This unique feature makes entanglement essential for many quantum information tasks. However, natural questions arise in these applications: how can we ensure that a group of particles is indeed entangled, and how can we detect entanglement?

To address these questions, much research has been put into developing efficient methods for detecting entanglement. One such method, which has received much attention in recent years, is based on a phenomenon known as quantum steering. Quantum steering describes the fact that when one of two entangled particles is subjected to a suitable measurement, it appears as though the state of the other particle is instantaneously influenced (“steered”) at a distance. Therefore, if we can demonstrate that an unknown state, composed of two particles, is so-called steerable, we can also verify that it was entangled.

To prove that a quantum system is steerable, we must perform suitable measurements on it. Since quantum measurements cannot be implemented with perfect control, this leads to the issue that steering must be verified using these imprecise measurements. Moreover, even small measurement deviations can make it very difficult to verify steering. As a result, it is easy to draw the false conclusion that steering has been demonstrated in the experiments, hence stating that the two particles are entangled, although this may not be true. Such false positives can have detrimental effects on transmitting and storing information in a secure way in quantum communication tasks.

Nevertheless, in this project, we proved the existence of a new type of simple criterion for detecting quantum steering. Interestingly, this criterion exhibits an "imprecision plateau", i.e., a limited regime in which imprecise measurements do not affect the criterion's ability to detect quantum steering. Therefore, the imprecision plateau may be of significance for relaxing the assumptions of perfect quantum measurements without increasing the requirements for experimental detection capability. In practice, this means that the plateau offers a promising solution to reduce the risk of false positives with important applications in quantum communication security.

• author: Svegborn, Elna
• supervisor: Armin Tavakoli
• organization: Mathematical Physics; Department of Physics
• course: PHYM01 20241
• year: 2024
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• language: English
• id: 9163035
• date added to LUP: 2024-07-03 09:06:35
• date last changed: 2024-07-03 09:21:24