Tripartite Quantum Steering: Imprecision Plateaus

Abstract

Quantum entanglement is a fundamental resource for various quantum information applications including quantum computing, cryptography, and teleportation. However, detecting entanglement in practice can be challenging due to noisy measurements and limited control over the systems being studied.

Steering, which is a distinct nonlocal property between entanglement and bell nonlocality (the strongest form of nonlocality), implies entanglement and only requires precise measurements to be performed by one party, the trusted party. Generally, if the trusted party measurements deteriorate in precision, this leads to higher steering detection cost or otherwise, to false positives. In [1], it was shown that in the bipartite qubit case, it is possible to develop steering detection methods; inequalities, which remain constant despite a deterioration in the trusted party’s measurements. The region where the inequality remains constant is called an imprecision plateau.

In this work, steering plateaus in the bipartite qubit case are studied, and the necessary conditions to obtain a plateau are identified. Accordingly, we introduce steering inequalities which support plateaus in the tripartite case. The tripartite case is more rich for two reasons, the first is due to the increased freedom in choosing the number of parties that perform precise measurements, either one or two. The second is due to the more rich structure of entanglement; genuine tripartite entanglement. We establish that it is possible to obtain steering and genuine steering plateaus, when one party (steering only) and two parties perform precise measurements up to a finite imprecision for tripartite qubit systems. Finally, we identify the necessary conditions for obtaining these plateaus.

[1] Phys. Rev. A 111, L020404 (2025)

Popular Abstract

"The whole generates the particulars." With this simple phrase, physicist David Bohm captured one of the most mind-bending ideas in quantum physics: entanglement. A system -whether made of particles, atoms, or even (in theory) cats- is entangled when its parts can’t be fully described on their own. At first, this might sound obvious. After all, a building is made of bricks stacked together, and its existence depends on how those bricks connect. But quantum mechanics isn’t that simple. Imagine two balls: one on Earth, the other on the Moon. They’re so far apart that what you do to one shouldn’t instantly affect the other. Yet, if these balls are entangled, something truly strange happens; affecting one immediately influences the other, no matter the distance.

Unlike our everyday experience, where looking at things does not change them, in quantum physics, looking -or more precisely, measuring- affects the system being measured. It is as if looking at a ball makes it change direction. Accordingly, measuring one part of the system affects the other part immediately, regardless of the distance between them. Physicists initially thought that this could not be so; they believed that if we had more information about the systems being studied, no such effect would happen. However, in 1964, John Bell proved that even if we knew everything knowable about the interaction between particles, we still cannot avoid this instant effect across distance, due to entanglement and known as nonlocality.
Despite early resistance, nonlocality or entanglement is now seen as a valuable resource in both theory and technology. For example, quantum computers use entanglement to perform tasks in minutes that would take classical computers billions of years. But to benefit from entanglement, it must first be detected, this is not so easy, especially in tiny systems. Even small measurement errors can lead to incorrect conclusions. Precision matters: trying to measure the radius of a grape with a meter stick just won’t work. One way to partially address imprecise measurements is through quantum steering.
Quantum steering is a method for detecting entanglement that requires only one party to perform precise measurements. Steering is useful because other detection methods require both parties to perform precise measurements. Still, precise measurements by one party is something experimentalists can only aspire, can we do better? It was recently shown, by scientists at Lund University, that one can design detection methods which allow the party that is supposed to perform precise measurements to be slightly imprecise, without affecting our ability to detect steering. It is as if our trust in the measurements does not matter as long as the distrust is not too big. This phenomenon is called a steering plateau, coming from the Greek word platys meaning flat or broad.

In this project, we take things a step further by showing that plateaus can also be obtained in systems with three parties. This setup is especially interesting because it offers more possibilities. For example, we can choose whether one person uses precise measurements while the other two are not restricted, or let two use precise tools while the remaining party is not restricted. Furthermore, we can decide whether this nonlocal effect from one party influences the other two as a group or affects each of them individually.

Influenced by the case of two parties, we design a set of measurement instructions. Then we calculate the criterion that identifies steering based on the measurements’ outcomes. This criterion does not increase if we allow small imprecision in one or two parties, and if we want the nonlocal effect to influence the two parties as a group or individually. We have accordingly found a plateau.

• author: Abou-Hachem, Amro
• supervisor: Armin Tavakoli; Elna Svegborn
• organization: Mathematical Physics; Department of Physics
• course: FYSK04 20251
• year: 2025
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• keywords: Quantum Steering, Steering Plateaus, Imprecise Measurements, Quantum Nonlocality, Bell Inequalities
• language: English
• id: 9204853
• date added to LUP: 2025-06-24 13:31:53
• date last changed: 2025-06-24 13:31:53