Cost of Simulating Entanglement in Steering Scenario

• URL: http://arxiv.org/abs/2302.09060v3
• Date: Sat, 01 Feb 2025 04:33:17 GMT
• Title: Cost of Simulating Entanglement in Steering Scenario
• Authors: Yujie Zhang, Jiaxuan Zhang, Eric Chitambar,
• Abstract summary: We quantify the resource content of unsteerable quantum states in terms of the amount of shared randomness required to simulate their behavior.<n>We rigorously demonstrate that the simulation cost is even for some two-qubit unsteerable states.
• Score: 14.065759682652745
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum entanglement is a fundamental feature of quantum mechanics, yet certain entangled states that are unsteerable can be classically simulated in steering scenarios, making them unable to exhibit non-locality in quantum steering. Despite their significance, a systematic comparison of such entangled states has not been fully explored. In this work, we quantify the resource content of unsteerable quantum states in terms of the amount of shared randomness required to simulate their dynamical behavior in the steering scenario. We rigorously demonstrate that the simulation cost is unbounded even for some two-qubit unsteerable states. Moreover, the simulation cost of entangled two-qubit states is always strictly greater than that for any separable state. \par A significant portion of our results rely on the relationship between the simulation cost of two-qubit Werner states and that of noisy spin measurements. Using noisy spin measurements as a central example, we investigate the minimal number of outcomes required for a parent measurement to simulate a given set of compatible measurements. Although some continuous sets of measurements can be simulated using a finite-outcome parent, we identify scenarios where the simulation cost diverges. Our results provide previously unknown lower bounds on the simulation cost, supported by connections between the simulation cost of noisy spin measurements and various geometric inequalities, including those studied in the zonotope-approximation problem in Banach space theory.

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