Determinism, Separability, and Quantum Mechanics

Harjit K. Bhogal, Zee R. Perry

Abstract Tim Maudlin has influentially argued that Humeanism about laws of nature stands in conflict with quantum mechanics. Specifically Humeanism implies the principle Separability: the complete physical state of a world is determined by the intrinsic physical state of each space‐time point. Maudlin argues Separability is violated by the entangled states posited by QM. We argue that Maudlin only establishes that a stronger principle, which we call Strong Separability, is in tension with QM. Separability is not in tension with QM. Moreover, while the Humean requires Separability to capture the core tenets of her view, there's no Humean‐specific motivation for accepting Strong Separability. We go on to give a Humean account of entangled states which satisfies Separability. The core idea is that certain quantum states depend upon the Humean mosaic in much the same way as the laws do. In fact, we offer a variant of the Best System account on which the systemization procedure that generates the laws also serves to ground these states. We show how this account works by applying it to the example of Bohmian Mechanics. The 3N‐dimensional configuration space, the world particle in it and the wave function on it are part of the best system of the Humean mosaic, which consists of N particles moving in 3‐dimensional space. We argue that this account is superior to the Humean account of Bohmian Mechanics defended by Loewer and Albert, which takes the 3N‐dimensional space, and its inhabitants, as fundamental.

Niall Shanks

Grete Hermann

Bang-Hai Wang

Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and sufficient, and operational separability condition to determine whether an arbitrary quantum state is entangled or separable. In this paper, we show that whether a quantum state is entangled or not is determined by a threshold within the quantum state. We first introduce the concept of finer and optimal separable states based on the properties of separable states in the role of higher-level witnesses. Then we show that any bipartite quantum state can be decomposed into a convex mixture of its optimal entangled state and its optimal separable state. Furthermore, we show that whether an arbitrary quantum state is entangled or separable, as well as positive partial transposition (PPT) or not, is determined by the robustness of its optimal entangled state to its optimal separable state with reference to a crucial threshold. Moreover, for an arbitrary quantum state, we provide operational algorithms to obtain its optimal entangled state, its optimal separable state, its best separable approximation (BSA) decomposition, and its best PPT approximation decomposition. And the open question of how to calculate the BSA in high-dimension systems is partially done.

Olímpia Lombardi

The purpose of this talk is to briefly recall the main principles of quantum mechanics in order to understand the ontological challenges introduced by the theory. In particular, I will argue that quantum mechanics defies the category of individual for three different reasons: contextuality, non-separability, and indistinguishability. Each one of these three features of the theory violates a traditional ontological principle: the Principle of Omnimode Determination, the Principle of Separability, and the Principle of Identity of Indiscernibles, respectively. Therefore, any interpretation of quantum mechanics should formulate a “global” solution, according to which the three ontological challenges could be adequately tackled in terms of a single ontology.

Mosh� Flato