Meaning and Measurability of Nonlocal Quantum States

Angelo C. M. Carollo, G. Massimo Palma, Christoph Simon +1 more

In a recent paper, Bennett et al. [Phys. Rev. A 59, 1070 (1999)] have shown the existence of a basis of product states of a bipartite system with manifest nonlocal properties. In particular these states cannot be completely discriminated by means of bilocal measurements. In this paper we propose an optical realization of these states and we will show that they cannot be completely discriminate by means of a global measurement using only optical linear elements, conditional transformation, and auxiliary photons.

Andrey Anatoljevich Grib, Waldyr A. Rodrigues

Sandu Popescu

Mordecai Waegell, Kelvin J. McQueen

According to a common view, Everettian quantum mechanics (EQM) is a local theory because it avoids nonlocal action at a distance, and this is an important point in EQM's favor. Unlike collapse theories, EQM does not allow an action on one system to change the reduced density matrix (RDM) of a remote entangled system - a clear case of nonlocal action. However, EQM does allow an action on one system to change the global state of the system and its remote entangled partners. We argue that such changes should also count as nonlocal actions, meaning EQM is not local after all. First, we consider an argument to the contrary, which deems such global changes to be mere extrinsic changes, whereas nonlocal action requires intrinsic changes to the remote system. We respond that the intrinsic-extrinsic distinction is problematic and cannot hold the weight of this argument. We then try to clarify when actions that change global states count as nonlocal actions. We argue that it is when the global states are essential explanatory mechanisms of the theory. In EQM, the global state is needed to explain why, in an anti-correlated Bell state, Alice's measuring spin-up ensures that she encounters only the branch where Bob measures spin-down.

Christoph Spengler, Marcus Huber, Beatrix C. Hiesmayr

We compare entanglement with quantum nonlocality employing a geometric structure of the state space of bipartite qudits. The central object is a regular simplex spanned by generalized Bell states. The Collins–Gisin–Linden–Massar–Popescu–Bell inequality is used to reveal states of this set that cannot be described by local-realistic theories. Optimal measurement settings necessary to ascertain nonlocality are determined by means of a recently proposed parameterization of the unitary group combined with robust numerical methods. The main results of this paper are descriptive geometric illustrations of the state space that emphasize the difference between entanglement and quantum nonlocality. Namely, it is found that the shape of the boundaries of separability and Bell inequality violation are essentially different. Moreover, it is also shown that for mixtures of states sharing the same amount of entanglement, Bell inequality violations and entanglement measures are non-monotonically related.

Yuri Ozhigov