Recently, it has been argued that no extension of quantum theory can have improved predictive power under a strong assumption of free choice of the experimental settings and validity of quantum mechanics. Here, under a different free choice assumption, we describe a model which violates this statement for almost all states of a bipartite two-level system, in a possibly experimentally testable way. From consistency with quantum mechanics and the nonsignaling principle, we derive a bound on the local averages for the family of deterministic ontological theories that our model belongs to.
Comment on ``Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty''
在Phys.Rev.A70，032104（2004），M. Montesinos和G. F. Torres del Castillo考虑了二维各向同性谐振子经典相空间上的各种辛结构。利用狄拉克量子化条件，研究了这些不同的辛形式对系统量子化的影响。他们声称这些辛结构导致了相互不等价的量子理论。事实上，我们在这里证明了在两个表示空间之间存在酉映射，使得各种量化是等价的。
Mutually unbiased bases (MUBs) provide a standard tool in the verification of quantum states, especially when harnessing a complete set for optimal quantum state tomography. In this work, we investigate the detection of entanglement via inequivalent sets of MUBs, with a particular focus on unextendible MUBs. These are bases for which an additional unbiased basis cannot be constructed and, consequently, are unsuitable for quantum state verification. Here, we show that unextendible MUBs, as well as other inequivalent sets in higher dimensions, can be more effective in the verification of entangl…
A multipartite system comprised of $n$ subsystems, each of which is described with `local variables' in ${\mathbb Z}(d)$ and with a $d$-dimensional Hilbert space $H(d)$, is considered. Local Fourier transforms in each subsystem are defined and related phase space methods are discussed (displacement operators, Wigner and Weyl functions, etc). A holistic view of the same system might be more appropriate in the case of strong interactions, which uses `global variables' in ${\mathbb Z}(d^n)$ and a $d^n$-dimensional Hilbert space $H(d^n)$. A global Fourier transform is then defined and related phas…
Quantum coherence has received significant attention in recent years, but its study is mostly conducted in single party settings. In this paper, we generalize important results in multipartite entanglement theory to their counterparts in quantum coherence theory. First, we give a necessary and sufficient condition for when two pure multipartite states are equivalent under local quantum incoherent operations and classical communication (LICC), i.e., two states can be deterministically transformed to each other under LICC operations. Next, we investigate and give the conditions in which such a t…
We discuss the representations of the algebra of quantization, the canonical commutation relations, in a scalar quantum field theory with spontaneously broken U(1) internal symmetry, when a topological defect of the vortex type is formed via the condensation of Nambu-Goldstone particles. We find that the usual thermodynamic limit is not necessary in order to have the inequivalent representations needed for the existence of physically disjoint phases of the system. This is a new type of inequivalence, due to the nontrivial topological structure of the phase space, that appears at finite volume.…
From equivalent Lagrangians to inequivalent open quantum system dynamics
University of Trieste（的里雅斯特大学）；Department of Physics, University of Trieste（的里雅斯特大学物理系）；Istituto Nazionale di Fisica Nucleare, Trieste Section（意大利国家核物理研究所的里雅斯特分部）
It is known that "quantum non locality", leading to the violation of Bell's inequality and more generally of classical local realism, can be attributed to the conjunction of two properties, that we call here elementary locality and predictive completeness. Taking this point of view, we show again that quantum mechanics violates predictive completeness, allowing to make contextual inferences, which can in turn explain why quantum non locality does not contradict relativistic causality. But if the usual quantum state $ψ$ is predictively incomplete, how to complete it ? We give here a set of new …
The non-relativistic quantum mechanics with the generalized uncertainty principle (GUP) is examined when the potential is one-dimensional $δ-$function. It is shown that unlike usual quantum mechanics, the Schrödinger and Feynman's path-integral approaches are inequivalent at the first order of GUP parameter.
