Determinism and locality in quantum systems

Ingemar Nordin

Giacomo De Palma, Antonella De Pasquale, Vittorio Giovannetti

The ultimate precision of any measurement of the temperature of a quantum system is the inverse of the local quantum thermal susceptibility [A. De Pasquale et al., Nat. Commun. 7, 12782 (2016)] of the subsystem with which the thermometer interacts. If this subsystem can be described with the canonical ensemble, such quantity reduces to the variance of the local Hamiltonian, which is proportional to the heat capacity of the subsystem. However, the canonical ensemble might not apply in the presence of interactions between the subsystem and the rest of the system. In this work, we address this problem in the framework of locally interacting quantum systems. We prove that the local quantum thermal susceptibility of any subsystem is close to the variance of its local Hamiltonian, provided the volume-to-surface ratio of the subsystem is much larger than the correlation length. This result greatly simplifies the determination of the ultimate precision of any local estimate of the temperature and rigorously determines the regime where interactions can affect this precision.

W. Michael Dickson

Hayato Arai, Masahito Hayashi

We study the entanglement structure, i.e., the structure of quantum composite system from operational aspects. The structure is not uniquely determined in General Probabilistic Theories (GPTs) even if we impose reasonable postulate about local systems. In this paper, we investigate the possibility that the standard entanglement structure can be determined uniquely by repeatability of measurement processing and its saturated situation called self-duality. Surprisingly, self-duality cannot determine the standard entanglement structure even if we additionally impose local unitary symmetry assumption. In this paper, we show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry. Besides, we also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable. In addition, as a byproduct, we derive an sufficient condition to achieve the detection of the entanglement property with a finite number of parameterized minimizations.

Alexey V. Shvetsov, Сатанин Аркадий Михайлович, Franco Nori +2 more

A quantum metamaterial can be implemented as a quantum coherent one-dimensional array of qubits placed in a transmission line. The properties of quantum metamaterials are determined by the local quantum state of the system. Here we show that a spatially periodic quantum state of such a system can be realized without direct control of the constituent qubits, by their interaction with the initializing (``priming'') pulses sent through the system in opposite directions. The properties of the resulting quantum photonic crystal are determined by the choice of the priming pulses. This proposal can be readily generalized to other implementations of quantum metamaterials.

Jeffrey Bub