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Thermodynamical Quantum Information Sharing

Marcin Wieśniak, Vlatko Vedral, Časlav Brukner

Published Mar 3, 2005• 0 citations
OpenAlex

Abstract

We show that, when measured along orthogonal spatial directions, magnetic susceptibility can reveal entanglement between individual constituents of a solid, while magnetisation describes their local properties. We then show that these two thermodynamical quantities satisfy complementary relation in the quantum-mechanical sense. It describes sharing of (quantum) information in the solid between entanglement and local properties of its individual constituents. Magnetic susceptibility is shown to be universal macroscopic entanglement witness that can be applied independently of the model of the solid (without the knowledge of its Hamiltonian).

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We show that, when measured along orthogonal spatial directions, magnetic susceptibility can reveal entanglement between individual constituents of a solid, while magnetisation describes their local properties. We then show that these two thermodynamical quantities satisfy complementary relation in the quantum-mechanical sense. It describes sharing of (quantum) information in the solid between entanglement and local properties of its individual constituents. Magnetic susceptibility is shown to be universal macroscopic entanglement witness that can be applied independently of the model of the solid (without the knowledge of its Hamiltonian).
We show that magnetic susceptibility can reveal spin entanglement between individual constituents of a solid, while magnetization describes their local properties. We then show that magnetization and its variance (equivalent to magnetic susceptibility for a wide class of systems) satisfy complementary relation in the quantum-mechanical sense. It describes sharing of (quantum) information in the solid between spin entanglement and local properties of its individual constituents. Magnetic susceptibility is shown to be a macroscopic (thermodynamical) spin entanglement witness that can be applied without complete knowledge of the specific model (Hamiltonian) of the solid.
We study the macroscopic entanglement properties of a low dimensional quantum spin system by investigating its magnetic properties at low temperatures and high magnetic fields. The tempera- ture and magnetic field dependence of entanglement from the susceptibility and magnetization data comparing the experimental extraction with theoretical estimates are given. Extraction of entan- glement has been made possible through the macroscopic witness operators magnetic susceptibility. The protocol followed in doing so has been outlined in some recent work. Various plots of entan- glement comparing the experimental extraction with theoretical estimates are given. Quantitative comparison between concurrence and entanglement witness is given for both the theoretical and experimental results. Theory and experiments match over a wide range of temperature and field. The spin system studied is a chain, which exhibits dimerisation and yields fascinating entanglement properties when the temperature and magnetic field is varied. These spin systems exhibit quantum phase transition (QPT) at low temperatures, when the magnetic field is swept through a critical value. We show explicitly for the first time, using tools used in quantum information processing (QIP), that quantum phase transition (QPT) can be captured experimentally using canonically conjugate observables. Macroscopically, quantum complementarity relation clearly delineates entangled states from separable states across the QPT. We have estimated the partial information sharing in this system from our magnetization and susceptibility data. The complementarity relation has been experimentally verified to hold in this system
The realization that entanglement can affect macroscopic properties of bulk solid-state systems is a challenge in physics and Chemistry. Theoretical physicists often are considered the entanglement between nearest-neighbor (NN) spins and tried to find its characterizations in terms of macroscopic thermodynamics observables as magnetization and specific heat. Here, we focus on the entanglement between next nearest neighbor (NNN) and the next to next nearest neighbor (NNNN) spins in an exactly solvable model. We show that there is a much clearer fingerprint of the longer-distance entanglement on the thermodynamic properties like the specific heat, the magnetocaloric effect and the magnetic susceptibility.
Some thermodynamical properties of solids, such as heat capacity and magnetic susceptibility, have recently been shown to be linked to the amount of entanglement in a solid. Until now, however, it was not clear whether this entanglement can be used as a resource in quantum information theory. Here we show that this entanglement is physical, demonstrating the principles of its extraction from a typical spin chain by scattering two particles off the system. Moreover, we show how to simulate this process using present-day optical lattice technology.
We demonstrate that two well-established experimental techniques of condensed-matter physics, neutron-diffraction scattering and measurement of magnetic susceptibility, can be used to detect and quantify macroscopic entanglement in solids. Specifically, magnetic susceptibility of copper nitrate (CN) measured in 1963 cannot be described without presence of entanglement. A detailed analysis of the spin correlations in CN as obtained from neutron-scattering experiment from 2000 provides microscopic support for this interpretation and gives the value for the amount of entanglement. We present a quantitative analysis resulting in the critical temperature of 5 K in both, completely independent, experiments below which entanglement exists.