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Detecting entanglement with a thermometer

Janet Anders, Dagomir Kaszlikowski, Christian Lunkes, Toshio Ohshima, Vlatko Vedral

Published Jan 1, 2005• 21 citations
OpenAlex

Abstract

Abstract. We present a general argument showing that the temperature as well as other thermodynamical state variables qualify as entanglement witnesses for spatial entanglement. This holds for a variety of systems and we exemplify our ideas using a simple non-interacting Bosonic gas. We find that entanglement can exist at arbitrarily high temperatures, provided that we can probe smaller and smaller regions of space. We close with a short discussion of the relationship between the occurrence of Bose-Einstein condensation and our conditions for the presence of entanglement. PACS numbers: Submitted to: New Journal of Physics Keywords: macroscopic entanglement, entanglement witnesses, bosonic gas, BEC, continuous variable systemsDetecting entanglement with a thermometer 2 1.

Related papers

Detecting entanglement with a thermometer

Janet Anders, Dagomir Kaszlikowski, Christian Lunkes +2 more

We present a general argument showing that the temperature as well as other thermodynamical state variables can qualify as entanglement witnesses (EWs) for spatial entanglement. This holds for a variety of systems and we exemplify our ideas using a simple free non-interacting bosonic gas. We find that entanglement can exist at arbitrarily high temperatures, provided that we can probe smaller and smaller regions of space. We then discuss the relationship between the occurrence of Bose–Einstein condensation and our conditions for the presence of entanglement and compare the respective critical temperatures. We close with a short discussion of the idea of seeing entanglement as a macroscopic property in thermodynamical systems and its possible relation to phase transitions in general.

arXiv:quant-ph/0512181•New Journal of Physics•Aug 18, 2006•35 citations

Entanglement in the Bose-Einstein condensate phase transition

Libby Heaney

We determine the behaviour of entanglement between regions of space in a Bose gas of fixed particle number around the critical temperature condensation. Long-range correlations develop in the Bose-Einstein condensate (BEC) phase transition and the aim here is to find out whether spatial coherence alone implies entanglement. We use a purity measure of entanglement to derive an entanglement witness that detects entanglement between two regions of space in the BEC. It is shown that spatial coherence between the two regions is necessary for entanglement with coherence and entanglement becoming equivalent only when the regions occupy the entire confining volume of the gas. The probabilities for Bosons to occupy the regions is the only other parameter that influences the amount of entanglement. We calculate explicitly the amount of entanglement between two regions for a cigar-shaped harmonic potential and find that it increases with decreasing temperature. A second entanglement witness is derived for entanglement between three regions of space, where again spatial coherence between each pair of regions is precursor to entanglement. It is shown that the state with the maximum amount of entanglement occurs when the probabilities for the Bosons to occupy the three regions are equal.

arXiv:0711.0942•Nov 6, 2007•1 citation

Macroscopic Entanglement and Phase Transitions

Janet Anders, Vlatko Vedral

This paper summarises the results of our research on macroscopic entanglement in spin systems and free Bosonic gases. We explain how entanglement can be observed using entanglement witnesses which are themselves constructed within the framework of thermodynamics and thus macroscopic observables. These thermodynamical entanglement witnesses result in bounds on macroscopic parameters of the system, such as the temperature, the energy or the susceptibility, below which entanglement must be present. The derived bounds indicate a relationship between the occurrence of entanglement and the establishment of order, possibly resulting in phase transition phenomena. We give a short overview over the concepts developed in condensed matter physics to capture the characteristics of phase transitions in particular in terms of order and correlation functions. Finally we want to ask and speculate whether entanglement could be a generalised order concept by itself, relevant in (quantum induced) phase transitions such as BEC, and that taking this view may help us to understand the underlying process of high-T superconductivity.

arXiv:quant-ph/0610268•Open Systems & Information Dynamics•Mar 1, 2007•18 citations

Spatial Entanglement of a Free Bosonic Field

Libby Heaney, Janet Anders, Vlatko Vedral

In this paper we discuss the entanglement properties of a thermal non-relativistic free bosonic field. We demonstrate how to formally construct spatial modes in order to use a continuous variable separability criterion and show that the construction of the modes plays a significant role in the way the entanglement manifests itself. For instance the presence of entanglement depends on the shape of the modes and their separation. The temperature of the gas is another crucial factor and for one choice of modes we show that entanglement can be found at arbitrarily high temperatures as long as we can zoom in on suitably small regions in space. Moreover, we show that the entanglement here is useful as it can be extracted to a pair of localised systems.

arXiv:quant-ph/0607069•Jul 11, 2006•7 citations

Macroscopic Entanglement and Phase Transitions

Janet Anders, Vlatko Vedral

This paper summarises the results of our research on macroscopic entanglement in spin systems and free Bosonic gases. We explain how entanglement can be observed using entanglement witnesses which are themselves constructed within the framework of thermodynamics and thus macroscopic observables. These thermodynamical entanglement witnesses result in bounds on macroscopic parameters of the system, such as the temperature, the energy or the susceptibility, below which entanglement must be present. The derived bounds indicate a relationship between the occurrence of entanglement and the establishment of order, possibly resulting in phase transition phenomena. We give a short overview over the concepts developed in condensed matter physics to capture the characteristics of phase transitions in particular in terms of order and correlation functions. Finally we want to ask and speculate whether entanglement could be a generalised order concept by itself, relevant in (quantum induced) phase transitions such as BEC, and that taking this view may help us to understand the underlying process of high-T superconductivity.

•Oct 31, 2006•9 citations

A Simple Thermodynamical Witness Showing Universality of Macroscopic Entanglement

Vlatko Vedral

We show that if the ground state entanglement exceeds the total entropy of a given system, then this system is in an entangled state. This is a universal entanglement witness that applies to any physical system and yields a temperature below which we are certain to find some entanglement. Our witness is then applied to generic bosonic and fermionic many-body systems to derive the corresponding "critical" temperatures that have a very broad validity.

arXiv:0905.3057•Open Systems & Information Dynamics•Aug 13, 2009•4 citations
Abstract. We present a general argument showing that the temperature as well as other thermodynamical state variables qualify as entanglement witnesses for spatial entanglement. This holds for a variety of systems and we exemplify our ideas using a simple non-interacting Bosonic gas. We find that entanglement can exist at arbitrarily high temperatures, provided that we can probe smaller and smaller regions of space. We close with a short discussion of the relationship between the occurrence of Bose-Einstein condensation and our conditions for the presence of entanglement. PACS numbers: Submitted to: New Journal of Physics Keywords: macroscopic entanglement, entanglement witnesses, bosonic gas, BEC, continuous variable systemsDetecting entanglement with a thermometer 2 1.
We present a general argument showing that the temperature as well as other thermodynamical state variables can qualify as entanglement witnesses (EWs) for spatial entanglement. This holds for a variety of systems and we exemplify our ideas using a simple free non-interacting bosonic gas. We find that entanglement can exist at arbitrarily high temperatures, provided that we can probe smaller and smaller regions of space. We then discuss the relationship between the occurrence of Bose–Einstein condensation and our conditions for the presence of entanglement and compare the respective critical temperatures. We close with a short discussion of the idea of seeing entanglement as a macroscopic property in thermodynamical systems and its possible relation to phase transitions in general.
We determine the behaviour of entanglement between regions of space in a Bose gas of fixed particle number around the critical temperature condensation. Long-range correlations develop in the Bose-Einstein condensate (BEC) phase transition and the aim here is to find out whether spatial coherence alone implies entanglement. We use a purity measure of entanglement to derive an entanglement witness that detects entanglement between two regions of space in the BEC. It is shown that spatial coherence between the two regions is necessary for entanglement with coherence and entanglement becoming equivalent only when the regions occupy the entire confining volume of the gas. The probabilities for Bosons to occupy the regions is the only other parameter that influences the amount of entanglement. We calculate explicitly the amount of entanglement between two regions for a cigar-shaped harmonic potential and find that it increases with decreasing temperature. A second entanglement witness is derived for entanglement between three regions of space, where again spatial coherence between each pair of regions is precursor to entanglement. It is shown that the state with the maximum amount of entanglement occurs when the probabilities for the Bosons to occupy the three regions are equal.
This paper summarises the results of our research on macroscopic entanglement in spin systems and free Bosonic gases. We explain how entanglement can be observed using entanglement witnesses which are themselves constructed within the framework of thermodynamics and thus macroscopic observables. These thermodynamical entanglement witnesses result in bounds on macroscopic parameters of the system, such as the temperature, the energy or the susceptibility, below which entanglement must be present. The derived bounds indicate a relationship between the occurrence of entanglement and the establishment of order, possibly resulting in phase transition phenomena. We give a short overview over the concepts developed in condensed matter physics to capture the characteristics of phase transitions in particular in terms of order and correlation functions. Finally we want to ask and speculate whether entanglement could be a generalised order concept by itself, relevant in (quantum induced) phase transitions such as BEC, and that taking this view may help us to understand the underlying process of high-T superconductivity.
In this paper we discuss the entanglement properties of a thermal non-relativistic free bosonic field. We demonstrate how to formally construct spatial modes in order to use a continuous variable separability criterion and show that the construction of the modes plays a significant role in the way the entanglement manifests itself. For instance the presence of entanglement depends on the shape of the modes and their separation. The temperature of the gas is another crucial factor and for one choice of modes we show that entanglement can be found at arbitrarily high temperatures as long as we can zoom in on suitably small regions in space. Moreover, we show that the entanglement here is useful as it can be extracted to a pair of localised systems.
This paper summarises the results of our research on macroscopic entanglement in spin systems and free Bosonic gases. We explain how entanglement can be observed using entanglement witnesses which are themselves constructed within the framework of thermodynamics and thus macroscopic observables. These thermodynamical entanglement witnesses result in bounds on macroscopic parameters of the system, such as the temperature, the energy or the susceptibility, below which entanglement must be present. The derived bounds indicate a relationship between the occurrence of entanglement and the establishment of order, possibly resulting in phase transition phenomena. We give a short overview over the concepts developed in condensed matter physics to capture the characteristics of phase transitions in particular in terms of order and correlation functions. Finally we want to ask and speculate whether entanglement could be a generalised order concept by itself, relevant in (quantum induced) phase transitions such as BEC, and that taking this view may help us to understand the underlying process of high-T superconductivity.