Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0608051 · Optics and Spectroscopy

Excitation and entanglement transfer near quantum critical points

Michael J. Hartmann, M. E. Reuter, Martin Bodo Plenio

Published Jul 1, 2007• 0 citations
arXivHTMLPDF

Abstract

Recently, there has been growing interest in employing condensed matter systems such as quantum spin or harmonic chains as quantum channels for short distance communication. Many properties of such chains are determined by the spectral gap between their ground and excited states. In particular this gap vanishes at critical points of quantum phase transitions. In this article we study the relation between the transfer speed and quality of such a system and the size of its spectral gap. We find that the transfer is almost perfect but slow for large spectral gaps and fast but rather inefficient for small gaps.

DOI
10.1134/s0030400x0707003x

Related papers

Excitation and Entanglement Transfer Versus Spectral Gap

Michael J. Hartmann, M. E. Reuter, Martin Bodo Plenio

Condensed matter systems have recently been proposed as quantum channels for short distance communication. One characteristic of these systems is whether they feature a spectral gap between their ground and excited states. In this paper we study the transfer of excitations and entanglement between two ancillas, which are weakly coupled to a one dimensional chain at different sites. We find that the transfer is almost perfect but slow for large spectral gaps and fast but rather inefficient for small gaps.

AIP conference proceedings•Jan 1, 2006•0 citations

Excitation and entanglement transfer versus spectral gap

Michael J. Hartmann, M. E. Reuter, Martin Bodo Plenio

We consider quantum many body systems as quantum channels and study the relation between the transfer quality and the size of the spectral gap between the system's ground and excited states. In our setup, two ancillas are weakly coupled to the quantum many body system at different sites, and we study the propagation of an excitation and quantum information from one ancilla to the other. We observe two different scenarios: a slow, but perfect transfer if the gap is large and a fast, but incomplete transfer otherwise. We provide a numerical and analytical approach as well as a simplified physical model explaining our findings. Our results relate the potential of spin chains acting as quantum channels to the concept of quantum phase transitions and offer a different approach to the characterization of these.

arXiv:quant-ph/0511185•New Journal of Physics•Jun 9, 2006•70 citations

Closure of the entanglement gap at quantum criticality : The case of the Quantum Spherical Model

Sascha Wald, Raúl Arias, Vincenzo Alba

The study of entanglement spectra is a powerful tool to detect or elucidate universal behavior in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap δξ , i.e., the lowest-laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spherical model, which exhibits a second-order transition and is mappable to free bosons with an additional external constraint. We analytically show that the Schmidt gap vanishes at the critical point, although only logarithmically. For a system on a torus and the half-system bipartition, the entanglement gap vanishes as π2/ ln(L), with L the linear system size. The entanglement gap is nonzero in the paramagnetic phase and exhibits a faster decay in the ordered phase. The rescaled gap δξ ln(L) exhibits a crossing for different system sizes at the transition, although logarithmic corrections prevent a precise verification of the finite-size scaling. Interestingly, the change of the entanglement gap across the phase diagram is reflected in the zero-mode eigenvector of the spin-spin correlator. At the transition quantum fluctuations give rise to a nontrivial structure of the eigenvector, whereas in the ordered phase it is flat. We also show that the vanishing of the entanglement gap at criticality can be qualitatively but not quantitatively captured by neglecting the structure of the zero-mode eigenvector.

•Jan 1, 2020•7 citations

Entanglement Spectrum, Critical Exponents, and Order Parameters in Quantum Spin Chains

Gabriele De Chiara, Luca Lepori, Maciej Lewenstein +1 more

We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix λ(1), λ(2), signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.

arXiv:1104.1331•Physical Review Letters•Dec 5, 2012•149 citations

Quantum quench and scaling of entanglement entropy

Paweł Caputa, Sumit R. Das, Masahiro Nozaki A +1 more

Global quantum quench with a finite quench rate which crosses critical points is known to lead to universal scaling of correlation functions as functions of the quench rate. In this work, we explore scaling properties of the entanglement entropy of a subsystem in a harmonic chain during a mass quench which asymptotes to finite constant values at early and late times and for which the dynamics is exactly solvable. When the initial state is the ground state, we find that for large enough subsystem sizes the entanglement entropy becomes independent of size. This is consistent with Kibble–Zurek scaling for slow quenches, and with recently discussed “fast quench scaling” for quenches fast compared to physical scales, but slow compared to UV cutoff scales.

arXiv:1702.04359•Physics Letters B•Jun 20, 2017•37 citations

Long quantum channels for high-quality entanglement transfer

Leonardo Banchi, Tony J. G. Apollaro, Alessandro Cuccoli +2 more

High-quality quantum-state and entanglement transfer can be achieved in an unmodulated spin bus operating in the ballistic regime, which occurs when the endpoint qubits A and B are nonperturbatively coupled to the chain by a suitable exchange interaction j 0 . Indeed, the transition amplitude characterizing the transfer quality exhibits a maximum for a finite optimal value j opt 0 ( N ), where N is the channel length. We show that j opt 0 ( N ) scales as N −1/6 for large N and that it ensures a high-quality entanglement transfer even in the limit of arbitrarily long channels, almost independently of the channel initialization. For instance, for any chain length the average quantum-state transmission fidelity exceeds 90% and decreases very little in a broad neighbourhood of j opt 0 ( N ). We emphasize that, taking the reverse point of view, should j 0 be experimentally constrained, high-quality transfer can still be obtained by adjusting the channel length to its optimal value.

arXiv:1105.6058•New Journal of Physics•Dec 2, 2011•89 citations
Recently, there has been growing interest in employing condensed matter systems such as quantum spin or harmonic chains as quantum channels for short distance communication. Many properties of such chains are determined by the spectral gap between their ground and excited states. In particular this gap vanishes at critical points of quantum phase transitions. In this article we study the relation between the transfer speed and quality of such a system and the size of its spectral gap. We find that the transfer is almost perfect but slow for large spectral gaps and fast but rather inefficient for small gaps.
Condensed matter systems have recently been proposed as quantum channels for short distance communication. One characteristic of these systems is whether they feature a spectral gap between their ground and excited states. In this paper we study the transfer of excitations and entanglement between two ancillas, which are weakly coupled to a one dimensional chain at different sites. We find that the transfer is almost perfect but slow for large spectral gaps and fast but rather inefficient for small gaps.
We consider quantum many body systems as quantum channels and study the relation between the transfer quality and the size of the spectral gap between the system's ground and excited states. In our setup, two ancillas are weakly coupled to the quantum many body system at different sites, and we study the propagation of an excitation and quantum information from one ancilla to the other. We observe two different scenarios: a slow, but perfect transfer if the gap is large and a fast, but incomplete transfer otherwise. We provide a numerical and analytical approach as well as a simplified physical model explaining our findings. Our results relate the potential of spin chains acting as quantum channels to the concept of quantum phase transitions and offer a different approach to the characterization of these.
The study of entanglement spectra is a powerful tool to detect or elucidate universal behavior in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap δξ , i.e., the lowest-laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spherical model, which exhibits a second-order transition and is mappable to free bosons with an additional external constraint. We analytically show that the Schmidt gap vanishes at the critical point, although only logarithmically. For a system on a torus and the half-system bipartition, the entanglement gap vanishes as π2/ ln(L), with L the linear system size. The entanglement gap is nonzero in the paramagnetic phase and exhibits a faster decay in the ordered phase. The rescaled gap δξ ln(L) exhibits a crossing for different system sizes at the transition, although logarithmic corrections prevent a precise verification of the finite-size scaling. Interestingly, the change of the entanglement gap across the phase diagram is reflected in the zero-mode eigenvector of the spin-spin correlator. At the transition quantum fluctuations give rise to a nontrivial structure of the eigenvector, whereas in the ordered phase it is flat. We also show that the vanishing of the entanglement gap at criticality can be qualitatively but not quantitatively captured by neglecting the structure of the zero-mode eigenvector.
We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix λ(1), λ(2), signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.
Global quantum quench with a finite quench rate which crosses critical points is known to lead to universal scaling of correlation functions as functions of the quench rate. In this work, we explore scaling properties of the entanglement entropy of a subsystem in a harmonic chain during a mass quench which asymptotes to finite constant values at early and late times and for which the dynamics is exactly solvable. When the initial state is the ground state, we find that for large enough subsystem sizes the entanglement entropy becomes independent of size. This is consistent with Kibble–Zurek scaling for slow quenches, and with recently discussed “fast quench scaling” for quenches fast compared to physical scales, but slow compared to UV cutoff scales.
High-quality quantum-state and entanglement transfer can be achieved in an unmodulated spin bus operating in the ballistic regime, which occurs when the endpoint qubits A and B are nonperturbatively coupled to the chain by a suitable exchange interaction j 0 . Indeed, the transition amplitude characterizing the transfer quality exhibits a maximum for a finite optimal value j opt 0 ( N ), where N is the channel length. We show that j opt 0 ( N ) scales as N −1/6 for large N and that it ensures a high-quality entanglement transfer even in the limit of arbitrarily long channels, almost independently of the channel initialization. For instance, for any chain length the average quantum-state transmission fidelity exceeds 90% and decreases very little in a broad neighbourhood of j opt 0 ( N ). We emphasize that, taking the reverse point of view, should j 0 be experimentally constrained, high-quality transfer can still be obtained by adjusting the channel length to its optimal value.