We develop a scheme to distill entanglement from bipartite Fermionic systems in an arbitrary quasifree state. It can be applied if either one system containing infinite one-copy entanglement is available or if an arbitrary amount of equally prepared systems can be used. We show that the efficiency of the proposed scheme is in general very good and in some cases even optimal. Furthermore we apply it to Fermions hopping on an infinite lattice and demonstrate in this context that an efficient numerical analysis is possible for more then 10^6 lattice sites.We develop a scheme to distill entanglement from bipartite Fermionic systems in an arbitrary quasifree state. It can be applied if either one system containing infinite one-copy entanglement is available or if an arbitrary amount of equally prepared systems can be used. We show that the efficiency of the proposed scheme is in general very good and in some cases even optimal. Furthermore we apply it to Fermions hopping on an infinite lattice and demonstrate in this context that an efficient numerical analysis is possible for more then 10^6 lattice sites.

arXiv:1003.2797Mar 14, 20100 citations

Distilling Entanglement from Fermions

Michael Keyl

Since fermions are based on anti-commutation relations, their entanglement cannot be studied in the usual way, such that the available theory has to be modified appropriately. Recent publications consider in particular the structure of separable and of maximally entangled states. In this paper we want to discuss local operations and entanglement distillation from bipartite fermionic systems. To this end we apply an algebraic point of view where algebras of local observables, rather than tensor product Hilbert spaces play the central role. We apply our scheme in particular to fermionic Gaussian states, where the whole discussion can be reduced to properties of the covariance matrix. Finally, the results are demonstrated with free fermions on an infinite, one-dimensional lattice.Since fermions are based on anti-commutation relations, their entanglement cannot be studied in the usual way, such that the available theory has to be modified appropriately. Recent publications consider in particular the structure of separable and of maximally entangled states. In this paper we want to discuss local operations and entanglement distillation from bipartite fermionic systems. To this end we apply an algebraic point of view where algebras of local observables, rather than tensor product Hilbert spaces play the central role. We apply our scheme in particular to fermionic Gaussian states, where the whole discussion can be reduced to properties of the covariance matrix. Finally, the results are demonstrated with free fermions on an infinite, one-dimensional lattice.

arXiv:0812.0763Open Systems & Information DynamicsAug 13, 20091 citation

The Purification and Distillation of Entanglement

Cheng-Zu Li

Distillation and purification of entanglement is an important field of quantum information both in theory and in experiment. This paper presents some main conclusions in this field, and discusses mainly the distillation of entanglement from finite copies of a mixed state. By using the conceptions of quasiseparable state and distillable subspace, we show a necessary condition and a sufficient and necessary condition of the distillability from finite copies of a mixed state. We also get the most efficient protocols of entanglement distillation for the case of finite copies. Finally we consider the generalization of these results to the case of infinite copies of a mixed state.Distillation and purification of entanglement is an important field of quantum information both in theory and in experiment. This paper presents some main conclusions in this field, and discusses mainly the distillation of entanglement from finite copies of a mixed state. By using the conceptions of quasiseparable state and distillable subspace, we show a necessary condition and a sufficient and necessary condition of the distillability from finite copies of a mixed state. We also get the most efficient protocols of entanglement distillation for the case of finite copies. Finally we consider the generalization of these results to the case of infinite copies of a mixed state.

Acta Sinica Quantum OpticaJan 1, 20030 citations

Single-copy entanglement in critical quantum spin chains

Jens Eisert, M. Cramer

We consider the single-copy entanglement as a quantity to assess quantum correlations in the ground state in quantum many-body systems. We show for a large class of models that already on the level of single specimens of spin chains, criticality is accompanied with the possibility of distilling a maximally entangled state of arbitrary dimension from a sufficiently large block deterministically, with local operations and classical communication. These analytical results---which refine previous results on the divergence of block entropy as the rate at which maximally entangled pairs can be distilled from many identically prepared chains---are made quantitative for general isotropic translationally invariant spin chains that can be mapped onto a quasifree fermionic system, and for the anisotropic $XY$ model. For the $XX$ model, we provide the asymptotic scaling of $\ensuremath{\sim}(1∕6){\mathrm{log}}_{2}(L)$, and contrast it with the block entropy.We consider the single-copy entanglement as a quantity to assess quantum correlations in the ground state in quantum many-body systems. We show for a large class of models that already on the level of single specimens of spin chains, criticality is accompanied with the possibility of distilling a maximally entangled state of arbitrary dimension from a sufficiently large block deterministically, with local operations and classical communication. These analytical results---which refine previous results on the divergence of block entropy as the rate at which maximally entangled pairs can be distilled from many identically prepared chains---are made quantitative for general isotropic translationally invariant spin chains that can be mapped onto a quasifree fermionic system, and for the anisotropic $XY$ model. For the $XX$ model, we provide the asymptotic scaling of $\ensuremath{\sim}(1∕6){\mathrm{log}}_{2}(L)$, and contrast it with the block entropy.

arXiv:quant-ph/0506250Physical Review AOct 25, 2005101 citations

Computational entanglement distillation beyond pure states: efficient protocols and fundamental limitations

Takeru Utsumi, Jacopo Rizzo, Ryuji Takagi +1 more

The information-theoretic approach to entanglement typically relies on arbitrarily many input copies and unboundedly complex operations; however, the available resources are constrained in reality. This motivates the study of entanglement theory with limited resources. One of its central questions is which quantities characterize entanglement manipulations, and so far, only the idealized case of pure states has been well explored. In this work, we address entanglement distillation from mixed states and identify the Rényi coherent information as the quantity determining the optimal rate in the worst case under two distinct resource constraints. We first characterize the sample-efficient regime, in which unbounded computational power is allowed. Our universal protocol achieves this rate without knowledge of the input state under certain polynomial rank constraints. This rate is optimal among universal protocols: we construct states whose distillable entanglement is nearly extensive, yet from which no universal sample-efficient protocol attains a rate above their Rényi coherent information. We then push this characterization to the computationally efficient frontier: the same bound holds for any efficient protocol even when the input state is known, and another universal protocol achieves this rate efficiently under additional polynomial constraints on the marginal ranks. Overall, our results give the Rényi coherent information a novel operational meaning in two computational settings: universal distillation with limited copies and efficient distillation even with knowledge of the input state.The information-theoretic approach to entanglement typically relies on arbitrarily many input copies and unboundedly complex operations; however, the available resources are constrained in reality. This motivates the study of entanglement theory with limited resources. One of its central questions is which quantities characterize entanglement manipulations, and so far, only the idealized case of pure states has been well explored. In this work, we address entanglement distillation from mixed states and identify the Rényi coherent information as the quantity determining the optimal rate in the worst case under two distinct resource constraints. We first characterize the sample-efficient regime, in which unbounded computational power is allowed. Our universal protocol achieves this rate without knowledge of the input state under certain polynomial rank constraints. This rate is optimal among universal protocols: we construct states whose distillable entanglement is nearly extensive, yet from which no universal sample-efficient protocol attains a rate above their Rényi coherent information. We then push this characterization to the computationally efficient frontier: the same bound holds for any efficient protocol even when the input state is known, and another universal protocol achieves this rate efficiently under additional polynomial constraints on the marginal ranks. Overall, our results give the Rényi coherent information a novel operational meaning in two computational settings: universal distillation with limited copies and efficient distillation even with knowledge of the input state.

quant-pharXiv:2610.06787Oct 6, 20260 citations

Optimizing practical entanglement distillation

Filip Rozpędek, Thomas Schiet, Lê Phuc Thinh +3 more

The goal of entanglement distillation is to turn a large number of weakly entangled states into a smaller number of highly entangled ones. Practical entanglement distillation schemes offer a trade-off between the fidelity to the target state and the probability of successful distillation. Exploiting such trade-offs is of interest in the design of quantum repeater protocols. Here, we present a number of methods to assess and optimize entanglement distillation schemes. We start by giving a numerical method to compute upper bounds on the maximum achievable fidelity for a desired probability of success. We show that this method performs well for many known examples by comparing it to well-known distillation protocols. This allows us to show optimality for many well-known distillation protocols for specific states of interest. As an example, we analytically prove optimality of the distillation protocol utilized within the Extreme Photon Loss entanglement generation scheme, even in the asymptotic limit. We proceed to present a numerical method that can improve an existing distillation scheme for a given input state, and we present an example for which this method finds an optimal distillation protocol. An implementation of our numerical methods is available as a Julia package.The goal of entanglement distillation is to turn a large number of weakly entangled states into a smaller number of highly entangled ones. Practical entanglement distillation schemes offer a trade-off between the fidelity to the target state and the probability of successful distillation. Exploiting such trade-offs is of interest in the design of quantum repeater protocols. Here, we present a number of methods to assess and optimize entanglement distillation schemes. We start by giving a numerical method to compute upper bounds on the maximum achievable fidelity for a desired probability of success. We show that this method performs well for many known examples by comparing it to well-known distillation protocols. This allows us to show optimality for many well-known distillation protocols for specific states of interest. As an example, we analytically prove optimality of the distillation protocol utilized within the Extreme Photon Loss entanglement generation scheme, even in the asymptotic limit. We proceed to present a numerical method that can improve an existing distillation scheme for a given input state, and we present an example for which this method finds an optimal distillation protocol. An implementation of our numerical methods is available as a Julia package.

arXiv:1803.10111Physical Review AJun 21, 2018127 citations

10^6

lattice sites.

XY

model. For the

XX

model, we provide the asymptotic scaling of $\ensuremath{\sim}(1∕6){\mathrm{log}}_{2}(L)$, and contrast it with the block entropy.