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/0312123 · Physical Review Letters

Many Copies May Be Required for Entanglement Distillation

John Watrous

Published Jul 1, 2004• 80 citations
arXivHTMLPDF

Abstract

A mixed quantum state $\ensuremath{\rho}$ shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of $\ensuremath{\rho}$ into a single shared pair of qubits having high fidelity with the maximally entangled state $|{\ensuremath{\varphi}}^{+}\ensuremath{\rangle}=(|00\ensuremath{\rangle}+|11\ensuremath{\rangle})/\sqrt{2}$. In this Letter it is proved that there exist states that are distillable, but for which an arbitrarily large number of copies is required before any distillation procedure can produce a shared pair of qubits with even a small amount of entanglement. Specifically, for every positive integer $n$ there exists a state $\ensuremath{\rho}$ that is distillable, but, given $n$ or fewer copies of $\ensuremath{\rho}$, every distillation procedure outputting a single shared pair of qubits outputs those qubits in a separable (i.e., unentangled) state.

DOI
10.1103/physrevlett.93.010502

Related papers

Necessary and sufficient condition for distillability with unit fidelity from finite copies of a mixed state: The most efficient purification protocol

Ping‐Xing Chen, Lin-Mei Liang, Cheng-Zu Li +1 more

It is well known that any entangled mixed state in $2\ensuremath{\bigotimes}2$ systems can be purified via infinite copies of the mixed state. But, can one distill a pure maximally entangled state from finite copies of a mixed state in any bipartite system by local operation and classical communication? This is more meaningful in practical application. We give a necessary and sufficient condition for this distillability. This condition requires that there exist distillable subspaces. According to this condition, one can judge easily whether a mixed state is distillable or not. We also analyze some properties of distillable subspaces, and discuss the most efficient purification protocol. Finally, we discuss the distillable enanglement of a two-qubit system for the case of finite copies.

arXiv:quant-ph/0110045•Physical Review A•Aug 21, 2002•12 citations

Bell-pair distillation under imperfect operations

András Kinyó, Tamás Kiss, Orsolya Kálmán

We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.

quant-pharXiv:2610.35699•Oct 27, 2026•0 citations

Gaussian Transformations and Distillation of Entangled Gaussian States

Jaromı́r Fiurášek

We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled Gaussian state via local Gaussian operations and classical communication. More generally, we show that any hypothetical distillation protocol for Gaussian states involving only Gaussian operations would be a deterministic protocol. Finally, we argue that the protocol considered by Eisert et al. [preceding Letter, Phys. Rev. Lett. 89, 137903 ()]] is the optimum Gaussian distillation protocol for two copies of entangled Gaussian states.

arXiv:quant-ph/0204069•Physical Review Letters•Sep 4, 2002•411 citations

Hardware-Efficient Entanglement Distillation Using Bosonic Systems

Shoham Jacoby, Rotem Arnon-Friedman, Serge Rosenblum

High-fidelity entanglement shared between distant quantum systems is an essential resource for quantum communication and computation. Entanglement distillation addresses this need by converting multiple noisy Bell pairs into fewer higher-fidelity pairs, using only local quantum operations and classical communication. However, this approach typically requires a substantial overhead in the number of qubits. To bypass this hurdle, we propose to leverage the high-dimensional Hilbert space of a single pair of bosonic systems to store a large amount of entanglement, replacing the need for multi-qubit systems. To distill entanglement in such a setup, we devise a new entanglement distillation protocol, tailored for bosonic systems. The protocol converts a highly-entangled noisy state between two bosonic systems into a lower-dimensional but high-fidelity entangled state, using only local bosonic operations. We show that our protocol significantly enhances the fidelity of the entangled state in the presence of naturally occurring loss and dephasing errors. Compared to methods relying on multiple Bell pairs, our scheme offers a more hardware-efficient strategy, providing a practical route toward the realization of entanglement distillation.

arXiv:2503.09700•Mar 12, 2025•0 citations

Experimental Single-Copy Entanglement Distillation

Sebastian Ecker, Philipp Sohr, Lukas Bulla +3 more

The phenomenon of entanglement marks one of the furthest departures from classical physics and is indispensable for quantum information processing. Despite its fundamental importance, the distribution of entanglement over long distances through photons is unfortunately hindered by unavoidable decoherence effects. Entanglement distillation is a means of restoring the quality of such diluted entanglement by concentrating it into a pair of qubits. Conventionally, this would be done by distributing multiple photon pairs and distilling the entanglement into a single pair. Here, we turn around this paradigm by utilizing pairs of single photons entangled in multiple degrees of freedom. Specifically, we make use of the polarization and the energy-time domain of photons, both of which are extensively field tested. We experimentally chart the domain of distillable states and achieve relative fidelity gains up to 13.8%. Compared to the two-copy scheme, the distillation rate of our single-copy scheme is several orders of magnitude higher, paving the way towards high-capacity and noise-resilient quantum networks.

arXiv:2101.11503•Physical Review Letters•Jul 23, 2021•94 citations

Towards the Communication Complexity of Entanglement Distillation Protocols

Andris Ambainis, Ke Yang

Quantum entanglement distillation protocols are LOCC protocols that, over ``imperfect'' EPR pairs shared between Alice and Bob as input, output perfect or near-perfect EPR pairs. In this paper, we study the communication complexity of these protocols, that is, the minimal number of (classical) bits needed for Alice and Bob. To our knowledge, it is the first paper that studies entanglemend distillation protocols in the resource-bounded case. We consider 3 models for imperfect EPR pairs. In the measure-$r$ model, $r$ out of $n$ EPR pairs are measured by an adversary (and thus become ``corrupted''); in the depolarization model, the qubits of Bob underwent a depolarization channel; in the fidelity model, the only information Alice and Bob possess is the fidelity of the shared state. For the first 2 models, we prove tight and almost-tight bounds on the base case, i.e., how well Alice and Bob can do if they are not allowed to communicate. For the fidelity model, we prove a very tight lower bound (up to an additive constant) on the communication complexity. This lower bound implies the optimality of the Random Hash protocol in [ASY02].

•Jul 17, 2002•0 citations
A mixed quantum state \ensuremathρ\ensuremath{\rho}\ensuremathρ shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of \ensuremathρ\ensuremath{\rho}\ensuremathρ into a single shared pair of qubits having high fidelity with the maximally entangled state ∣\ensuremathφ+\ensuremath⟩=(∣00\ensuremath⟩+∣11\ensuremath⟩)/2|{\ensuremath{\varphi}}^{+}\ensuremath{\rangle}=(|00\ensuremath{\rangle}+|11\ensuremath{\rangle})/\sqrt{2}∣\ensuremathφ+\ensuremath⟩=(∣00\ensuremath⟩+∣11\ensuremath⟩)/2​. In this Letter it is proved that there exist states that are distillable, but for which an arbitrarily large number of copies is required before any distillation procedure can produce a shared pair of qubits with even a small amount of entanglement. Specifically, for every positive integer nnn there exists a state \ensuremathρ\ensuremath{\rho}\ensuremathρ that is distillable, but, given nnn or fewer copies of \ensuremathρ\ensuremath{\rho}\ensuremathρ, every distillation procedure outputting a single shared pair of qubits outputs those qubits in a separable (i.e., unentangled) state.
It is well known that any entangled mixed state in $2\ensuremath{\bigotimes}2$ systems can be purified via infinite copies of the mixed state. But, can one distill a pure maximally entangled state from finite copies of a mixed state in any bipartite system by local operation and classical communication? This is more meaningful in practical application. We give a necessary and sufficient condition for this distillability. This condition requires that there exist distillable subspaces. According to this condition, one can judge easily whether a mixed state is distillable or not. We also analyze some properties of distillable subspaces, and discuss the most efficient purification protocol. Finally, we discuss the distillable enanglement of a two-qubit system for the case of finite copies.
We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.
We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled Gaussian state via local Gaussian operations and classical communication. More generally, we show that any hypothetical distillation protocol for Gaussian states involving only Gaussian operations would be a deterministic protocol. Finally, we argue that the protocol considered by Eisert et al. [preceding Letter, Phys. Rev. Lett. 89, 137903 ()]] is the optimum Gaussian distillation protocol for two copies of entangled Gaussian states.
High-fidelity entanglement shared between distant quantum systems is an essential resource for quantum communication and computation. Entanglement distillation addresses this need by converting multiple noisy Bell pairs into fewer higher-fidelity pairs, using only local quantum operations and classical communication. However, this approach typically requires a substantial overhead in the number of qubits. To bypass this hurdle, we propose to leverage the high-dimensional Hilbert space of a single pair of bosonic systems to store a large amount of entanglement, replacing the need for multi-qubit systems. To distill entanglement in such a setup, we devise a new entanglement distillation protocol, tailored for bosonic systems. The protocol converts a highly-entangled noisy state between two bosonic systems into a lower-dimensional but high-fidelity entangled state, using only local bosonic operations. We show that our protocol significantly enhances the fidelity of the entangled state in the presence of naturally occurring loss and dephasing errors. Compared to methods relying on multiple Bell pairs, our scheme offers a more hardware-efficient strategy, providing a practical route toward the realization of entanglement distillation.
The phenomenon of entanglement marks one of the furthest departures from classical physics and is indispensable for quantum information processing. Despite its fundamental importance, the distribution of entanglement over long distances through photons is unfortunately hindered by unavoidable decoherence effects. Entanglement distillation is a means of restoring the quality of such diluted entanglement by concentrating it into a pair of qubits. Conventionally, this would be done by distributing multiple photon pairs and distilling the entanglement into a single pair. Here, we turn around this paradigm by utilizing pairs of single photons entangled in multiple degrees of freedom. Specifically, we make use of the polarization and the energy-time domain of photons, both of which are extensively field tested. We experimentally chart the domain of distillable states and achieve relative fidelity gains up to 13.8%. Compared to the two-copy scheme, the distillation rate of our single-copy scheme is several orders of magnitude higher, paving the way towards high-capacity and noise-resilient quantum networks.
Quantum entanglement distillation protocols are LOCC protocols that, over ``imperfect'' EPR pairs shared between Alice and Bob as input, output perfect or near-perfect EPR pairs. In this paper, we study the communication complexity of these protocols, that is, the minimal number of (classical) bits needed for Alice and Bob. To our knowledge, it is the first paper that studies entanglemend distillation protocols in the resource-bounded case. We consider 3 models for imperfect EPR pairs. In the measure-rrr model, rrr out of nnn EPR pairs are measured by an adversary (and thus become ``corrupted''); in the depolarization model, the qubits of Bob underwent a depolarization channel; in the fidelity model, the only information Alice and Bob possess is the fidelity of the shared state. For the first 2 models, we prove tight and almost-tight bounds on the base case, i.e., how well Alice and Bob can do if they are not allowed to communicate. For the fidelity model, we prove a very tight lower bound (up to an additive constant) on the communication complexity. This lower bound implies the optimality of the Random Hash protocol in [ASY02].