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Multiparty quantum protocols for assisted entanglement distillation
Quantum Physics · Submitted 23 May 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In the one-shot regime, we achieve multiparty state merging with entanglement costs not restricted to corner points of the entanglement cost region.
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The abstract, sentence by sentence
Quantum information theory is a multidisciplinary field whose objective is to understand what happens when information is stored in the state of a quantum system. Quantum mechanics provides us with a new resource, called quantum entanglement, which can be exploited to achieve novel tasks such as teleportation and superdense coding. Current technologies allow the transmission of entangled photon pairs across distances up to roughly 100 kilometers. For longer distances, noise arising from various sources degrade the transmission of entanglement to the point that it becomes impossible to use the entanglement as a resource for future tasks. A strategy for dealing with this difficulty is to employ quantum repeaters, stations intermediate between the sender and receiver which participate in the process of entanglement distillation, thereby improving on what the sender and receiver could do on their own. In this work, we study entanglement distillation between two recipients sharing a mixed state and with the help of repeater stations. We extend the notion of entanglement of assistance to arbitrary states and give a protocol for extracting pure entanglement. We also study quantum communication protocols in a more general context. We give a new protocol for the task of multiparty state merging. The previous multiparty state merging protocol required the use of time-sharing. Our protocol does not require time-sharing for distributed compression of two senders. In the one-shot regime, we achieve multiparty state merging with entanglement costs not restricted to corner points of the entanglement cost region. Our analysis of the entanglement cost is performed using (smooth) min- and max-entropies. We illustrate the benefits of our approach by looking at different examples.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Quantum information theory is a multidisciplinary field whose objective is to understand what happens when information is stored in the state of a quantum system. | background 1.00 | 0.03 | 0.02 | asserted 1.00 |
| s1 | Quantum mechanics provides us with a new resource, called quantum entanglement, which can be exploited to achieve novel tasks such as teleportation and superdense coding. | background 1.00 | 0.04 | 0.02 | asserted 0.98 |
| s2 | Current technologies allow the transmission of entangled photon pairs across distances up to roughly 100 kilometers. | background 1.00 | 0.06 | 0.02 | asserted 0.97 |
| s3 | For longer distances, noise arising from various sources degrade the transmission of entanglement to the point that it becomes impossible to use the entanglement as a resource for future tasks. | background 0.99 | 0.07 | 0.02 | asserted 1.00 |
| s4 | A strategy for dealing with this difficulty is to employ quantum repeaters, stations intermediate between the sender and receiver which participate in the process of entanglement distillation, thereby improving on what the sender and receiver could do on their own. | background 0.95 | 0.05 | 0.06 | asserted 0.90 |
| s5 | In this work, we study entanglement distillation between two recipients sharing a mixed state and with the help of repeater stations. | contribution 0.98 | 0.81 | 0.07 | asserted 0.96 |
| s6 | We extend the notion of entanglement of assistance to arbitrary states and give a protocol for extracting pure entanglement. | contribution 1.00 | 0.96 | 0.28 | asserted 1.00 |
| s7 | We also study quantum communication protocols in a more general context. | contribution 0.97 | 0.74 | 0.04 | asserted 0.80 |
| s8 | We give a new protocol for the task of multiparty state merging. | contribution 1.00 | 0.96 | 0.14 | asserted 1.00 |
| s9 | The previous multiparty state merging protocol required the use of time-sharing. | background 0.85 | 0.05 | 0.04 | asserted 1.00 |
| s10 | Our protocol does not require time-sharing for distributed compression of two senders. | contribution 0.66 | 0.93 | 0.14 | asserted 1.00 |
| s11 | In the one-shot regime, we achieve multiparty state merging with entanglement costs not restricted to corner points of the entanglement cost region. | result 0.96 | 0.94 | 0.20 | asserted 1.00 |
| s12 | Our analysis of the entanglement cost is performed using (smooth) min- and max-entropies. | method 0.98 | 0.93 | 0.05 | asserted 1.00 |
| s13 | We illustrate the benefits of our approach by looking at different examples. | contribution 0.54 | 0.86 | 0.06 | asserted 0.97 |
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The paper
Original abstract
Quantum information theory is a multidisciplinary field whose objective is to understand what happens when information is stored in the state of a quantum system. Quantum mechanics provides us with a new resource, called quantum entanglement, which can be exploited to achieve novel tasks such as teleportation and superdense coding. Current technologies allow the transmission of entangled photon pairs across distances up to roughly 100 kilometers. For longer distances, noise arising from various sources degrade the transmission of entanglement to the point that it becomes impossible to use the entanglement as a resource for future tasks. A strategy for dealing with this difficulty is to employ quantum repeaters, stations intermediate between the sender and receiver which participate in the process of entanglement distillation, thereby improving on what the sender and receiver could do on their own. In this work, we study entanglement distillation between two recipients sharing a mixed state and with the help of repeater stations. We extend the notion of entanglement of assistance to arbitrary states and give a protocol for extracting pure entanglement. We also study quantum communication protocols in a more general context. We give a new protocol for the task of multiparty state merging. The previous multiparty state merging protocol required the use of time-sharing. Our protocol does not require time-sharing for distributed compression of two senders. In the one-shot regime, we achieve multiparty state merging with entanglement costs not restricted to corner points of the entanglement cost region. Our analysis of the entanglement cost is performed using (smooth) min- and max-entropies. We illustrate the benefits of our approach by looking at different examples.
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References
How the literature uses it
19 arXiv papers cite this in 40 sentences
Papers citing it · 26 sentences without a confident label
Builds on it 1 paper
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This conjecture is a generalization of the multiparty typicality conjecture of [ref] to general states that are possibly not tensor powers.
On simultaneous min-entropy smoothing · Conjecture · 0.97
Uses its method or tool 1 paper
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This could be done by applying the point-to-point state merging protocol successively [ref] or alternatively, by applying the multiparty simultaneous decoding state merging [ref] .
Unconstrained distillation capacities of a pure-loss bosonic broadcast channel · Achievability part · 0.99
Compares with it 4 papers
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Note that the protocol for concentrating quantum information is applicable to arbitrarily small-dimensional systems as well as achieving zero error, while the existing protocols for the one-shot distributed source compression [ref] are inefficient for small- and intermediate-scale states and cannot avoid nonzero approximation error, similarly to the case of $N=2$ discussed in Remark [ref].
Entanglement theory in distributed quantum information processing · Applications · 0.99
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The present procedure was previously analyzed by Dutil [ref] and shown to work assuming the simultaneous smoothing conjecture in the i.i.d. case.
Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks · Multi-party entanglement of assistance and assisted distillation · 0.87
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The analog of the calculations justifying reconstruction of a bulk operator contained in the entanglement wedge of a boundary region $A$ has even appeared, again with a different motivation, as the “split-transfer protocol” [ref] .
Holographic duality from random tensor networks · Relation to random measurements and the entanglement of assistance · 0.96
Cites it as background 7 papers
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Quantum state merging [ref] is a communication task playing crucial roles in distributed quantum information processing [ref] and multipartite entanglement transformations [ref] .
Entanglement theory in distributed quantum information processing · Entanglement as a resource for distributed quantum information processing · 0.86
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Quantum state merging [ref] is a task playing crucial roles in distributed quantum information processing [ref] and multipartite entanglement transformations [ref] .
Quantum State Merging for Arbitrarily Small-Dimensional Systems · Introduction · 0.98
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Namely, the basic tool of joint typicality in multi-user settings, which is used to define and analyze codes and decoders and which serves as a single conceptual integrator of many constructions (even if it does not always yield the best possible performance) [ref] , is simply not available in the required generality for multipartite quantum states, although it has been conjectured both in a form suited to i.i.d. systems [ref] and in a general form for min-entropies [ref] .
Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks · Introduction · 0.81
What it cites · 94 sentences without a confident label
Builds on 4 papers
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The main technical challenge to overcome was to adapt the decoupling lemma of [ref] and the upper bound on the quantum decoupling error (Proposition 4 in [ref] ) for the case of $m$ senders and a single receiver sharing a multipartite state.
Quantum state merging and negative information · Summary · 0.81
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The last part of this chapter generalizes the multipartite entanglement of assistance of [ref] to allow an arbitrary multipartite mixed state shared between $m$ helpers and two receivers.
Entanglement of assistance and multipartite state distillation · V. Multipartite entanglement of assistance · 1.00
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The first contribution of this chapter is to extend the one-shot entanglement of assistance quantity, first defined in [ref] , to handle mixed states $ψ^ABC$ shared between two recipients (Alice and Bob) and a helper Charlie.
Entanglement of Assistance · I. Generalizing the entanglement of assistance · 0.99
Uses the method or tool of 5 papers
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Using the approach of Horodecki et al. [ref] for achieving a distributed compression of a multipartite state $ψ^C_1C_2…C_mR$, we analyze the entanglement cost associated with multiparty merging when a single-shot state merging protocol is applied iteratively, according to some ordering $π: {1,2,…, m} →{1,2,…, m}$ on the senders.
Quantum state merging and negative information · II. Smooth min-entropy characterization · 0.98
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The one-shot analysis was performed using the quantum min- and max-entropy formalism of [ref] , and presented other difficulties than in the asymptotic setting.
Security of Quantum Key Distribution · Summary · 0.99
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Alice and Bob can distill arbitrarily close to the min-cut rate by applying an entanglement distillation protocol, as in [ref] , on the state $φ^A^n__min A^n B^n__min B^n$.
Distillation of secret key and entanglement from quantum states · An application: entanglement of assistance · 0.99
Compares with 2 papers
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If time-sharing is not required for performing distributed compression for the case of three senders, we show that for certain states our protocol needs no catalytic entanglement, in contrast to the distributed compression protocol of [ref] , which needs catalytic entanglement even if some of the entanglement rates for such states are negative.
Quantum state merging and negative information · II. Freedom in the distribution of catalytic entanglement · 1.00
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Horodecki et al., however, took a more direct approach, similar to what is found in Abeyesinghe et al. [ref] , by considering random (Haar distributed) measurements on the $A^n$ system.
The mother of all protocols: Restructuring quantum information's family tree · Introduction · 0.93
Cites as support 1 paper
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In fact, as was shown in [ref] , no measurement strategy can keep the SCP between Alice and Bob from decreasing exponentially with the number of repeaters, making them useless for establishing entanglement over long distances.
Entanglement Percolation in Quantum Networks · Motivation · 0.99
Cites as background 9 papers
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For the task of distributed compression (i.e., no side information at the decoder), the rate region was characterized in [ref] by the inequalities [equation] If a rate $R_i$ is negative for an achievable rate-tuple $(R_1, R_2, …, R_m)$, close to $-nR_i$ ebits shared between the sender $C_i$ and the receiver are also returned by the protocol.
Quantum state merging and negative information · Definitions and main theorem · 0.88
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The main result obtained by Horodecki et al. [ref] is a proof of the existence of protocols achieving near optimal ebit rates, arbitrarily close to the conditional von Neumann entropy $S(A|B)_ψ$.
Quantum information can be negative · Introduction · 0.86
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Abeyesinghe et al. [ref] showed that by applying a random (Haar distributed) unitary $U:Ã →A_1A_2$ to a subspace $Ã$ of $A^n$, transmission rates arbitrarily close to $1/2I(A;R)_ψ$ are achievable.
The mother of all protocols: Restructuring quantum information's family tree · Introduction · 0.80
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