• Corpus ID: 18176398

# One-shot Multiparty State Merging

@article{Dutil2010OneshotMS,
title={One-shot Multiparty State Merging},
author={Nicolas Dutil and Patrick M. Hayden},
journal={ArXiv},
year={2010},
volume={abs/1011.1974}
}
• Published 8 November 2010
• Computer Science
• ArXiv
We present a protocol for performing state merging when multiple parties share a single copy of a mixed state, and analyze the entanglement cost in terms of min- and max-entropies. Our protocol allows for interpolation between corner points of the rate region without the need for time-sharing, a primitive which is not available in the one-shot setting. We also compare our protocol to the more naive strategy of repeatedly applying a single-party merging protocol one party at a time, by…

## Figures from this paper

Assisted entanglement distillation
• Computer Science
Quantum Inf. Comput.
• 2011
This work extends the notion of entanglement of assistance to arbitrary mixed tripartite states and exhibits a protocol, based on a random coding strategy, for extracting pureEntanglement, and demonstrates by the use of a simple example that this random measurement strategy outperforms hierarchical distillation strategies when the individual helper stations' states fail to individually factorize into portions associated specifically with Alice and Bob.
Multiparty quantum protocols for assisted entanglement distillation
This work extends the notion of entanglement of assistance to arbitrary states and gives a protocol for extracting pure Entanglement, a new protocol for the task of multiparty state merging, which does not require time-sharing for distributed compression of two senders.
Quantum Residual Correlation: Interpreting through State Merging
• Computer Science
• 2014
It is claimed that this result establishes a re conceptualization of information processing tasks in tripartite situations where the authors can use suitable measurement and states to bring down the cost of the protocol.
A Generalized Quantum Slepian–Wolf
• Computer Science
IEEE Transactions on Information Theory
• 2018
A quantum generalization of the task considered by Slepian and Wolf regarding distributed source compression and provides the asymptotic and independent identically distributed analysis in the case when there is no side information with Charlie.
Distributed Encoding and Decoding of Quantum Information over Networks
• Computer Science, Physics
• 2018
The results suggest that a quantitative difference in entanglement cost between encoding and decoding arises due to the difference between quantum state merging and splitting.
Quantum State Merging for Arbitrarily Small-Dimensional Systems
• Physics, Computer Science
IEEE Transactions on Information Theory
• 2019
In the algorithms, the entanglement cost can be reduced depending on a structure of the given state derived from the Koashi-Imoto decomposition, and improved converse bounds are provided by applying smoothing to those for exact state merging.
Entanglement theory in distributed quantum information processing
Distributed quantum information processing is a promising platform for scaling up quantum information processing, where small- and intermediate-scale quantum devices are connected by a network of
Hypergraph min-cuts from quantum entropies
• Computer Science
Journal of Mathematical Physics
• 2021
It is proved that the min-cut function of any weighted hypergraph can be approximated by the entropies of quantum states known as stabilizer states, and it shows that the recently defined hypergraph cones are contained in the quantum stabilizer entropy cones, as has been conjecture in the recent literature.
Holographic duality from random tensor networks
• Physics
• 2016
A bstractTensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of

## References

SHOWING 1-10 OF 44 REFERENCES
How many singlets are needed to create a bipartite state using LOCC
• Computer Science
• 2009
This paper evaluates the minimum number of singlets needed to achieve the one-shot entanglement cost of the target state in the most general case where dilution is achieved with a fixed accuracy and extends this result to the asymptotic scenario, yielding an alternative proof of the equivalence.
Single-shot Quantum State Merging
It is shown that the minimal amount of quantum communication needed to achieve this single-shot state merging is given by minus the smooth conditional min-entropy of Alice conditioned on the environment, which gives an operational meaning to the smooth conditionality of Alice.
Quantum State Merging and Negative Information
• Computer Science
• 2006
A quantum state shared between many distant locations is considered, and a quantum information processing primitive, state merging, that optimally merges the state into one location is defined, finding that quantum information can be negative.
Entanglement of assistance and multipartite state distillation
• Computer Science
• 2005
It is found that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies, which implies a capacity theorem for quantum channels where the environment helps transmission by broadcasting the outcome of an optimally chosen measurement.
General theory of assisted entanglement distillation
We evaluate the one-shot entanglement of assistance for an arbitrary bipartite state. This yields another interesting result, namely a characterization of the one-shot distillable entanglement of a
Communication cost of entanglement transformations
• Computer Science
• 2003
A matching lower bound of the same asymptotic order is proved, demonstrating the optimality of the Lo-Popescu protocol up to a constant factor and establishing the existence of a fundamental asymmetry between the concentration and dilution tasks.
The Power of LOCCq State Transformations
• Computer Science
• 2002
It is shown that LOCCq state transformations are only as powerful as asymptotic LOCC state transformations for multipartite pure states and that any irreducible m ( m ≥ 2) party pure state can be used to create any other state, using only local operations and classical communication (LOCC).
Entanglement spread and clean resource inequalities
This article will examine states that superpose different amounts of entanglement and protocols that run in superposition but generate or consume different amounts of entanglement. In both cases we
Mixed-state entanglement and quantum error correction.
• Computer Science
Physical review. A, Atomic, molecular, and optical physics
• 1996
It is proved that an EPP involving one-way classical communication and acting on mixed state M (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa, and it is proved Q is not increased by adding one- way classical communication.
One-Shot Classical Data Compression With Quantum Side Information and the Distillation of Common Randomness or Secret Keys
• Computer Science
IEEE Transactions on Information Theory
• 2012
In this hybrid classical-quantum version of the famous Slepian-Wolf problem, the smooth max entropy is found to govern the number of bits into which classical information can be compressed so that it can be reliably recovered from the compressed version and quantum side information.