Non-Asymptotic Entanglement Distillation

Fang, Kun; Wang, Xin; Tomamichel, Marco; Duan, Runyao

doi:10.1109/tit.2019.2914688

Cited by 48 publications

(48 citation statements)

References 95 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our work improves many earlier results in the characterisation of one-shot entanglement distillation [16,17,19,20,29], which relied on approximate bounds and were only exact asymptotically; crucially, our formalism allows for a precise description of distillation already at the one-shot level, providing an exact characterisation of the operational power of several classes of operations which extend LOCC and shedding light on the capabilities of LOCC themselves.…”

Section: Introductionsupporting

confidence: 66%

“…The proof proceeds analogously to Theorem 9. The crucial step is to notice that for the isotropic operator  , it is then easy to verify that we have [20]), but we were not able to establish this.…”

Section: Rains Set and Distillationmentioning

confidence: 93%

“…We now characterise the operational capabilities of the different sets of operations. Note that the fidelity of distillation under the class PPT has previously been obtained by Rains [25], and an explicit expression for the rate of distillation in terms of e D H appeared more recently in [20]. Reference [26] considered the class PPTP in this context, but the capabilities of + PPTP have not been explicitly investigated before.…”

Section: Ppt and Ppt-preserving Operationsmentioning

confidence: 98%

“…Many such schemes require the use of entanglement in the pure, maximal form of singlets-the efficient conversion of entanglement into such form, dubbed entanglement distillation [5,6], is thus of vital importance, and the development of effective theoretical and practical methods to characterise entanglement distillation remains at the forefront of quantum information research [7]. First studied in the asymptotic regime under the assumption of being able to manipulate an unbounded number of independent and identically distributed copies of a quantum system [5,6,[8][9][10][11], distillation later attracted a significant amount of research using the tools of non-asymptotic quantum information theory [12][13][14][15][16][17][18][19][20][21]. The latter setting is of particular importance due to the physical limitations of near-term quantum technologies, preventing us from being able to manipulate large numbers of quantum systems effectively.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

One-shot entanglement distillation beyond local operations and classical communication

et al. 2019

Self Cite

View full text Add to dashboard Cite

We study the task of entanglement distillation in the one-shot setting under different classes of quantum operations which extend the set of local operations and classical communication (LOCC). Establishing a general formalism which allows for a straightforward comparison of their exact achievable performance, we relate the fidelity of distillation under these classes of operations with a family of entanglement monotones and the rates of distillation with a class of smoothed entropic quantities based on the hypothesis testing relative entropy. We then characterise exactly the one-shot distillable entanglement of several classes of quantum states and reveal many simplifications in their manipulation. We show in particular that the ε-error one-shot distillable entanglement of any pure state is the same under all sets of operations ranging from one-way LOCC to separability-preserving operations or operations preserving the set of states with positive partial transpose, and can be computed exactly as a quadratically constrained linear program. We establish similar operational equivalences in the distillation of isotropic and maximally correlated states, reducing the computation of the relevant quantities to linear or semidefinite programs. We also show that all considered sets of operations achieve the same performance in environment-assisted entanglement distillation from any state.

show abstract

Section: Introductionsupporting

confidence: 66%

Section: Rains Set and Distillationmentioning

confidence: 93%

Section: Ppt and Ppt-preserving Operationsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

One-shot entanglement distillation beyond local operations and classical communication

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is known that quantum states with non-negative Wigner function are classically simulable and thus are useless in magic state distillation [18], which can be seen as the analog of states with positive partial transpose (PPT) in entanglement distillation [34,35]. Motivated by the Rains bound [36] and its variants [37][38][39][40][41][42][43] in entanglement theory, the set of subnormalized states with non-positive mana was introduced as follows [20] to explore the resource theory of magic states: (16)).…”

Section: Discrete Wigner Functionmentioning

confidence: 99%

Quantifying the magic of quantum channels

2019

Self Cite

View full text Add to dashboard Cite

Keywords: resource theory of magic quantum channels, completely positive-Wigner-preserving quantum operations, thauma of a quantum channel, distillable magic, classical simulation of noisy quantum circuits Abstract To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum 'magic' or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension d, it is known that quantum states with non-negative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positive-Wigner-preserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing non-Clifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore the threshold of non-stabilizerness for basic quantum circuits under depolarizing noise.states also motivates the resource theory of magic states [15][16][17][18][19][20], where the free operations are the SOs and the free states are the stabilizer states (abbreviated as 'Stab'). On the other hand, since a key step of fault-tolerant quantum computing is to implement non-SOs, a natural and fundamental problem is to quantify the nonstabilizerness or 'magic' of quantum operations. As we are at the stage of noisy intermediate-scale quantum (NISQ) technology, a resource theory of magic for noisy quantum operations is desirable both to exploit the power and to identify the limitations of NISQ devices in fault-tolerant quantum computation (FTQC). Overview of resultsIn this paper, we develop a framework for the resource theory of magic quantum channels, based on qudit systems with odd prime dimension d. Related work on this topic has appeared recently [21], but the set of free operations that we take in our resource theory is larger, given by the completely positive-Wigner-preserving (CPWP) perations as we detail below. We note here that d-level FTQC based on qudits with prime d is of considerable interest for both theoretical and practical purposes [22][23][24][25][26].Our paper is structured as follows.• In section 2, we first review the stabilizer formalism [4] and the discrete Wigner function [27][28][29]. We further review various magic m...

show abstract

Simplest non-additive measures of quantum resources

Melo

Parisio

2021

Quantum Inf Process

View full text Add to dashboard Cite

Non-Asymptotic Entanglement Distillation

Cited by 48 publications

References 95 publications

One-shot entanglement distillation beyond local operations and classical communication

One-shot entanglement distillation beyond local operations and classical communication

Quantifying the magic of quantum channels

Simplest non-additive measures of quantum resources

Contact Info

Product

Resources

About