ORCID Profile
0000-0002-9232-6846
Current Organisation
University of Cambridge
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Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 06-2021
Publisher: Springer Science and Business Media LLC
Date: 24-05-2021
DOI: 10.1007/S00220-021-04064-4
Abstract: Having a distance measure between quantum states satisfying the right properties is of fundamental importance in all areas of quantum information. In this work, we present a systematic study of the geometric Rényi ergence (GRD), also known as the maximal Rényi ergence, from the point of view of quantum information theory. We show that this ergence, together with its extension to channels, has many appealing structural properties, which are not satisfied by other quantum Rényi ergences. For ex le we prove a chain rule inequality that immediately implies the “amortization collapse” for the geometric Rényi ergence, addressing an open question by Berta et al. [Letters in Mathematical Physics 110:2277–2336, 2020, Equation (55)] in the area of quantum channel discrimination. As applications, we explore various channel capacity problems and construct new channel information measures based on the geometric Rényi ergence, sharpening the previously best-known bounds based on the max-relative entropy while still keeping the new bounds single-letter and efficiently computable. A plethora of ex les are investigated and the improvements are evident for almost all cases.
Publisher: American Physical Society (APS)
Date: 06-08-2020
Publisher: American Physical Society (APS)
Date: 03-07-2018
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 07-2019
Publisher: American Physical Society (APS)
Date: 03-08-2017
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 10-2019
Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Date: 19-10-2018
DOI: 10.22331/Q-2018-10-19-100
Abstract: Coherent superposition is a key feature of quantum mechanics that underlies the advantage of quantum technologies over their classical counterparts. Recently, coherence has been recast as a resource theory in an attempt to identify and quantify it in an operationally well-defined manner. Here we study how the coherence present in a state can be used to implement a quantum channel via incoherent operations and, in turn, to assess its degree of coherence. We introduce the robustness of coherence of a quantum channel-which reduces to the homonymous measure for states when computed on constant-output channels-and prove that: i) it quantifies the minimal rank of a maximally coherent state required to implement the channel ii) its logarithm quantifies the amortized cost of implementing the channel provided some coherence is recovered at the output iii) its logarithm also quantifies the zero-error asymptotic cost of implementation of many independent copies of a channel. We also consider the generalized problem of imperfect implementation with arbitrary resource states. Using the robustness of coherence, we find that in general a quantum channel can be implemented without employing a maximally coherent resource state. In fact, we prove that every pure coherent state in dimension larger than 2 , however weakly so, turns out to be a valuable resource to implement some coherent unitary channel. We illustrate our findings for the case of single-qubit unitary channels.
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 04-2020
Publisher: American Physical Society (APS)
Date: 17-08-2018
Publisher: IEEE
Date: 06-2018
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 04-2018
Publisher: IEEE
Date: 06-2018
Publisher: IOP Publishing
Date: 10-2019
Abstract: 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.
Publisher: Springer Science and Business Media LLC
Date: 06-07-2020
DOI: 10.1007/S10107-020-01537-7
Abstract: We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of sum-of-squares relaxations. Exploiting the polynomial kernel technique , we obtain a quadratic improvement of the known convergence rate by Reznick and Doherty and Wehner. Specifically, we show that the rate of convergence is no worse than $$O(d^2/\\ell ^2)$$ O ( d 2 / ℓ 2 ) in the regime $$\\ell = \\Omega (d)$$ ℓ = Ω ( d ) where $$\\ell $$ ℓ is the level of the hierarchy and d the dimension, solving a problem left open in the recent paper by de Klerk and Laurent ( arXiv:1904.08828 ). Importantly, our analysis also works for matrix-valued polynomials on the sphere which has applications in quantum information for the Best Separable State problem. By exploiting the duality relation between sums of squares and the Doherty–Parrilo–Spedalieri hierarchy in quantum information theory, we show that our result generalizes to nonquadratic polynomials the convergence rates of Navascués, Owari and Plenio.
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Kun Fang.