arXiv subjects

Chung-Yun Hsieh

Publications and source records attributed to Chung-Yun Hsieh.

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arXiv2023

Quantum complementarity: A novel resource for unambiguous exclusion and encryption

Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily forbids useful knowledge about the other. Two quantum measurements that do not commute form an example of complementary measurements, and this phenomenon can also be defined for ensembles of states. Although a key quantum feature, it is unclear whether complementarity can be understood more operationally, as a necessary resource in some quantum information task. Here we show this is the case, and relates to a novel task which we term $η$-unambiguous exclusion. As well as giving complementarity a clear operational definition, this also uncovers the foundational underpinning of unambiguous exclusion tasks for the first time. We further show that a special type of measurement complementarity is equivalent to advantages in certain encryption tasks. Finally, our analysis suggest that complementarity of measurement and state ensemble can be interpreted as strong forms of measurement incompatibility and quantum steering, respectively.

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arXiv2023

Characterisation and fundamental limitations of irreversible stochastic steering distillation

Steering resources, central for quantum advantages in one-sided device-independent quantum information tasks, can be enhanced via local filters. Recently, reversible steering conversion under local filters has been fully characterised. Here, we solve the problem in the irreversible scenario, which leads to a complete understanding of stochastic steering distillation. This result also provides an operational interpretation of the max-relative entropy as the optimal filter success probability. We further show that all steering measures can be used to quantify measurement incompatibility in certain stochastic steering distillation scenarios. Finally, for a broad class of steering robustness measures, we show that their maximally achievable values in stochastic steering distillation are always upper bounded by different types of incompatibility robustness measures. Hence, measurement incompatibility sets the fundamental limitations for stochastic steering distillation.

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arXiv2022

Complete classification of steerability under local filters and its relation with measurement incompatibility

Quantum steering is the central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another one via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables measurement assemblage (SEO), first proposed to connect the problem of steerability with measurement incompatibility. We provide an efficient method to compute the maximal extractable steerability via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples.

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arXiv2022

Entanglement transitivity problems

One of the goals of science is to understand the relation between a whole and its parts, as exemplified by the problem of certifying the entanglement of a system from the knowledge of its reduced states. Here, we focus on a different but related question: can a collection of marginal information reveal new marginal information? We answer this affirmatively and show that (non-) entangled marginal states may exhibit (meta)transitivity of entanglement, i.e., implying that a different target marginal must be entangled. By showing that the global $n$-qubit state compatible with certain two-qubit marginals in a tree form is unique, we prove that transitivity exists for a system involving an arbitrarily large number of qubits. We also completely characterize -- in the sense of providing both the necessary and sufficient conditions -- when (meta)transitivity can occur in a tripartite scenario when the two-qudit marginals given are either the Werner states or the isotropic states. Our numerical results suggest that in the tripartite scenario, entanglement transitivity is generic among the marginals derived from pure states.

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arXiv2022

Quantum Channel Marginal Problem

Given a set of local dynamics, are they compatible with a global dynamics? We systematically formulate these questions as quantum channel marginal problems. These problems are strongly connected to the generalization of the no-signaling conditions to quantized inputs and outputs and can be understood as a general toolkit to study notions of quantum incompatibility. In fact, they include as special cases channel broadcasting, channel extendibility, measurement compatibility, and state marginal problems. After defining the notion of compatibility between global and local dynamics, we provide a solution to the channel marginal problem that takes the form of a semidefinite program. Using this formulation, we construct channel incompatibility witnesses, discuss their operational interpretation in terms of an advantage for a state-discrimination task, prove a gap between classical and quantum dynamical marginal problems and show that the latter is irreducible to state marginal problems.

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arXiv2021

Communication, Dynamical Resource Theory, and Thermodynamics

Recently, new insights have been obtained by jointly studying communication and resource theory. This interplay consequently serves as a potential platform for interdisciplinary studies. To continue this line, we analyze the role of dynamical resources in a communication setup, and further apply our analysis to thermodynamics. To start with, we study classical communication scenarios constrained by a given resource, in the sense that the information processing channel is unable to supply additional amounts of the resource. We show that the one-shot classical capacity is upper bounded by resource preservability, which is a measure of the ability to preserve the resource. A lower bound can be further obtained when the resource is asymmetry. As an application, unexpectedly, under a recently-studied thermalization model, we found that the smallest bath size needed to thermalize all outputs of a Gibbs-preserving coherence-annihilating channel upper bounds its one-shot classical capacity. When the channel is coherence non-generating, the upper bound is given by a sum of coherence preservability and the bath size of the channel's incoherent version. In this sense, bath sizes can be interpreted as the thermodynamic cost of transmitting classical information. This finding provides a dynamical analogue of Landauer's principle, and therefore bridges classical communication and thermodynamics. As another implication, we show that, in bipartite settings, classically correlated local baths can admit classical communication even when both local systems are completely thermalized. Hence, thermalizations can transmit information by accessing only classical correlation as a resource. Our results demonstrate interdisciplinary applications enabled by dynamical resource theory.

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arXiv2020

Entanglement preserving local thermalization

We investigate whether entanglement can survive the thermalization of subsystems. We present two equivalent formulations of this problem: (1) Can two isolated agents, accessing only pre-shared randomness, locally thermalize arbitrary input states while maintaining some entanglement? (2) Can thermalization with local heat baths, which may be classically correlated but do not exchange information, locally thermalize arbitrary input states while maintaining some entanglement? We answer these questions in the positive at every nonzero temperature and provide bounds on the amount of preserved entanglement. We provide explicit protocols and discuss their thermodynamic interpretation: we suggest that the underlying mechanism is a speed-up of the subsystem thermalization process. We also present extensions to multipartite systems. Our findings show that entanglement can survive locally performed thermalization processes accessing only classical correlations as a resource. They also suggest a broader study of the channel's ability to preserve resources and of the compatibility between global and local dynamics.

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arXiv2020

Resource Preservability

Resource theory is a general, model-independent approach aiming to understand the qualitative notion of resource quantitatively. In a given resource theory, free operations are physical processes that do not create the resource and are considered zero-cost. This brings the following natural question: For a given free operation, what is its ability to preserve a resource? We axiomatically formulate this ability as the resource preservability, which is constructed as a channel resource theory induced by a state resource theory. We provide two general classes of resource preservability monotones: One is based on state resource monotones, and another is based on channel distance measures. Specifically, the latter gives the robustness monotone, which has been recently found to have an operational interpretation. As examples, we show that athermality preservability of a Gibbs-preserving channel can be related to the smallest bath size needed to thermalize all its outputs, and it also bounds the capacity of a classical communication scenario under certain thermodynamic constraints. We further apply our theory to the study of entanglement preserving local thermalization (EPLT) and provide a new family of EPLT which admits arbitrarily small nonzero entanglement preservability and free entanglement preservation at the same time. Our results give the first systematic and general formulation of the resource preservation character of free operations.

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arXiv2017

Work extraction and fully entangled fraction

For a bipartite state with equal local dimension d, we prove that one can obtain work gain under Landauer's erasure process on one party in identically and independently distributed (iid) limit when the corresponding fully entangled fraction is larger than 1/d. By processing a given state to the maximally mixed state, we give an approximation for the largest extractable work with an error in the energy scale, which becomes negligible in the large system limit. As a step to link quantum thermodynamics and quantum nonlocality, we also provide a simple picture to approximate the optimal work extraction and suggest a potential thermodynamic interpretation of fully entangled fraction for isotropic states.

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arXiv2017

Quantum steerability: characterization, quantification, superactivation and unbounded amplification

Quantum steering, also called Einstein-Podolsky-Rosen steering, is the intriguing phenomenon associated with the ability of spatially separated observers to steer---by means of local measurements---the set of conditional quantum states accessible by a distant party. In the light of quantum information, all steerable quantum states are known to be resources for quantum information processing tasks. Here, via a quantity dubbed steering fraction, we derive a simple, but general criterion that allows one to identify quantum states that can exhibit quantum steering, thus making an important step towards the characterization of steerable quantum states. The criterion, in turn, also provides upper bounds on the largest steering-inequality violation achievable by arbitrary finite-dimensional maximally entangled states. For the quantification of steerability, we prove that a strengthened version of the steering fraction is a convex steering monotone and demonstrate how it is related to two others, namely, steerable weight and steering robustness. Using these tools, we further demonstrate the superactivation of steerability, i.e., we show how the steerability of certain entangled, but unsteerable quantum states can be recovered by allowing joint measurements on multiple copies of the same state. In particular, our approach allows one to explicitly construct a steering inequality to manifest this phenomenon. Finally, we prove that there exist quantum states (including some unsteerable under projective measurements) whose steering-inequality violation can be arbitrarily amplified by allowing joint measurements on three copies of the same state. For completeness, we also demonstrate how the largest steering-inequality violation can be used to bound the largest Bell-inequality violation and derive, analogously, a simple sufficient condition for Bell-nonlocality from the latter.

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