arXiv subjects

Sixia Yu

Publications and source records attributed to Sixia Yu.

At least 37 records · Page 2Linked to original sources

arXiv2019

No Disturbance Without Uncertainty as a Physical Principle

Finding physical principles lying behind quantum mechanics is essential to understand various quantum features, e.g., the quantum correlations, in a theory-independent manner. Here we propose such a principle, namely, no disturbance without uncertainty, stating that the disturbance caused by a measurement to a subsequent incompatible measurement is no larger than the uncertainty of the first measurement, equipped with suitable theory-independent measures for disturbance and uncertainty. When applied to local systems in a multipartite scenario, our principle imposes such a strong constraint on non-signaling correlations that quantum correlations can be recovered in many cases: i. it accounts for the Tsirelsons bound; ii. it provides the so far tightest boundary for a family of the noisy super-nonlocal box with 3 parameters, and iii. it rules out an almost quantum correlation from quantum correlations by which all the previous principles fail, as well as the celebrated quantum criterion due to Navascues, Pironio, and Acin. Our results pave the way to understand nonlocality exhibited in quantum correlations from local principles.

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arXiv2018

Uncertainty-Complementarity Balance as a General Constraint on Non-locality

We propose an uncertainty-complementarity balance relation and build quantitative connections among non-locality, complementarity, and uncertainty. Our balance relation, which is formulated in a theory-independent manner, states that for two measurements performed sequentially, the complementarity demonstrated in the first measurement in terms of disturbance is no greater than the uncertainty of the first measurement. Quantum theory respects our balance relation, from which the Tsirelson bound can be derived, up to an inessential assumption. In the simplest Bell scenario, we show that the bound of Clauser-Horne-Shimony-Holt inequality for a general non-local theory can be expressed as a function of the balance strength, a constance for the given theory. As an application, we derive the balance strength as well as the nonlocal bound of Popescu-Rohrlich box. Our results shed light on quantitative connections among three fundamental concepts, i.e., uncertainty, complementarity and non-locality.

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arXiv2018

Phase amplification in optical interferometry with weak measurement

Improving the phase resolution of interferometry is crucial for high-precision measurements of various physical quantities. Systematic phase errors dominate the phase uncertainties in most realistic optical interferometers. Here we propose and experimentally demonstrate a weak measurement scheme to considerably suppress the phase uncertainties by the direct amplification of phase shift in optical interferometry. Given an initial ultra-small phase shift between orthogonal polarization states, we observe the phase amplification effect with a factor of 388. Our weak measurement scheme provides a practical approach to significantly improve the interferometric phase resolution, which is favorable for precision measurement applications.

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arXiv2018

Theory-Independent Measure of Coherence

We provide a theory independent framework to quantify coherence. In comparison with Bell's theory independent approach to quantum nonlocality, we characterize a general coherence phenomenon with statistics arising from sequential measurements of observables that might not be compatible. By introducing a "decohered" state after the sharp measurement of some preferred observable, we quantify coherence by either the difference of initial "superposed" state from the "decohered" state or the measurement outcome deviations when they subjected to further measurements. Applied to quantum mechanics, the outcome-difference measures yield two novel quantum coherence measures, one of which upper-bounds quantum interference visibility. In the Bell's scenario, we find a finite gap of coherences between a super non-local model and quantum mechanic and therefore our framework can help to single out quantum mechanics beyond non-locality.

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arXiv2017

Construction of State-independent Proofs for Quantum Contextuality

Since the enlightening proofs of quantum contextuality first established by Kochen and Specker, and also by Bell, various simplified proofs have been constructed to exclude the non-contextual hidden variable theory of our nature at the microscopic scale. The conflict between the non-contextual hidden variable theory and quantum mechanics is commonly revealed by Kochen-Specker (KS) sets of yes-no tests, represented by projectors (or rays), via either logical contradictions or noncontextuality inequalities in a state-(in)dependent manner. Here we first propose a systematic and programmable construction of a state-independent proof from a given set of nonspecific rays in $\mC^3$ according to their Gram matrix. This approach brings us a greater convenience in the experimental arrangements. Besides, our proofs in $\mC^3$ can also be generalized to any higher dimensional systems by a recursive method.

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arXiv2017

Graphical Non-contextual Inequalities for Qutrit Systems

One of the interesting topics in quantum contextuality is the construction for various non-contextual inequalities. By introducing a new structure called hyper-graph, we present a general method, which seems to be analytic and extensible, to derive the non-contextual inequalities for the qutrit systems. Based on this, several typical families of non-contextual inequalities are discussed. And our approach may also help us to simplify some state-independent proofs for quantum contextuality in one of our recent works.

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arXiv2017

Pushing the Qubit Rate Limit for Fast Quantum Data Transmission by Quantum Error Correction

Fast quantum data transmission faces several shortcomings such as the indistinguishability of some partly overlapping signals, the channel noises, and so on. Based on the encoded quantum data transmission protocol, an unconventional scheme is presented to overcome the indistinguishability problem of the encoded qubits effectively, so that the upper bound for qubit transmission rate can be considerably raised compared with the un-encoded cases. It can be regarded as a combination of an entanglement swapping technique and a quantum error-correcting scheme, which also provides us a new way of thinking for improving other technologies such as quantum communication, quantum storage technology etc. Besides, from the quantum error correction's point of view, our technique can also be regarded as a method to deal with some families of nonlocal errors, which may facilitate the research in the relevant field.

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arXiv2016

Evaluation of entanglement measures by a single observable

We present observable lower bounds for several bipartite entanglement measures including entanglement of formation, geometric measure of entanglement, concurrence, convex-roof extended negativity, and G-concurrence. The lower bounds facilitate estimates of these entanglement measures for arbitrary finite-dimensional bipartite states. Moreover, these lower bounds can be calculated analytically from the expectation value of a single observable. Based on our results, we use several real experimental measurement data to get lower bounds of entanglement measures for these experimentally realized states. In addition, we also study the relations between entanglement measures.

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arXiv2016

Hierarchy of multipartite nonlocality in the nonsignaling scenario

We propose a hierarchy of Bell-type inequalities for arbitrary $n$-partite systems that identify the different degrees of nonlocality ranging from standard to genuine multipartite nonlocality. After introducing the definition of nonsignaling $m$-locality, we show that the observed joint probabilities in any nonsignaling $m$-local realistic models should satisfy the $(m-1)$-th Bell-type inequality. When $m=2$ the corresponding inequality reduces to the one shown in [Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates genuine multipartite nonlocality, and when $m=n$ the corresponding inequality is just Hardy's inequality whose violation indicates standard multipartite nonlocality. Furthermore, several examples are provided to demonstrate their hierarchy of multipartite nonlocality.

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arXiv2016

Multi-setting Greenberger-Horne-Zeilinger Paradoxes

Greenberger-Horne-Zeilinger (GHZ) paradox provides an all-versus-nothing test for the quantum nonlocality. In all the GHZ paradoxes known so far each observer is allowed to measure only two alternative observables. Here we shall present a general construction for GHZ paradoxes in which each observer measuring more than two observables given that the system is prepared in the $n$-qudit GHZ state. By doing so we are able to construct a multi-setting GHZ paradox for the $n$-qubit GHZ state, with $n$ being arbitrary, that is genuine $n$-partite, i.e., no GHZ paradox exists when restrict to a subset of number of observers for a given set of Mermin observables. Our result fills up the gap of the absence of a genuine GHZ paradox for the GHZ state of an even number of qubits, especially the four-qubit GHZ state as used in GHZ's original proposal.

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arXiv2016

Effect of weak measurement on entanglement distribution over noisy channels

Being able to implement effective entanglement distribution in noisy environments is a key step towards practical quantum communication, and long-term efforts have been made on the development of it. Recently, it has been found that the null-result weak measurement (NRWM) can be used to enhance probabilistically the entanglement of a single copy of amplitude-damped entangled state. This paper investigates remote distributions of bipartite and multipartite entangled states in the amplitudedamping environment by combining NRWMs and entanglement distillation protocols (EDPs). We show that the NRWM has no positive effect on the distribution of bipartite maximally entangled states and multipartite Greenberger-Horne-Zeilinger states, although it is able to increase the amount of entanglement of each source state (noisy entangled state) of EDPs with a certain probability. However, we find that the NRWM would contribute to remote distributions of multipartite W states. We demonstrate that the NRWM can not only reduce the fidelity thresholds for distillability of decohered W states, but also raise the distillation efficiencies of W states. Our results suggest a new idea for quantifying the ability of a local filtering operation in protecting entanglement from decoherence.

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arXiv2016

Separability criteria with angular and Hilbert space averages

The practically useful criteria of separable states $ρ=\sum_{k}w_{k}ρ_{k}$ in $d=2\times2$ are discussed. The equality $G({\bf a},{\bf b})= 4[\langle ψ|P({\bf a})\otimes P({\bf b})|ψ\rangle-\langle ψ|P({\bf a})\otimes{\bf 1}|ψ\rangle\langle ψ|{\bf 1}\otimes P({\bf b})|ψ\rangle]=0$ for any two projection operators $P({\bf a})$ and $P({\bf b})$ provides a necessary and sufficient separability criterion in the case of a separable pure state $ρ=|ψ\rangle\langleψ|$. We propose the separability criteria of mixed states, which are given by ${\rm Tr}ρ\{{\bf a}\cdot {\bf σ}\otimes {\bf b}\cdot {\bf σ}\}=(1/3)C\cosφ$ for two spin $1/2$ systems and $4{\rm Tr}ρ\{P({\bf a})\otimes P({\bf b})\}=1+(1/2)C\cos2φ$ for two photon systems, respectively, after taking a geometrical angular average of ${\bf a}$ and ${\bf b}$ with fixed $\cosφ={\bf a}\cdot{\bf b}$. Here $-1\leq C\leq 1$, and the difference in the numerical coefficients $1/2$ and $1/3$ arises from the different rotational properties of the spinor and the transverse photon. If one instead takes an average over the states in the $d=2$ Hilbert space, the criterion for two photon systems is replaced by $4{\rm Tr}ρ\{P({\bf a})\otimes P({\bf b})\}=1+(1/3)C\cos2φ$. Those separability criteria are shown to be very efficient using the existing experimental data of Aspect et al. in 1981 and Sakai et al. in 2006. When the Werner state is applied to two photon systems, it is shown that the Hilbert space average can judge its inseparability but not the geometrical angular average.

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arXiv2016

Experimental test of non-classicality of quantum mechanics using an individual atomic solid-state quantum system

Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of classicality, the Bell theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS) . Tests of the Bell inequality and the BKS theorem are both of fundamental interests and of great significance . The Bell theorem has already been experimentally verified extensively on many different systems , while the quantum contextuality, which is independent of nonlocality and manifests itself even in a single object, is experimentally more demanding. Moreover, the contextuality has been shown to play a critical role to supply the `magic' for quantum computation, making more extensive experimental verifications in potential systems for quantum computing even more stringent. Here we report an experimental verification of quantum contextuality on an individual atomic nuclear spin-1 system in solids under ambient condition. Such a three-level system is indivisible and thus the compatibility loophole, which exists in the experiments performed on bipartite systems, is closed. Our experimental results confirm that the quantum contextuality cannot be explained by nonlocal entanglement, revealing the fundamental quantumness other than locality/nonlocality within the intrinsic spin freedom of a concrete natural atomic solid-state system at room temperature.

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arXiv2015

Complete condition for nonzero quantum correlation in continuous variable systems

Quantum correlation provides a promising measure beyond entanglement. Here, we propose a necessary and sufficient condition for nonzero quantum correlation in continuous variable systems, which is simple and easy to perform in terms of a marker $Q_r$. In order to get this condition, we introduce continuous-variable local orthogonal bases of the operator space, which are generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we obtain the marker $Q_r$ for all bipartite continuous variable states, and provide several examples including two-mode Gaussian and non-Gaussian states. Our result may provide a candidate for quantum correlation measures, and can be measured by designed quantum circuits.

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arXiv2015

A family of nonlocal bound entangled states

Bound entanglement, being entangled yet not distillable, is essential to our understandings of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we shall construct such kind of nonlocal bound entangled states for all finite dimensions larger than two, making possible their experimental demonstrations on most general systems. We propose a Bell inequality, based on a Hardy-type argument for nonlocality, and a steering inequality to identify their nonlocality. We also provide a family of entanglement witnesses to detect their entanglement beyond the Bell inequality and the steering inequality.

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arXiv2015

Robust quantum metrological schemes based on protection of quantum Fisher information

Fragile quantum features such as entanglement are employed to improve the precision of parameter estimation and as a consequence the quantum gain becomes vulnerable to noise. As an established tool to subdue noise, quantum error correction is unfortunately overprotective because the quantum enhancement can still be achieved even if the states are irrecoverably affected, provided that the quantum Fisher information, which sets the ultimate limit to the precision of metrological schemes, is preserved and attained. Here, we develop a theory of robust metrological schemes that preserve the quantum Fisher information instead of the quantum states themselves against noise. After deriving a minimal set of testable conditions on this kind of robustness, we construct a family of $2t+1$ qubits metrological schemes being immune to $t$-qubit errors after the signal sensing. In comparison at least five qubits are required for correcting arbitrary 1-qubit errors in standard quantum error correction.

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arXiv2015

Detecting the local indistinguishability of maximally entangled states

By incorporating the asymmetry of local protocols, i.e., some party has to start with a nontrivial measurement, into an operational method of detecting the local indistinguishability proposed by Horodecki {\it et al.} [Phys.Rev.Lett. 90 047902 (2003)], we derive a computable criterion to efficiently detect the local indistinguishability of maximally entangled states. Locally indistinguishable sets of $d$ maximally entangled states in a $d\otimes d$ system are systematically constructed for all $d\ge 4$ as an application. Furthermore, by exploiting the fact that local protocols are necessarily separable, we explicitly construct small sets of $k$ locally indistinguishable maximally entangled states with the ratio $k/d$ approaching 3/4. In particular, in a $d\otimes d$ system with even $d\ge 6$, there always exist $d-1$ maximally entangled states that are locally indistinguishable by separable measurements.

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arXiv2014

Hardy's Paradox and Measurement-disturbance Relations

We establish a quantitative relation between Hardy's paradox and the breaking of uncertainty principle in the sense of measurement-disturbance relations in the conditional measurement of non-commuting operators. The analysis of the inconsistency of local realism with entanglement by Hardy is simplified if this breaking of measurement-disturbance relations is taken into account, and a much simplified experimental test of local realism is illustrated in the framework of Hardy's thought experiment. The essence of Hardy's model is identified as a combination of two conditional measurements, which give rise to definite eigenvalues to two non-commuting operators simultaneously in hidden-variables models. Better understanding of the intimate interplay of entanglement and measurement-disturbance is crucial in the current discussions of Hardy's paradox using the idea of weak measurement, which is based on a general analysis of measurement-disturbance relations.

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