arXiv subjects

Qiu-Cheng Song

Publications and source records attributed to Qiu-Cheng Song.

11 recordsLinked to original sources

arXiv2026

One pure steered state implies Einstein-Podolsky-Rosen steering

In this work, we show that a two-qubit entangled state admitting at least one pure steered state is Einstein-Podolsky-Rosen (EPR) steerable from Alice to Bob. Pure steered states signifies that the quantum steering ellipsoid of Bob is tangent to his Bloch sphere at least at a single point. Furthermore, we prove that for a two-qubit entangled state, Bob's quantum steering ellipsoid is tangent to his Bloch sphere at exactly $N$ points, for $N\in \{ 0,1,2,\infty\}$, if and only if Alice's quantum steering ellipsoid is tangent to her Bloch sphere at exactly $N$ points. For any two-qubit entangled state, therefore, if one party can steer the other to at least one pure state, the state is two-way EPR steerable. We also present several illuminating examples of two-qubit entangled states such that the EPR steering can be verified in terms of pure steered states. Our result addresses the Gisin theorem in a EPR steering scenario: at least a single pure steered state implies two-way steering.

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arXiv2024

On the power of one pure steered state for EPR-steering with a pair of qubits

As originally introduced, the EPR phenomenon was the ability of one party (Alice) to steer, by her choice between two measurement settings, the quantum system of another party (Bob) into two distinct ensembles of pure states. As later formalized as a quantum information task, EPR-steering can be shown even when the distinct ensembles comprise mixed states. Consider the scenario where Alice and Bob each have a qubit and Alice performs dichotomic projective measurements. In this case, the states in the ensembles to which she can steer form the surface of an ellipsoid ${\cal E}$ in Bob's Bloch ball. Further, let the steering ellipsoid ${\cal E}$ have nonzero volume. It has previously been shown that if Alice's first measurement setting yields an ensemble comprising two pure states, then this, plus any one other measurement setting, will demonstrate EPR-steering. Here we consider what one can say if the ensemble from Alice's first setting contains only one pure state $\mathsf{p}\in{\cal E}$, occurring with probability $p_\mathsf{p}$. Using projective geometry, we derive the necessary and sufficient condition analytically for Alice to be able to demonstrate EPR-steering of Bob's state using this and some second setting, when the two ensembles from these lie in a given plane. Based on this, we show that, for a given ${\cal E}$, if $p_\mathsf{p}$ is high enough [$p_{\sf p} > p_{\rm max}^{\cal E} \in [0,1)$] then any distinct second setting by Alice is sufficient to demonstrate EPR-steering. Similarly we derive a $p_{\rm min}^{\cal E}$ such that $p_\mathsf{p}>p_{\rm min}^{\cal E}$ is necessary for Alice to demonstrate EPR-steering using only the first setting and some other setting. Moreover, the expressions we derive are tight; for spherical steering ellipsoids, the bounds coincide: $p_{\rm max}^{\cal E} = p_{\rm min}^{\cal E}$.

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arXiv2024

Shareability of steering in 2-producible states

Quantum steering is the phenomenon whereby one party (Alice) proves entanglement by "steering'' the system of another party (Bob) into distinct ensembles of states, by performing different measurements on her subsystem. Here, we investigate steering in a network scenario involving $n$ parties, who each perform local measurements on part of a global quantum state, that is produced using only two-party entangled states, and mixing with ancillary separable states. We introduce three scenarios which can be straightforwardly implemented in standard quantum optics architecture, which we call random $\frac{n}{2}$-pair entanglement, random pair entanglement and semi-random pair entanglement. We study steerability of the states across two-party marginals which arise in the three scenarios, and derive analytically the necessary and sufficient steering criteria for different sets of measurement settings. Strikingly, using the semi-random pair entanglement construction, one party can steer every one of the $n-1$ other parties, for arbitrarily large $n$, using only two measurements. Finally, exploiting symmetry, we study various small network configurations (three or four parties) in the three scenarios, under different measurements and produced by different two-party entangled states.

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arXiv2023

Scalable multiparty steering based on a single pair of entangled qubits

The distribution and verification of quantum nonlocality across a network of users is essential for future quantum information science and technology applications. However, beyond simple point-to-point protocols, existing methods struggle with increasingly complex state preparation for a growing number of parties. Here, we show that, surprisingly, multiparty loophole-free quantum steering, where one party simultaneously steers arbitrarily many spatially separate parties, is achievable by constructing a quantum network from a set of qubits of which only one pair is entangled. Using these insights, we experimentally demonstrate this type of steering between three parties with the detection loophole closed. With its modest and fixed entanglement requirements, this work introduces a scalable approach to rigorously verify quantum nonlocality across multiple parties, thus providing a practical tool towards developing the future quantum internet.

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arXiv2019

Experimental investigation of the uncertainty relations with coherent light

Taking advantage of coherent light beams, we experimentally investigate the variancebased uncertainty relations and the optimal majorization uncertainty relation for the two-dimensional quantum mechanical system.Different from most of the experiments which devoted to record each individual quantum, we examine the uncertainty relations by measuring an ensemble of photons with two polarization degree of freedom characterized by the Stokes parameters which allow us to determine the polarization density matrix with high precision. The optimality of the recently proposed direct-sum majorization uncertainty relation is verified by measuring the Lorenz curves. Results show that the Lorenz curve method represents a faithful verification of the majorization uncertainty relation and the uncertainty relation is indeed an ensemble property of quantum system.

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arXiv2019

Tight $N$-observable uncertainty relations and their experimental demonstrations

The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty relations for $N(N\ge2)$ observables with discrete and bounded spectra, one in multiplicative form and the other in additive form. To verify their validity, for illustration, we implement in the spin-1/2 system an experiment with single-photon measurement. The experimental results exhibit the validity and robustness of these uncertainty relations, and indicate the existence of stringent lower bounds.

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arXiv2017

Experimental investigation of multi-observable uncertainty relations

The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved lower bounds and were deemed capable of incorporating multiple observables. Here we report an experimental verification of seven uncertainty relations of this type with single-photon measurements. The results, while confirming these uncertainty relations, show as well the relative stringency of various uncertainty lower bounds.

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arXiv2017

A Stronger Multi-observable Uncertainty Relation

Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty relation. Here we present a variance-based sum uncertainty relation for $N$ incompatible observables stronger than the simple generalization of the uncertainty relation for two observables derived by Maccone and Pati [Phys. Rev. Lett. {\bf113}, 260401 (2014)]. Further comparisons of our uncertainty relation with other related ones for spin-$\frac{1}{2}$ and spin-$1$ particles indicate that the obtained uncertainty relation gives a better lower bound.

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arXiv2017

Stronger Schrödinger-like Uncertainty Relations

Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger Schrödinger-like uncertainty relation, which is stronger than the relation recently derived by L. Maccone and A. K. Pati [Phys. Rev. Lett. 113 (2014) 260401]. Furthermore, we give an additive uncertainty relation which holds for three incompatible observables, which is stronger than the relation newly obtained by S. Kechrimparis and S. Weigert [Phys. Rev. A 90 (2014) 062118] and the simple extension of the Schrödinger uncertainty relation.

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arXiv2015

Uncertainty equalities and uncertainty relation in weak measurement

Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak measurement which captures the limitation on the preparation of pre- and post-selected ensemble and hold for two non-Hermitian operators corresponding to two non-commuting observables.

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arXiv2014

Synchronous concentration and purification schemes of arbitrary unknown hyperentangled mixed states

We present two efficient schemes which can simultaneously accomplish hyperentanglement concentration and purification for two-photon four-qubit systems in an unknown partially hyperentangled mixed states. The first can correct errors in the polarization entanglement and extract maximal hyperentanglement in polarization and spatial mode with additional partial frequency entanglement. The second uses additional maximal frequency entanglement to purify and concentrate hyperentanglement in polarization and spatial mode deterministically. Both of the two schemes are only based on existing optical devices and cross-Kerr nonlinearities.

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