Self-error-rejecting multipartite entanglement purification for electron systems assisted by quantum-dot spins in optical microcavities

We present a self-error-rejecting multipartite entanglement purification protocol (MEPP) for N-electron-spin entangled states, resorting to the single-side cavity-spin-coupling system. Our MEPP has a high efficiency containing two steps. One is to obtain high-fidelity N-electron-spin entangled systems with error-heralded parity-check devices (PCDs) in the same parity-mode outcome of three electron-spin pairs, as well as M-electron-spin entangled subsystems (2 ≤ M < N) in the different parity-mode outcomes of those. The other is to regain the N-electron-spin entangled systems from M-electron-spin entangled states utilizing entanglement link. Moreover, the quantum circuits of PCDs make our MEPP works faithfully, due to the practical photon-scattering deviations from the finite side leakage of the microcavity, and the limited coupling between a quantum dot and a cavity mode, converted into a failed detection in a heralded way.

Mathematical framework for describing multipartite entanglement in terms of rows or columns of coefficient matrices

In this paper, we develop a mathematical framework for describing entanglement quantitatively and qualitatively for multipartite qudit states in terms of rows or columns of coefficient matrices. More specifically, we propose an entanglement measure and separability criteria based on rows or columns of coefficient matrices. This entanglement measure has an explicit mathematical expression by means of exterior products of all pairs of rows or columns in coefficient matrices. It is introduced via our result that the [Formula: see text]-concurrence coincides with the entanglement measure based on two-by-two minors of coefficient matrices. Depending on our entanglement measure, we obtain the separability criteria and maximal entanglement criteria in terms of rows or columns of coefficient matrices. Our conclusions show that just like every two-by-two minor in a coefficient matrix of a multipartite pure state, every pair of rows or columns can also exhibit its entanglement properties, and thus can be viewed as its smallest entanglement contribution unit too. The great merit of our entanglement measure and separability criteria is two-fold. First, they are very practical and convenient for computation compared to other methods. Second, they have clear geometric interpretations.

Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks

Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger–Horne–Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger–Horne–Zeilinger states and for detecting genuine multipartite entanglement.

Probing multipartite entanglement, coherence and quantum information preservation under classical Ornstein-Uhlenbeck noise

We address entanglement, coherence, and information protection in a system of four non-interacting qubits coupled with different classical environments, namely: common, bipartite, tripartite, and independent environments described by Ornstein-Uhlenbeck (ORU) noise. We show that quantum information preserved by the four qubit state is more dependent on the coherence than the entanglement using time-dependent entanglement witness, purity, and Shannon entropy. We find these two quantum phenomena directly interrelated and highly vulnerable in environments with ORU noise, resulting in the pure exponential decay of a considerable amount. The current Markovian dynamical map, as well as suppression of the fluctuating character of the environments, are observed to be entirely attributable to the Gaussian nature of the noise. The increasing number of environments are witnessed to speed up the amount of decay. Unlike other noises, the current noise parameter's flexible range is readily exploitable, ensuring long enough preserved memory properties. The four-qubit GHZ state, besides having a large information storage potential, stands partially entangled and coherent in common environments for an indefinite duration. In addition, we derive computational values for each system-environment interaction, which will help quantum practitioners to optimize the related classical environments.

Construction of genuinely entangled subspacesand the associated bounds on entanglement measures for mixed states

Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information processing. A recent direction of research is the construction of genuinely entangled subspaces — the class of subspaces consisting entirely of genuinely entangled pure states. In this paper we present methods of construction of such subspaces including those of maximal possible dimension. The approach is based on the composition of bipartite entangled subspaces and quantum channels of certain types. The examples include maximal subspaces for systems of three qubits, four qubits, three qutrits. We also provide lower bounds on two entanglement measures for mixed states, the concurrence and the convex-roof extended negativity, which are directly connected with the projection on genuinely entangled subspaces.

Multipartite entanglement of billions of motional atoms heralded by single photon

Quantum theory does not prevent entanglement from being created and observed in macroscopic physical systems, in reality however, the accessible scale of entanglement is still very limited due to decoherence effects. Recently, entanglement has been observed among atoms from thousands to millions levels in extremely low-temperature and well isolated systems. Here, we create multipartite entanglement of billions of motional atoms in a quantum memory at room temperature and certify the genuine entanglement via M-separability witness associated with photon statistics. The information contained in a single photon is found strongly correlated with the excitation shared by the motional atoms, which intrinsically address the large system and therefore stimulate the multipartite entanglement. Remarkably, our heralded and quantum memory built-in entanglement generation allows us to directly observe the dynamic evolution of entanglement depth and further to reveal the effects of decoherence. Our results verify the existence of genuine multipartite entanglement among billions of motional atoms at ambient conditions, significantly extending the boundary of the accessible scale of entanglement.

The Markov gap for geometric reflected entropy

The reflected entropy SR(A : B) of a density matrix ρAB is a bipartite correlation measure lower-bounded by the quantum mutual information I(A : B). In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-N2 gap between SR and I. We provide an information-theoretic interpretation of this gap by observing that SR− I is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason, we call the quantity SR− I the Markov gap. We then prove that for time-symmetric states in pure AdS3 gravity, the Markov gap is universally lower bounded by log(2)ℓAdS/2GN times the number of endpoints of the cross-section. We provide evidence that this lower bound continues to hold in the presence of bulk matter, and comment on how it might generalize above three bulk dimensions. Finally, we explore the Markov recovery problem controlling SR− I using fixed area states. This analysis involves deriving a formula for the quantum fidelity — in fact, for all the sandwiched Rényi relative entropies — between fixed area states with one versus two fixed areas, which may be of independent interest. We discuss, throughout the paper, connections to the general theory of multipartite entanglement in holography.

Hyperthreads in holographic spacetimes

We generalize bit threads to hyperthreads in the context of holographic spacetimes. We define a “k-thread” to be a hyperthread which connects k different boundary regions and posit that it may be considered as a unit of k-party entanglement. Using this new object, we show that the contribution of hyperthreads to calculations of holographic entanglement entropy are generically finite. This is accomplished by constructing a surface whose area determines their maximum allowed contribution. We also identify surfaces whose area is proportional to the maximum number of k-threads, motivating a possible measure of multipartite entanglement. We use this to make connections to the current understanding of multipartite entanglement in holographic spacetimes.