Mahya Karbalaii
In this thesis work, we have studied the role of positive and completely positive maps in detecting entanglement.
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Entanglement witnesses are invaluable for efficient quantum entanglement certification without the need for expensive quantum state tomography. Yet, standard entanglement witnessing requires multiple measurements and its bounds can be elusive as a result of experimental imperfections. Here we introduce and demonstrate a novel procedure for entanglement detection which seamlessly and easily improves any standard witnessing procedure by using additional available information to tighten the witnessing bounds. Moreover, by relaxing the requirements on the witness operators, our method removes the …
Entanglement polytopes have been recently proposed as the way of witnessing the SLOCC multipartite entanglement classes using single particle information. We present first asymptotic results concerning feasibility of this approach for large number of qubits. In particular we show that entanglement polytopes of $L$-qubit system accumulate in the distance $\frac{1}{2\sqrt{L}}$ from the point corresponding to the maximally mixed reduced one-qubit density matrices. This implies existence of a possibly large region where many entanglement polytopes overlap, i.e where the witnessing power of entangl…
The purpose of an entanglement witness experiment is to certify the creation of an entangled state from a finite number of trials. The statistical confidence of such an experiment is typically expressed as the number of observed standard deviations of witness violations. This method implicitly assumes that the noise is well-behaved so that the central limit theorem applies. In this work, we propose two methods to analyze witness experiments where the states can be subject to arbitrarily correlated noise. Our first method is a rejection experiment, in which we certify the creation of entangleme…
We derive quantitative relations among several naturally defined measures of classical and nonclassical correlations in a bipartite quantum state. We also obtain an upper bound of entanglement irreversibility and a sufficient condition for reversible entanglement. The additivity of entanglement of formation is directly related to the additivity of quantum discord as well as a certain measure of classical correlation.
We prove an upper bound proportional to the surface area for the bipartite entanglement of the ground state and thermal states of harmonic oscillator systems with disorder, as measured by the logarithmic negativity. Our assumptions are satisfied for some standard models that are almost surely gapless in the thermodynamic limit.
In the following manuscript we propose a quaternionic map which transforms a single quantum state into a bipartite entanglement. Until now such a transformation has not been defined yet. To define such a map, we embed one particle state within the algebra of complex quaternions. Next, on the basis of rotational features of quaternions, we choose a special quaternion which in combination with a quaternion describing a particle state, causes its splitting in a specified direction in 4D space. Finally, we prove that the proposed operation, under several restrictions, always causes bipartite entan…
For a multipartite quantum state, the maximal violation of all Bell inequalities constitutes a measure of its nonlocality [Loubenets, J. Math. Phys. 53, 022201 (2012)]. In the present article, for the maximal violation of Bell inequalities by a pure bipartite state, possibly infinite-dimensional, we derive a new upper bound expressed in terms of the Schmidt coefficients of this state. This new upper bound allows us also to specify general analytical relations between the maximal violation of Bell inequalities by a bipartite quantum state, pure or mixed, and such entanglement measures for this …
We provide a new perspective on the close relationship between entanglement and time. Our main focus is on bipartite entanglement, where this connection is foreshadowed both in the positive partial transpose criterion due to Peres [A. Peres, Phys. Rev. Lett., 77, 1413 (1996)] and in the classification of quantum within more general non-signalling bipartite correlations [M. Frembs and A. Döring, arXiv:2204.11471]. Extracting the relevant common features, we identify a necessary and sufficient condition for bipartite entanglement in terms of a compatibility condition with respect to time orienta…
The most general quantum object that can be shared between two distant parties is a bipartite channel, as it is the basic element to construct all quantum circuits. In general, bipartite channels can produce entangled states, and can be used to simulate quantum operations that are not local. While much effort over the last two decades has been devoted to the study of entanglement of bipartite states, very little is known about the entanglement of bipartite channels. In this work, we rigorously study the entanglement of bipartite channels as a resource theory of quantum processes. We present an…
Bundling of bipartite entanglement
研究约束能量子空间中的二分纠缠，证明多个二分纠缠谱在全子空间中相同，并揭示量子多体系统中纠缠熵在幺正时间演化下形成“捆绑”结构，提出验证方法及多项式时间算法。
We characterize the positive maps detecting the entangled bipartite states of n x n qubits that are diagonal with respect to the orthonormal basis constructed by tensor products of Pauli matrices acting on the totally symmetric state. We then discuss the case n=2 for a class of states completely determined by the geometric patterns of subsets of a 16 point lattice.
Entanglement in bipartite X-states: Analytical results for the volume of states with positive partial transpose
本文针对任意 m×n 二分系统，在 Hilbert-Schmidt 测度下推导出具有正部分转置的 X 态占所有 X 态体积比的解析公式，为二分 X 态纠缠结构提供了定量刻画。
We investigate the features of the entanglement spectrum (distribution of the eigenvalues of the reduced density matrix) of a large quantum system in a pure state. We consider all Rényi entropies and recover purity and von Neumann entropy as particular cases. We construct the phase diagram of the theory and unveil the presence of two critical lines.
Consider the model of bipartite entanglement for a random pure state emerging in quantum information and quantum chaos, corresponding to the fixed trace Laguerre unitary ensemble (LUE) in Random Matrix Theory. We focus on correlation functions of Schmidt eigenvalues for the model and prove universal limits of the correlation functions in the bulk and also at the soft and hard edges of the spectrum, as these for the LUE. Further we consider the bounded trace LUE and obtain the same universal limits.
We give a direct alternative proof of an area law for the entanglement entropy of the ground state of disordered oscillator systems---a result due to Nachtergaele, Sims and Stolz. Instead of studying the logarithmic negativity, we invoke the explicit formula for the entanglement entropy of Gaussian states to derive the upper bound. We also contrast this area law in the disordered case with divergent lower bounds on the entanglement entropy of the ground state of one-dimensional ordered oscillator chains.
We demonstrate the existence of general constraints on distributed quantum correlations, which impose a trade-off on bipartite and multipartite entanglement at once. For all N-mode Gaussian states under permutation invariance, we establish exactly a monogamy inequality, stronger than the traditional one, that by recursion defines a proper measure of genuine N-partite entanglement. Strong monogamy holds as well for subsystems of arbitrary size, and the emerging multipartite entanglement measure is found to be scale invariant. We unveil its operational connection with the optimal fidelity of con…
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