Bell inequalities have traditionally been used to demonstrate that quantum theory is nonlocal, in the sense that there exist correlations generated from composite quantum states that cannot be explained by means of local hidden variables. With the advent of device-independent quantum information protocols, Bell inequalities have gained an additional role as certificates of relevant quantum properties. In this work we consider the problem of designing Bell inequalities that are tailored to detect maximally entangled states. We introduce a class of Bell inequalities valid for an arbitrary number of measurements and results, derive analytically their tight classical, non-signalling and quantum bounds and prove that the latter is attained by maximally entangled states. Our inequalities can therefore find an application in device-independent protocols requiring maximally entangled states.
We present a generalized criterion for maximally entangled nine-qubit states, whose minimum averaged subsystem purity should be equal to 1/14. In this note, we prove that absolutely maximally entangled state for nine qubits does not exist. Further, we construct a new genuine nine-qubit maximally entangled states of 110,15 and 1 balanced purities equal to 1/16, , 1/8 and and 1/4, respectively. We found that, the marginal density matrices for subsystems of 1,2,3- qubits all completely mixed in these states, therefore, maximally entangled nine-qubit state is a 3-uniform state.
Gram matrix approach to an entanglement analysis of pure states describing $(d,\infty)$ -- quantum systems is being introduced. In particular, maximally entangled states are described as those having a special forms of the corresponding Gram matrices.
We describe quantum circuits generating four-qubit maximally entangled states, the amount of entanglement being quantified by using the absolute value of the Cayley hyperdeterminant as an entanglement monotone. More precisely, we show that this type of four-qubit entangled states can be obtained by the action of a family of CNOT circuits on some special states of the LU orbit of the state |0000 >.
The De Broglie-Bohm (DeBB)\cite{DeBB} Causal Quantum Mechanics played a crucial role in Bell's discovery \cite{Bell1964} that quantum mechanics violates EPR local reality \cite{EPR1935}, and also in Bell's search for an exact quantum mechanics. The experiments of Aspect et al \cite{Aspect1981} confirm quantum correlations between plane polarizations of two photons and violation of Bell's inequalities by a factor $\sqrt 2 $. I prove that similar experiments with elliptic polarizers can also show quantum violations of Bell's inequality by the same factor. I summarize our construction of a maxima…
我们通过几个纠缠单调来研究是否所有的最大纠缠态都是纯的。在两体情况下，我们发现导致纠缠熵作为纠缠度量的唯一性的相同条件，排除了最大混合纠缠态的存在。在多体情况下，我们的结论使我们能够推广一夫一妻的纠缠的想法：我们建立了\textit{polygamy of entanglement}，表示如果一个一般的状态是最大的纠缠相对于某种多体纠缠，那么它必然是任何其他系统的因式分解。
We study unextendible maximally entangled bases (UMEBs) in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) ($d<d'$). An operational method to construct UMEBs containing $d(d^{\prime}-1)$ maximally entangled vectors is established, and two UMEBs in \(\mathbb {C}^{5}\otimes \mathbb {C}^{6}\) and \(\mathbb {C}^{5}\otimes \mathbb {C}^{12}\) are given as examples. Furthermore, a systematic way of constructing UMEBs containing $d(d^{\prime}-r)$ maximally entangled vectors in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) is presented for $r=1,2,\cdots, d-1$. Correspondingly, two UMEBs in \(…
We study a general corresponding principle between discrete-variable quantum states and continuous-variable (especially, restricted on Gaussian) states via quantum purification method. In the previous work, we have already investigated an information-theoretic correspondence between the Gaussian maximally mixed states (GMMSs) and their purifications known as Gaussian maximally entangled states (GMESs) in [Phys. Lett. A {\bf 380}, 3607 (2016)]. We here compare an $N\times N$-dimensional maximally entangled state to the GMES we proposed previously, through an explicit calculation of quantum fide…
We construct a large family of Planar Maximally Entangled (PME) states which are a wider class of multi-partite entangled states than Absolutely Maximally Entangled (AME) states. These are states in which any half of the qudits are in a maximally mixed state, provided that they form a connected subset. We show that in contrast to AMEs, PMEs are easier to find and there are various PMEs for any even number of qudits. In particular, while it is known that no AME state of four qubits exists, we show that there are two distinct multi-parameter classes of four qubit PMEs. We also give explicit fami…
