In comparison with entanglement and Bell nonlocality, Einstein-Podolsky-Rosen steering is a newly emerged research topic and in its incipient stage. Although Einstein-Podolsky-Rosen steering has been explored via violations of steering inequalities b
oth theoretically and experimentally, the known inequalities in the literatures are far from well-developed. As a result, it is not yet possible to observe Einstein-Podolsky-Rosen steering for some steerable mixed states. Recently, a simple approach was presented to identify Einstein-Podolsky-Rosen steering based on all-versus-nothing argument, offering a strong condition to witness the steerability of a family of two-qubit (pure or mixed) entangled states. In this work, we show that the all-versus-nothing proof of Einstein-Podolsky-Rosen steering can be tested by measuring the projective probabilities. Through the bound of probabilities imposed by local-hidden-state model, the proposed test shows that steering can be detected by the all-versus-nothing argument experimentally even in the presence of imprecision and errors. Our test can be implemented in many physical systems and we discuss the possible realizations of our scheme with non-Abelian anyons and trapped ions.
We show that all pure entangled states of two $d$-dimensional quantum systems (i.e., two qudits) can be generated from an initial separable state via a universal Yang--Baxter matrix if one is assisted by local unitary transformations.
We investigate the maximal violations for both sides of the $d$-dimensional CGLMP inequality by using the Bell operator method. It turns out that the maximal violations have a decelerating increase as the dimension increases and tend to a finite valu
e at infinity. The numerical values are given out up to $d=10^6$ for positively maximal violations and $d=2times 10^5$ for negatively maximal violations. Counterintuitively, the negatively maximal violations tend to be a little stronger than the positively maximal violations. Further we show the states corresponding to these maximal violations and compare them with the maximally entangled states by utilizing entangled degree defined by von Neumann entropy. It shows that their entangled degree tends to some nonmaximal value as the dimension increases.
Spin interaction Hamiltonians are obtained from the unitary Yang--Baxter $breve{R}$-matrix. Based on which, we study Berry phase and quantum criticality in the Yang--Baxter systems.
In this Rapid Communication, we show analytically that all pure entangled states of two d-dimensional systems (qudits) violate the Collins-Gisin-Linden-Masser-Popoescu (CGLMP) inequality. Thus one has the Gisins theorem for two qudits.
We show that the relativistic hydrogen atom possesses an SO(4) symmetry by introducing a kind of pseudo-spin vector operator. The same SO(4) symmetry is still preserved in the relativistic quantum system in presence of an U(1) monopolar vector potent
ial as well as a nonabelian vector potential. Lamb shift and SO(4) symmetry breaking are also discussed.
The non-standard Schwinger fermionic representation of the unitary group is studied by using $n$-fermion operators. One finds that the Schwinger fermionic representation of the U(n) group is not unique when $nge 3$. In general, based on $n$-fermion o
perators, the non-standard Schwinger fermionic representation of the U(n) group can be established in a uniform approach, where all the generators commute with the total number operators. The Schwinger fermionic representation of $U(C^{m}_{n})$ group is also discussed.
We show that braiding transformation is a natural approach to describe quantum entanglement, by using the unitary braiding operators to realize entanglement swapping and generate the GHZ states as well as the linear cluster states. A Hamiltonian is c
onstructed from the unitary $check{R}_{i,i+1}(theta,phi)$-matrix, where $phi=omega t$ is time-dependent while $theta$ is time-independent. This in turn allows us to investigate the Berry phase in the entanglement space.
We established a physically utilizable Bell inequality based on the Peres-Horodecki criterion. The new quadratic probabilistic Bell inequality naturally provides us a necessary and sufficient way to test all entangled two-qubit or qubit-qutrit states
including the Werner states and the maximally entangled mixed states.
