Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe nine ways of four qubit entanglement and their threetangle
55
0
0.0
(
0
)
Authors
Andreas Osterloh
Ask ChatGPT about the research
No Arabic abstract
I calculate the mixed threetangle $tau_3[rho]$ for the reduced density matrices of the four-qubit representant states found in Phys. Rev. A {bf 65}, 052112 (2002). In most of the cases, the convex roof is obtained, except for one class, where I provide with a new upper bound, which is assumed to be very close to the convex roof. I compare with results published in Phys. Rev. Lett. {bf 113}, 110501 (2014). Since the method applied there usually results in higher values for the upper bound, in certain cases it can be understood that the convex roof is obtained exactly, namely when the zero-polytope where $tau_3$ vanishes shrinks to a single point.
rate research
Read More
We examine the various properties of the three four-qubit monogamy relations, all of which introduce the power factors in the three-way entanglement to reduce the tripartite contributions. On the analytic ground as much as possible we try to find the minimal power factors, which make the monogamy relations hold if the power factors are larger than the minimal powers. Motivated to the three-qubit monogamy inequality we also examine whether those four-qubit monogamy relations provide the SLOCC-invariant four-way entanglement measures or not. Our analysis indicate that this is impossible provided that the monogamy inequalities are derived merely by introducing weighting power factors.
We single out a class of states possessing only threetangle but distributed all over four qubits. This is a three-site analogue of states from the $W$-class, which only possess globally distributed pairwise entanglement as measured by the concurrence. We perform an analysis for four qubits, showing that such a state indeed exists. To this end we analyze specific states of four qubits that are not convexly balanced as for $SL$ invariant families of entanglement, but only affinely balanced. For these states all possible $SL$-invariants vanish, hence they are part of the $SL$ null-cone. Instead, they will possess at least a certain unitary invariant. As an interesting byproduct it is demonstrated that the exact convex roof is reached in the rank-two case of a homogeneous polynomial $SL$-invariant measure of entanglement of degree $2m$, if there is a state which corresponds to a maximally $m$-fold degenerate solution in the zero-polytope that can be combined with the convexified minimal characteristic curve to give a decomposition of $rho$. If more than one such state does exist in the zero polytope, a minimization must be performed. A better lower bound than the lowest convexified characteristic curve is obtained if no decomposition of $rho$ is obtained in this way.
Many-qubit entanglement is crucial for quantum information processing although its exploitation is hindered by the detrimental effects of the environment surrounding the many-qubit system. It is thus of importance to study the dynamics of general multipartite nonclassical correlation, including but not restricted to entanglement, under noise. We did this study for four-qubit GHZ state under most common noises in an experiment and found that nonclassical correlation is more robust than entanglement except when it is imposed to dephasing channel. Quantum discord presents a sudden transition in its dynamics for Pauli-X and Pauli-Y noises as well as Bell-diagonal states interacting with dephasing reservoirs and it decays monotonically for Pauli-Z and isotropic noises.
In Phys. Rev. A 62, 062314 (2000), D{u}r, Vidal and Cirac indicated that there are infinitely many SLOCC classes for four qubits. Verstraete, Dehaene, and Verschelde in Phys. Rev. A 65, 052112 (2002) proposed nine families of states corresponding to nine different ways of entangling four qubits. In Phys. Rev. A 75, 022318 (2007), Lamata et al. reported that there are eight true SLOCC entanglement classes of four qubits up to permutations of the qubits. In this paper, we investigate SLOCC classification of the nine families proposed by Verstraete, Dehaene and Verschelde, and distinguish 49 true SLOCC entanglement classes from them.
We study the relation between qubit entanglement and Lorentzian geometry. In an earlier paper, we had given a recipe for detecting two qubit entanglement. The entanglement criterion is based on Partial Lorentz Transformations (PLT) on individual qubits. The present paper gives the theoretical framework underlying the PLT test. The treatment is based physically, on the causal structure of Minkowski spacetime, and mathematically, on a Lorentzian Singular Value Decomposition. A surprising feature is the natural emergence of Energy conditions used in Relativity. All states satisfy a Dominant Energy Condition (DEC) and separable states satisfy the Strong Energy Condition(SEC), while entangled states violate the SEC. Apart from testing for entanglement, our approach also enables us to construct a separable form for the density matrix in those cases where it exists. Our approach leads to a simple graphical three dimensional representation of the state space which shows the entangled states within the set of all states.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
