Related papers: Entanglement classification via integer partitions
To characterize entanglement of tripartite $\mathbb{C}^d\otimes\mathbb{C}^d\otimes\mathbb{C}^d$ systems, we employ algebraic-geometric tools that are invariants under Stochastic Local Operation and Classical Communication (SLOCC), namely…
One of the key manifestations of quantum mechanics is the phenomenon of quantum entanglement. While the entanglement of bipartite systems is already well understood, our knowledge of entanglement in multipartite systems is still limited.…
We construct $\ell $-spin-flipping matrices from the coefficient matrices of pure states of $n$ qubits and show that the $\ell $-spin-flipping matrices are congruent and unitary congruent whenever two pure states of $n$ qubits are SLOCC and…
We investigate the behavior of quantum states under stochastic local quantum operations and classical communication (SLOCC) for fixed numbers of qubits. We explicitly exhibit the homomorphism between complex and real groups for two-qubits,…
We have devised an artificial intelligence algorithm with machine reinforcement learning (Q-learning) to construct remarkable entangled states with 4 qubits. This way, the algorithm is able to generate representative states for some of the…
We examine the SLOCC classification of the (non-normalized) pure states of four qubits obtained by F. Verstraete et al. The rigorous proofs of their basic results are provided and necessary corrections implemented. We use Invariant Theory…
Quantum entanglement, a cornerstone of quantum mechanics, remains challenging to classify, particularly in multipartite systems. Here, we present a new interpretation of entanglement classification by revealing a profound connection to…
We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable,…
Quantum states are represented by positive semidefinite Hermitian operators with unit trace, known as density matrices. An important subset of quantum states is that of separable states, the complement of which is the subset of…
Deep connections between invariant theory and entanglement have been known for some time and been the object of intense study. This includes the study of local unitary equivalence of density operators as well as entanglement that can be…
We calculate the amount of entanglement of the multiqubit quantum states employed in the Grover algorithm, by following its dynamics at each step of the computation. We show that genuine multipartite entanglement is always present.…
It has been shown by Versraete et. al [F. Versraete, J. Dehaene, B. De Moor, and H. Verschelde, Phys. Rev. A65, 052112 (2002)] that by stochastic local operations and classical communication (SLOCC), a pure state of four qubits can be…
Walgate and Scott have determined the maximum number of generic pure quantum states that can be unambiguously discriminated by an LOCC measurement [Journal of Physics A: Mathematical and Theoretical, 41:375305, 08 2008]. In this work, we…
We study the invariant theory of trilinear forms over a three-dimensional complex vector space, and apply it to investigate the behaviour of pure entangled three-partite qutrit states and their normal forms under local filtering operations…
The states in the three-qubit GHZ SLOCC class can exhibit diverse entanglement patterns, as they may have no entanglement in any reduced subsystems, or show entanglement across one, two, or all three bipartite cuts. Significant research has…
We analyze entanglement in the family of translationally-invariant matrix product states (MPS). We give a criterion to determine when two states can be transformed into each other by SLOCC transformations, a central question in entanglement…
We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In both cases we show that most of the eigenvalues of the perturbed matrix are very close to a circle with centre at the origin. In the…
We classify the local unitary equivalence classes of absolutely maximally entangled (AME) states of five qubits. We show that every 5-qubit AME state is equivalent to a state within the unique ((5,2,3)) quantum error-correcting code…
We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states into six classes. These include the stabilizer types of the Werner states, the GHZ state and its generalizations, and Dicke…
We explore the connection between quantum entanglement and the exchange symmetry of the states of N identical particles. Each particle has n-levels. The N particles span the nN dimensional Hilbert space. We shall call the general state of…