Related papers: LU transformation invariant operators and LU trans…
We present a classification of three-qubit states based in their three-qubit and reduced two-qubit entanglements. For pure states these criteria can be easily implemented, and the different types can be related with sets of equivalence…
We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations is presented for a class of mixed states. It is shown that two states in this class are…
In this paper we study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized…
We construct entanglement monotones for multi-qubit states based on Pl\"{u}cker coordinate equations of Grassmann variety, which are central notion in geometric invariant theory. As an illustrative example, we in details investigate…
We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a…
Much of the theory of entanglement concerns the transformations that are possible to a state under local operations with classical communication (LOCC); however, this set of operations is complicated and difficult to describe…
A three-dimensional $q$-Lie algebra of $SU_q(2)$ is realized in terms of first- and second-order differential operators. Starting from the $q$-Lie algebra one has constructed a left-covariant differential calculus on the quantum group. The…
We consider a single copy of a pure four-partite state of qubits and investigate its behaviour under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of…
We define quantum phase in terms of inverses of annihilation and creation operators. We show that like Susskind - Glogower phase operators, the measured phase operators and the unitary phase operators can be defined in terms of the inverse…
A six-qubit quantum network consisting of conditional unitary gates is presented which is capable of implementing a large class of covariant two-qubit quantum operations. Optimal covariant NOT operations for one and two-qubit systems are…
The paper [Phys. Lett. A 373 (2009) 3610] by D.-C. Li analyzes the transformation between two-qubit mixed states by local operations and classical communication. We show that the proof of the main theorem, Theorem 2.6 in [Phys. Lett. A 373…
It is challenging to build scalable quantum processors capable of both parallel control and local operation. As a promising platform to overcome this challenge, optical lattices offer exceptional parallelism. However, it has been struggling…
In this paper we establish a relation between quantum relative phase, $m$-tangle, and multi-local Lorentz-group invariant or $SL(2,\mathbb{C})^{\times m}$-invariant $S^{2}_{(m)}$. Our construction is based on the orthogonal complement of a…
The LULU operators for sequences are extended to multi-dimensional arrays via the morphological concept of connection in a way which preserves their essential properties, e.g. they are separators and form a four element fully ordered…
Non-local properties of symmetric two-qubit states are quantified in terms of a complete set of entanglement invariants. We prove that negative values of some of the invariants are signatures of quantum entanglement. This leads us to…
Recently, we introduced negativity fonts as the basic units of multipartite entanglement in pure states. We show that the relation between global negativity of partial transpose of N- qubit state and linear entropy of reduced single qubit…
We introduce and study the following modified version of the Invariant Subspace Problem: whether every operator T on a Banach space has an almost invariant half-space, that is, a subspace Y of infinite dimension and infinite codimension…
We propose a simple setup for the conversion of multipartite entangled states in a quantum network with restricted access. The scheme uses nonlocal operations to enable the preparation of states that are inequivalent under local operations…
The necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under Local Unitary (LU) operations derived in [B. Kraus Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different…
Quantum coherence is a fundamental property that can emerge within any quantum system. Incoherent operations, defined in terms of the Kraus decomposition, take an important role in state transformation. The maximum number of incoherent…