Related papers: Stabilizer States as a Basis for Density Matrices
Composite quantum states can be classified by how they behave under local unitary transformations. Each quantum state has a stabilizer subgroup and a corresponding Lie algebra, the structure of which is a local unitary invariant. In this…
Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous…
The operator-sum decomposition (OS) of a mapping from one density matrix to another has many applications in quantum information science. To this mapping there corresponds an affine map which provides a geometric description of the density…
The density of state for a complex $N\times N$ random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained.
We investigate the measurements of two-state quantum systems (qubits) at finite temperatures using a resonant harmonic oscillator as a quantum probe. The reduced density matrix and oscillator correlators are calculated by a scheme combining…
We consider a two dimensional random band matrix ensemble, in the limit of infinite volume and fixed but large band width $W$. For this model we rigorously prove smoothness of the averaged density of states. We also prove that the resulting…
Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent…
Fathoming out quantum state space is a challenging endeavor due to its exponentially growing dimensionality. At the expense of being bound in its expressiveness, the discrete and finite subspace of graph states is easier to investigate via…
We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…
Quantum dots (QDs) are one of the promising candidates of interconnection between electromagnetic field and electrons in solid-state devices. Dark states appear as a result of coherence between the electromagnetic fields and the discrete…
We consider the possibility of using stabilizer states to perform deterministic dense coding among multiple senders and a single receiver. In the model we studied, the utilized stabilizer state is partitioned into several subsystems and…
This note provides elementary proofs for necessary density conditions for frames and Riesz sequences in the lattice orbit of a discrete series representation that involve the projective stabiliser of the vector. The presented approach…
A generic scheme for the parametrization of mixed state systems is introduced, which is then adapted to bipartite systems, especially to a 2-qubit system. Various features of 2-qubit entanglement are analyzed based on the scheme. Our…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
We present three different matrix bases that can be used to decompose density matrices of $d$--dimensional quantum systems, so-called qudits: the \emph{generalized Gell-Mann matrix basis}, the \emph{polarization operator basis}, and the…
A continuous quantum walk on a graph $X$ with adjacency matrix $A$ is specified by the 1-parameter family of unitary matrices $U(t)=\exp(itA)$. These matrices act on the state space of a quantum system, the states of which we may represent…
An explicit parameterization for the state space of an $n$-level density matrix is given. The parameterization is based on the canonical coset decomposition of unitary matrices. We also compute, explicitly, the Bures metric tensor over the…
The amplitude encoding of an arbitrary $n$-qubit state vector requires $\Omega(2^n)$ gate operations, owing to the exponential dimension of the Hilbert space. We can, however, form dimensionality-reduced representations of quantum states…
Decoherence represents a major obstacle towards realizing reliable quantum technologies. Identifying states that can be uphold against decoherence by purely coherent means, i.e., {\it stabilizable states}, for which the dissipation-induced…
For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.