Related papers: No invariant perfect qubit codes
The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any "classical"…
Noisy intermediate-scale quantum computers hold the promise of tackling complex and otherwise intractable computational challenges through the massive parallelism offered by qubits. Central to realizing the potential of quantum computing…
In this paper we introduce and investigate the concept of a perfect quantum protractor, a pure quantum state $|\psi\rangle\in\mathcal{H}$ that generates three different orthogonal bases of $\mathcal{H}$ under rotations around each of the…
Three new graph invariants are introduced which may be measured from a quantum graph state and form examples of a framework under which other graph invariants can be constructed. Each invariant is based on distinguishing a different number…
We experimentally prepare a new type of continuous variable genuine four-partite entangled states, the quantum correlation property of which is different from that of the four-mode GHZ and cluster states, and which has not any qubit…
The difficulty of an optimization task in quantum information science depends on the proper mathematical expression of the physical target. Here we demonstrate the power of optimization functionals targeting an arbitrary perfect two-qubit…
We study a question which has natural interpretations in both quantum mechanics and in geometry. Let $V_1,..., V_n$ be complex vector spaces of dimension $d_1,...,d_n$ and let $G= SL_{d_1} \times \dots \times SL_{d_n}$. Geometrically, we…
We introduce a general framework for detecting genuine multipartite entanglement and non full-separability in multipartite quantum systems of arbitrary dimensions based on correlation tensors. Regarding genuine multipartite entanglement our…
Organising the space of entanglement structures of a multipartite quantum system is a much more challenging task than its bipartite version: while the local unitary (LU) orbit of a bipartite pure state can be conveniently characterized by…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
We determine the frequency ratios $\tau\equiv \omega_z/\omega_{\rho}$ for which the Hamiltonian system with a potential \[ V=\frac{1}{r}+\frac{1}{2}\Big({\omega_{\rho}}^2(x^2+y^2)+{\omega_z}^2 z^2\Big) \] is completely integrable. We relate…
Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully…
Spin network states are a powerful tool for constructing the $SU(2)$ gauge theories on a graph. In loop quantum gravity (LQG), they have yielded many promising predictions, although progress has been limited by the computational challenge…
We produce full strong exceptional collections consisting of vector bundles on the geometric invariant theory quotient of certain linear actions of a split reductive group $G$ of rank two. The vector bundles correspond to irreducible…
We consider the model of quantum computer, which is represented as a Ising spin lattice, where qubits (spin-half systems) are separated by the isolators (two spin-half systems). In the idle mode or at the single bit operations the total…
Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may…
From both theoretical and experimental points of view symmetric states constitute an important class of multipartite states. Still, entanglement properties of these states, in particular those with positive partial transposition (PPT), lack…
For a quantum system with broken parity symmetry, selection rules can not hold and cyclic transition structures are generated. With these loop-transitions we discuss how to achieve inversionless gain of the probe field by properly setting…
Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in…
We study $S=1$ quantum spin systems on the infinite chain with short ranged Hamiltonians which have certain rotational and discrete symmetry. We define a $\mathbb{Z}_2$ index for any gapped unique ground state, and prove that it is…