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Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many…
Preparing and observing quantum states of nanoscale particles is a challenging task with great relevance for quantum technologies and tests of fundamental physics. In contrast to atomic systems with discrete transitions, nanoparticles…
Following our recent development of the paradigm for extending the classic concepts of circuit elements to the infrared and optical frequencies [N. Engheta, A. Salandrino, A. Alu, Phys. Rev. Lett. 95, 095504 (2005)], in this paper we…
Quantum algorithms often assume independent spin qubits to produce trivial $|\uparrow\rangle=|0\rangle$, $|\downarrow\rangle=|1\rangle$ mappings. This can be unrealistic in many solid-state implementations with sizeable magnetic…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
In this paper, the distinguishability of multipartite geometrically uniform quantum states obtained from a single reference state is studied in the symmetric subspace. We specially focus our attention on the unitary transformation in a way…
An array of quantum rings with local (ring by ring) modulation of the spin orbit interaction (SOI) can lead to novel effects in spin state transformation of electrons. It is shown that already small (3x3, 5x5) networks are remarkably…
Exceptional modular invariants for the Lie algebras B2 (at levels 2,3,7,12) and G2 (at levels 3,4) can be obtained from conformal embeddings. We determine the associated alge bras of quantum symmetries and discover or recover, as a…
We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…
It is revealed that ensembles consisting of multipartite quantum states can exhibit different kinds of nonlocalities. An operational measure is introduced to quantify nonlocalities in ensembles consisting of bipartite quantum states.…
Measuring quantum observables by grouping terms that can be rotated to sums of only products of Pauli $\hat z$ operators (Ising form) is proven to be efficient in near term quantum computing algorithms. This approach requires extra unitary…
The problem of how to obtain quasi-classical states for quantum groups is examined. A measure of quantum indeterminacy is proposed, which involves expectation values of some natural quantum group operators. It is shown that within any…
It is shown that the use of extended sets of irreducible representations of the Lorentz group opens new possibilities for the theory of relativistic wave equations from the point of view of the space-time description of both the internal…
We revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's…
For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each…
We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of $\mathcal N \leq 2$ quantum mechanical systems is $\#P$-complete and therefore…
The usual notion of separability has to be reconsidered when applied to states describing identical particles. A definition of separability not related to any a priori Hilbert space tensor product structure is needed: this can be given in…
Distinguishing quantum states that admit a classical counterpart from those that exhibit nonclassicality has long been a central issue in quantum optics. Finding an implementable criterion certifying optical nonclassicality (i.e, the…