Related papers: States that are far from being stabilizer states
We study macroscopic entanglement of various pure states of a one-dimensional N-spin system with N>>1. Here, a quantum state is said to be macroscopically entangled if it is a superposition of macroscopically distinct states. To judge…
Magic describes the distance of a quantum state to its closest stabilizer state. It is -- like entanglement -- a necessary resource for a potential quantum advantage over classical computing. We study magic, quantified by stabilizer…
A complex projective $t$-design is a configuration of vectors which is ``evenly distributed'' on a sphere in the sense that sampling uniformly from it reproduces the moments of Haar measure up to order $2t$. We show that the set of all…
The four Bell states can be represented by separable coherent states which are products of individual non-hermitian spin operators. In the absence of interactions, the non-hermitian states are predicted to form a new quantum state of spin…
States which minimize the Schr\"odinger--Robertson uncertainty relation are constructed as eigenstates of an operator which is a element of the $h(1) \oplus \su(2)$ algebra. The relations with supercoherent and supersqueezed states of the…
Non-stabilizerness is an essential resource for quantum computational advantage, as stabilizer states admit efficient classical simulation. We develop a semi-device-independent framework for certifying non-stabilizer states in…
Quantum mechanics in the Rigged Hilbert Space formulation describes quasistationary phenomena mathematically rigorously in terms of Gamow vectors. We show that these vectors exhibit microphysical irreversibility, related to an intrinsic…
We consider particular entanglement of two particles whose state vectors are in bases that are mutually unbiased (MUB), i.e. "that exhibit maximum degree of incompatibility" (J.Schwinger,Nat. Ac. Sci. (USA), 1960)). We use this link between…
Distinct Clifford orbits of magic states can exhibit different stabilizer ranks at small tensor powers. We establish this for qutrits, where the single-qutrit Clifford group has four inequivalent orbits of magic states: Strange, Norrell,…
We consider the Unambiguous State Discrimination (USD) of two mixed quantum states. We study the rank and the spectrum of the elements of an optimal USD measurement. This naturally leads to a partial fourth reduction theorem. This theorem…
In the Majorana or stellar representation of quantum states, an arbitrary (pure) state of a spin-1 system is represented by a pair of points on the unit sphere or, equivalently, by a pair of unit vectors. This paper presents an expression…
In this paper, we investigate the relationship between entanglement and non-stabilizerness (also known as magic) in matrix product states (MPSs). We study the relation between magic and the bond dimension used to approximate the ground…
Absolute separable (AS) quantum states are those states from which it is impossible to create entanglement, even under global unitary operations. It is known from the resource theory of non-absolute separability that the set of absolute…
Magic states, pivotal for universal quantum computation via classically simulable Clifford gates, often undergo decomposition into resourceless stabilizer states, facilitating simulation through classical means. This approach yields three…
We propose a non-commutative extension of the Pauli stabilizer formalism. The aim is to describe a class of many-body quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are…
We discuss metastable states in the mean-field version of the strong coupling BCS-model and study the evolution of a superconducting equilibrium state subjected to a dynamical semi-group with Lindblad generator in detailed balance w.r.t.…
The Schwinger oscillator operator representation of SU(3), studied in a previous paper from the representation theory point of view, is analysed to discuss the intimate relationships between standard oscillator coherent state systems and…
Nonstabilizerness, or magic, is a necessary resource for quantum advantage beyond the classically simulatable Clifford framework. Recent works have begun to chart the structure of magic in many-body states, introducing the concepts of…
It is shown that the set of rank r separable states is measure zero within the set of low rank states provided r is less than an upper bound which depends upon the number of particles and the dimensions of the spaces they are modelled on.…
Magic or non-stabilizerness is a resource for quantum computing that has been extensively studied in qudit networks. It describes the degree to which Clifford gates cannot generate a given state, capturing the advantage of quantum over…