Multiqubit symmetric states with maximally mixed one-qubit reductions

Baguette, Dorian; Bastin, Thierry; Martin, John P.

doi:10.1103/physreva.90.032314

Cited by 39 publications

(67 citation statements)

References 40 publications

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“…However, anticoherent states to arbitrary order do not necessarily exist in a spin system with given spin quantum number j. For instance, no pure spin-j anticoherent states of order t > j do exist [12]. Nevertheless, it has been shown that pure anticoherent states to any order t exist provided that j is sufficiently large, typically j ∼ t 2 [8].…”

Section: A Examples and Propertiesmentioning

confidence: 99%

“…While spin rotations preserve the order of anticoherence of a spin state, all anticoherent states to a given order are not necessarily connected by rotations, as is the case for coherent states. For instance, for j = 2, it has been shown in [12] that there is an infinite number of 1-anticoherent states of the form…”

Section: A Examples and Propertiesmentioning

confidence: 99%

“…Such states have been studied in the literature, e.g. in the contexts of anticoherent spin states [6][7][8][9][10], completely entangled spin states [11,12] or multiphoton polarization states [13][14][15][16]. They also appear as some of the most non-classical spin states, where classicality of a spin state refers to the possibility of expressing it as a statistical mixture of spincoherent states with positive weights [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Anticoherence measures for pure spin states

Baguette

Martin

2017

Phys. Rev. A

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The set of pure spin states with vanishing spin expectation value can be regarded as the set of the less coherent pure spin states. This set can be divided into a finite number of nested subsets on the basis of higher order moments of the spin operators. This subdivision relies on the notion of anticoherent spin state to order t: A spin state is said to be anticoherent to order t if the moment of order k of the spin components along any directions are equal for k = 1, 2, . . . , t. Most spin states are neither coherent nor anticoherent, but can be arbitrary close to one or the other. In order to quantify the degree of anticoherence of pure spin states, we introduce the notion of anticoherence measures. By relying on the mapping between spin-j states and symmetric states of 2j spin-1/2 (Majorana representation), we present a systematic way of constructing anticoherence measures to any order. We briefly discuss their connection with measures of quantum coherence. Finally, we illustrate our measures on various spin states and use them to investigate the problem of the existence of anticoherent spin states with degenerated Majorana points.

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Section: A Examples and Propertiesmentioning

confidence: 99%

Section: A Examples and Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anticoherence measures for pure spin states

Baguette

Martin

2017

Phys. Rev. A

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“…Various results on entanglement for symmetric states have been obtained in the literature [5][6][7][8][9]. For instance, criteria for certifying separability in symmetric mixed states of N qubits were found in [10].…”

Section: Introductionmentioning

confidence: 99%

Entanglement and the truncated moment problem

2017

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We map the quantum entanglement problem onto the mathematically well-studied truncated moment problem. This yields a necessary and sufficient condition for separability that can be checked by a hierarchy of semi-definite programs. The algorithm always gives a certificate of entanglement if the state is entangled. If the state is separable, typically a certificate of separability is obtained in a finite number of steps and an explicit decomposition into separable pure states can be extracted.

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“…Such states have been studied in various contexts, such as quantum polarization of light (see e.g. [28,29]), spherical designs [30], as well as in the search for maximally entangled symmetric states [31]. We believe that our representation should prove useful in many of the contexts where the spin formalism is used.…”

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confidence: 99%

Tensor Representation of Spin States

et al. 2015

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We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light. The concept of spin is ubiquitous in quantum theory and all related fields of research, such as solidstate physics, molecular, atomic, nuclear or high-energy physics [1][2][3][4][5]. It has profound implications for the structure of matter as a consequence of the celebrated spinstatistics theorem [6]. The spin of a quantum system, be it an electron, a nucleus or an atom, has also been proven to be a key resource for many applications such as in spintronics [7], quantum information theory [8] or nuclear magnetic resonance [9]. Simple geometrical representations of spin states [10] allow one to develop physical insight regarding their general properties and evolution. Particularly well studied is the case of a single twolevel system, formally equivalent to a spin-1/2. In this case, the geometric representation is particularly simple. Indeed, the density matrix can be expressed in a basis formed of Pauli matrices and the identity matrix, leading to a parametrization in terms of a vector in R 3 . Pure states correspond to points on a unit sphere, the so-called Bloch sphere, and mixed states fill the inside of the sphere, the "Bloch ball". The simplicity of this representation help visualize the action and geometry of all possible spin-1/2 quantum channels [11]. For arbitrary pure spin states, another nice geometrical representation has been developed by Majorana in which a spin-j state is visualized as 2j points on the Bloch sphere [12]. This so-called Majorana or stellar representation has been exploited in various contexts (see, e. g., [11,[13][14][15][16][17]), but cannot be generalized to mixed spin states.Given the importance of geometrical representations, there have been numerous attempts to extend the previous representations to arbitrary mixed states. The former rely on a variety of sophisticated mathematical concepts such as su(N )-algebra generators [10,18,19], polarization operator basis [20][21][22] [26]. In the present Letter we propose an elegant generalisation to arbitrary spin-j of the spin-1/2 Bloch sphere representation based on matrices introduced by Weinberg in the context of relativistic quantum field theory [27]. The main result of the paper is theorem 2, which allows us to express any spin-j density matrix as a linear combination of matrices with convenient properties. The remarkable features of our representation are especially reflected in the simple coo...

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Multiqubit symmetric states with maximally mixed one-qubit reductions

Cited by 39 publications

References 40 publications

Anticoherence measures for pure spin states

Anticoherence measures for pure spin states

Entanglement and the truncated moment problem

Tensor Representation of Spin States

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