scholarly journals Characterization of Gram matrices of multimode coherent states

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
Ashutosh S. Marwah ◽  
Norbert Lütkenhaus
Keyword(s):  
Coherent States ◽  
Gram Matrices

scholarly journals Common Coherence Witnesses and Common Coherent States

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1136
Author(s):  
Bang-Hai Wang ◽  
Zi-Heng Ding ◽  
Zhihao Ma ◽  
Shao-Ming Fei
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
State Problem ◽  
Properties And Characterization ◽  
The Common ◽  
High Level

We show the properties and characterization of coherence witnesses. We show methods for constructing coherence witnesses for an arbitrary coherent state. We investigate the problem of finding common coherence witnesses for certain class of states. We show that finitely many different witnesses W1,W2,⋯,Wn can detect some common coherent states if and only if ∑i=1ntiWi is still a witnesses for any nonnegative numbers ti(i=1,2,⋯,n). We show coherent states play the role of high-level witnesses. Thus, the common state problem is changed into the question of when different high-level witnesses (coherent states) can detect the same coherence witnesses. Moreover, we show a coherent state and its robust state have no common coherence witness and give a general way to construct optimal coherence witnesses for any comparable states.

scholarly journals Coherent preorder of quantum states

2020 ◽  
Vol 20 (13&14) ◽  
pp. 1124-1137
Author(s):  
Zhaofang Bai ◽  
Shuanping Shuanping Du
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Coherent States ◽  
Quantum Coherence ◽  
Quantum Information Processing ◽  
Quantum States ◽  
Mixed States ◽  
Quantum Hypothesis ◽  
Quantum Hypothesis Testing

As an important quantum resource, quantum coherence play key role in quantum information processing. It is often concerned with manipulation of families of quantum states rather than individual states in isolation. Given two pairs of coherent states $(\rho_1,\rho_2)$ and $(\sigma_1,\sigma_2)$, we are aimed to study how can we determine if there exists a strictly incoherent operation $\Phi$ such that $\Phi(\rho_i) =\sigma_i,i = 1,2$. This is also a classic question in quantum hypothesis testing. In this note, structural characterization of coherent preorder under strongly incoherent operations is provided. Basing on the characterization, we propose an approach to realize coherence distillation from rank-two mixed coherent states to $q$-level maximally coherent states. In addition, one scheme of coherence manipulation between rank-two mixed states is also presented.

Maximally coherent states

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1355-1364
Author(s):  
Zhaofang Bai ◽  
Shuanping Du
Keyword(s):  
Quantum Information ◽  
Coherent State ◽  
Relative Entropy ◽  
Quantum Correlation ◽  
Coherent States ◽  
Entropy Measure ◽  
Product State ◽  
Quantum Operations ◽  
Maximal Entanglement

The relative entropy measure quantifying coherence, a key property of quantum system, is proposed recently. In this note, we firstly investigate structural characterization of maximally coherent states with respect to the relative entropy measure. It is shown that mixed maximally coherent states do not exist and every pure maximally coherent state has the form U|ψihψ|U† , |ψi = √1 d Pd k=1 |ki, U is diagonal unitary. Based on the characterization of pure maximally coherent states, for a bipartite maximally coherent state with dA = dB, we obtain that the super-additivity equality of relative entropy measure holds if and only if the state is a product state of its reduced states. From the viewpoint of resource in quantum information, we find there exists a maximally coherent state with maximal entanglement. Originated from the behaviour of quantum correlation under the influence of quantum operations, we further classify the incoherent operations which send maximally coherent states to themselves.

scholarly journals Characterization of phase-averaged coherent states

2013 ◽  
Vol 30 (10) ◽  
pp. 2621 ◽  
Author(s):  
Alessia Allevi ◽  
Maria Bondani ◽  
Paulina Marian ◽  
Tudor A. Marian ◽  
Stefano Olivares
Keyword(s):  
Coherent States

scholarly journals EXPERIMENTAL QUANTIFICATION OF NON-GAUSSIANITY OF PHASE-RANDOMIZED COHERENT STATES

2012 ◽  
Vol 10 (08) ◽  
pp. 1241006 ◽  
Author(s):  
ALESSIA ALLEVI ◽  
STEFANO OLIVARES ◽  
MARIA BONDANI
Keyword(s):  
Experimental Investigation ◽  
Wigner Function ◽  
Coherent States ◽  
The Other ◽  
Fock States ◽  
Two Measures ◽  
Non Gaussian

We present the experimental investigation of the non-Gaussian nature of some mixtures of Fock states by reconstructing their Wigner function and exploiting two recently introduced measures of non-Gaussianity. In particular, we demonstrate the consistency between the different approaches and the monotonicity of the two measures for states belonging to the class of phase-randomized coherent states. Moreover, we prove that the exact behavior of one measure with respect to the other depends on the states under investigation and devise possible criteria to discriminate which measure is more useful for the characterization of the states in realistic applications.

scholarly journals A Characterization of Gram Matrices of Polytopes

1999 ◽  
Vol 21 (4) ◽  
pp. 581-601 ◽  
Author(s):  
R. Díaz
Keyword(s):  
Gram Matrices

scholarly journals Characterization of SU(1, 1) coherent states in terms of affine group wavelets

2002 ◽  
Vol 35 (34) ◽  
pp. 7347-7357 ◽  
Author(s):  
Jacqueline Bertrand ◽  
Mich$egrave$le Irac-Astaud
Keyword(s):  
Coherent States ◽  
Affine Group

scholarly journals The varieties of minimal tomographically complete measurements

2020 ◽  
pp. 2040005
Author(s):  
John B. DeBrota ◽  
Christopher A. Fuchs ◽  
Blake C. Stacey
Keyword(s):  
Quantum Physics ◽  
Numerical Study ◽  
Quantum Measurements ◽  
Gram Matrix ◽  
Gram Matrices ◽  
Classical Phase Space ◽  
Equivalent Conditions ◽  
Complete Quantum ◽  
The Ideal

Minimal Informationally Complete quantum measurements, or MICs, illuminate the structure of quantum theory and how it departs from the classical. Central to this capacity is their role as tomographically complete measurements with the fewest possible number of outcomes for a given finite dimension. Despite their advantages, little is known about them. We establish general properties of MICs, explore constructions of several classes of them, and make some developments to the theory of MIC Gram matrices. These Gram matrices turn out to be a rich subject of inquiry, relating linear algebra, number theory and probability. Among our results are some equivalent conditions for unbiased MICs, a characterization of rank-1 MICs through the Hadamard product, several ways in which immediate properties of MICs capture the abandonment of classical phase space intuitions, and a numerical study of MIC Gram matrix spectra. We also present, to our knowledge, the first example of an unbiased rank-1 MIC which is not group covariant. This work provides further context to the discovery that the symmetric informationally complete quantum measurements (SICs) are in many ways optimal among MICs. In a deep sense, the ideal measurements of quantum physics are not orthogonal bases.

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