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**1 - 9**of**9**### ENTANGLEMENT AND OTHER QUANTUM CORRELATIONS OF A SINGLE QUDIT STATE AS A RESOURCE FOR QUANTUM TECHNOLOGIES

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by Eric A Carlen, Elliott H Lieb

Venue: | Journal of Mathematical Physics |

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by
Lin Zhang
, 2014

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...Golden Thompson inequalit (see Proposition 3.2) are used in the proof of this lower bound. My ideas towards the proof of these results in this paper originates from the observations made by Carlen in =-=[13]-=-. 2 Main results In this section, the first one of our main results is proved. Theorem 2.1. For an arbitrary tripartite state ρABC, we have that I(A : C|B)ρ > ∥∥∥∥√ρABC − √ exp(log ρAB − log ρB + log ...

by
Omar Fawzi, Renato Renner

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...onal mutual information in terms of a distance between certain operators derived from ρABC has recently been stated in [57]. This bound is based on a novel monotonicity bound for the relative entropy =-=[11]-=-. Our work may be used to obtain strengthened versions of some of these results. We are going to illustrate this for the case of squashed entanglement. Applications. For us, one motivation to study ho...

by
Margarita A. Man’ko, Vladimir I. Man’ko

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...trix, and it has the matrix elements (ã2)jn = (ã2)nj = 0 for all j = 1, 2, . . . , n. For an example of the qutrit density matrix a, the matrix ã2 reads ã2 = a11 + a33 a12 0a21 a22 0 0 0 0 . =-=(14)-=- In fact, the obtained matrix corresponds to the density 2×2-matrix of the qubit state. The positive map a→ ã2 provides the map of the qutrit density matrix onto the qubit density matrix a→ ˜̃a of th...

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unknown authors

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...antum channels. The method used is quantum α-Rényi relative entropy [11]. Once we get one of main results (Theorem 3.1), we can simply derive all improved version of some quantum entropy inequalities =-=[12]-=-. Note that the method taken in the present paper is much simpler than one in [13]. The paper is organized as follows. The definition and properties of quantum Rényi relative entropy are given in Sect...

by
Isaac Kim, Mary Beth Ruskai
, 2014

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...g ρ − log γ) denotes the relative entropy. In Section 2 present a simple proof of (2) and compare it to other possible lower bounds, particularly those resulting from recent work of Carlen and 1 Lieb =-=[4]-=-. Our results demonstrate that their methods do not always give stronger results than those obtained using Pinsker’s bound. We also consider upper bounds in Section 3. Finally, in section 4 we discuss...

by
Lin Zhang

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...rXiv:1403.6102]. These inequalities obtained extends some well-known inequalities. We also obtain a condition under which a tripartite operator becomes a Markov state. 1 Introduction Recently, Carlen =-=[1]-=- gives improvement of some entropy inequalities by Perels-Bogoliubov inequality and Golden Thompson inequality. It is this paper that sparked the present author to extend his work [2] and get a unifyi...

by
V. N. Chernega, O. V. Man’ko, V. I. Man’ko

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...ositive map approach it was shown [8, 9, 21, 22, 23, 24] that the entropic inequalities valid for composite systems can be extended to the arbitrary systems including systems without subsystems. In 1 =-=[25, 26, 27]-=- some inequalities associated with positive operators acting in the Hilbert space which has the structure of tensor product of Hilbert spaces were studied. The aim of our work is to obtain new matrix ...

by
V. N. Chernega, O. V. Man’ko, V. I. Man’ko

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...ite quantum system, noncomposite quantum system, entropic and information inequalities PACS: 42.50.-p,03.65 Bz 1 Introduction There exist different entropic inequalities for composite quantum systems =-=[1, 2, 3, 4, 5, 6, 7, 8]-=-. Recently it was formulated [9, 10, 11, 12, 13] that the inequalities known for composite systems uncluding subadditivity condition and strong subadditivity condition can be generalized for noncompos...

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