Noncommuting Mixed States Cannot Be Broadcast

Barnum, Howard; Caves, Carlton M.; Fuchs, Christopher A.; Jozsa, Richard; Schumacher, Benjamin

doi:10.1103/physrevlett.76.2818

Cited by 575 publications

(627 citation statements)

References 13 publications

(21 reference statements)

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“…However, in the mean time, there is one restricted result about information gain vs. disturbance for mixed states that brings out an interesting mystery. This result is known as the "no-broadcasting theorem" [8].…”

Section: Mixed Statesmentioning

confidence: 99%

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Information Gain vs. State Disturbance in Quantum Theory

Fuchs

1999

Quantum Computing

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Section: Mixed Statesmentioning

confidence: 99%

“…It turns out that the case just described is indeed a rather special one, for two statesρ 0 andρ 1 can be broadcast if and only if they commute [8]. That is, if and only if they can be simultaneously thought of as classical probability distributions for some underlying reality.…”

Section: Mixed Statesmentioning

confidence: 99%

Information Gain vs. State Disturbance in Quantum Theory

Fuchs

1999

Quantum Computing

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“…In particular, two classical mixtures can be defined as orthogonal if and only if their supports are disjoint. Furthermore, even the no-cloning theorem, originally obtained in the quantum context (Dieks 1982, Wootters andZurek 1982; see the extension to mixtures in Barnum et al 1996), can be proved in the classical statistical domain by taking overlapping probability distributions with non-trivial supports as dynamical variables (Daffertshofer, Plastino and Plastino 2002;see discussion in Teh 2012). …”

Section: -Quantum States or Non-orthogonal States?mentioning

confidence: 99%

What is Quantum Information?

Lombardi¹,

Fortín²,

Holik³

et al. 2017

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The word 'information' refers to a polysemantic concept associated with very different phenomena, such as communication, knowledge, reference and meaning (Floridi 2010(Floridi , 2011. In the discussions about this matter, the first distinction to be introduced is that between a semantic view, according to which information carries semantic content and, thus, is related to notions as reference and meaning, However, the problems of interpretation do not disappear even when the attention is restricted to a single formal concept (see Lombardi, Holik and Vanni 2014).During the last decades, new interpretive problems have arisen with the advent of quantum information, which combine the difficulties in the understanding of the concept of information with the well-known foundational puzzles derived from quantum mechanics itself. This situation contrasts with the huge development of the research field named 'quantum information', where new formal results multiply rapidly. In this context, the question 'What is quantum information?' is still far from having an answer on which the whole quantum information community agrees. In fact, the positions about the matter range from those who seem to deny the existence of quantum information (Duwell 2003), those who consider that it refers to information when it is encoded in quantum systems , and those who conceive it as a new kind of information absolutely different than Shannon information (Jozsa 1998;Brukner and Zeilinger 2001).In the present article we will address the question 'What is quantum information?' from a conceptual viewpoint. For this purpose, in Section 2 Schumacher's formalism is introduced by contrast with Shannon's theory. In Section 3 the definition of quantum information in terms of a quantum source is discussed. Section 4 is devoted to analyze the definition of information in terms of coding theorems. These tasks lead us to focus on the relationship between Shannon entropy and von Neumann entropy in Section 5, and to discuss the differences between the concepts of bit and

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“…One can also define the fidelity between continuous gaussian states in terms of Wigner functions. We use here the Bures-Uhlmann fidelity between two arbitrary statesρ 1 andρ 2 defined as [10] F(ρ 1 ,ρ 2 ) = tr ρ 1ρ2 ρ 1 which coincides with the so called Hilbert-Schmidt fidelity…”

Section: Formalismmentioning

confidence: 99%

Efficiency in Quantum Key Distribution Protocols with Entangled Gaussian States

Rodó

Romero‐Isart

Eckert

et al. 2007

Open Syst. Inf. Dyn.

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Abstract. Quantum key distribution (QKD) refers to specific quantum strategies which permit the secure distribution of a secret key between two parties that wish to communicate secretly. Quantum cryptography has proven unconditionally secure in ideal scenarios and has been successfully implemented using quantum states with finite (discrete) as well as infinite (continuous) degrees of freedom. Here, we analyze the efficiency of QKD protocols that use as a resource entangled gaussian states and gaussian operations only. In this framework, it has already been shown that QKD is possible [1] but the issue of its efficiency has not been considered. We propose a figure of merit (the efficiency E) to quantify the number of classical correlated bits that can be used to distill a key from a sample of N entangled states. We relate the efficiency of the protocol to the entanglement and purity of the states shared between the parties.

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Noncommuting Mixed States Cannot Be Broadcast

Cited by 575 publications

References 13 publications

Information Gain vs. State Disturbance in Quantum Theory

Information Gain vs. State Disturbance in Quantum Theory

What is Quantum Information?

Efficiency in Quantum Key Distribution Protocols with Entangled Gaussian States

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