Device-Independent Entanglement Quantification and Related Applications

Moroder, Tobias; Bancal, Jean-Daniel; Liang, Yeong-Cherng; Hofmann, Martin; Gühne, Otfried

doi:10.1103/physrevlett.111.030501

Cited by 173 publications

(354 citation statements)

References 59 publications

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“…Note that this definition was already used in Ref. [7] to quantify genuine multiparticle entanglement in a device independent manner.…”

Section: Modifying the Definition Of The Genuine Multiparticle Negatimentioning

confidence: 99%

“…[6], the GMN quantified how quantum reservoir engineering can create entangled states in cascaded quantum-optical networks driven by dissipative processes. Finally, it has been shown how the GMN can be measured experimentally in a device-independent way [7]. All these applications are based on the fact that the GMN can directly be computed, but this may also lead to the impression that the GMN is mainly a numerical tool and not accessible to an analytical treatment.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical characterization of the genuine multiparticle negativity

Hofmann¹,

Moroder²,

Gühne³

2014

J. Phys. A: Math. Theor.

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Abstract. The genuine multiparticle negativity is a measure of genuine multiparticle entanglement which can be numerically calculated. We present several results how this entanglement measure can be characterized in an analytical way. First, we show that with an appropriate normalization this measure can be seen as coming from a mixed convex roof construction. Based on this, we determine its value for n-qubit GHZdiagonal states and four-qubit cluster-diagonal states.

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“…Note that this definition was already used in Ref. [7] to quantify genuine multiparticle entanglement in a device independent manner.…”

Section: Modifying the Definition Of The Genuine Multiparticle Negatimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical characterization of the genuine multiparticle negativity

Hofmann¹,

Moroder²,

Gühne³

2014

J. Phys. A: Math. Theor.

Self Cite

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“…This possibility, unique to Bell inequalities, has been called deviceindependent certification. The first task to be studied this way was quantum key distribution [6]; it was followed by the task of generating certified randomness [7,8] and by the quantifications of some entanglement measures [9,10].…”

Section: Introductionmentioning

confidence: 99%

Quantum randomness extraction for various levels of characterization of the devices

Law

Thinh

Bancal

et al. 2014

J. Phys. A: Math. Theor.

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139

132

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The amount of intrinsic randomness that can be extracted from measurement on quantum systems depends on several factors: notably, the power given to the adversary and the level of characterization of the devices of the authorized partners. After presenting a systematic introduction to these notions, in this paper we work in the class of least adversarial power, which is relevant for assessing setups operated by trusted experimentalists, and compare three levels of characterization of the devices. Many recent studies have focused on the so-called "device-independent" level, in which a lower bound on the amount of intrinsic randomness can be certified without any characterization. The other extreme is the case when all the devices are fully characterized: this "tomographic" level has been known for a long time. We present for this case a systematic and efficient approach to quantifying the amount of intrinsic randomness, and show that setups involving ancillas (POVMs, pointer measurements) may not be interesting here, insofar as one may extract randomness from the ancilla rather than from the system under study. Finally, we study how much randomness can be obtained in presence of an intermediate level of characterization related to the task of "steering", in which Bob's device is fully characterized while Alice's is a black box. We obtain our results here by adapting the NPA hierarchy of semidefinite programs to the steering scenario.

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“…The corresponding statistics of the measurement outcomes is called a Bell correlation. It has been shown that the dimension and the entanglement of the underlying quantum state can be quantified in a device-independent way using only the Bell correlation data [5,[8][9][10]. In fact, some quantum states can even be pinned down completely by their violations of particular Bell inequalities, but this is only known to be possible for some special cases [1][2][3][4][15][16][17].…”

mentioning

confidence: 99%

Device-independent characterizations of a shared quantum state independent of any Bell inequalities

Wei

Sikora

2017

Phys. Rev. A

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In a Bell experiment two parties share a quantum state and perform local measurements on their subsystems separately, and the statistics of the measurement outcomes are recorded as a Bell correlation. For any Bell correlation, it turns out that a quantum state with minimal size that is able to produce this correlation can always be pure. In this work, we first exhibit two deviceindependent characterizations for the pure state that Alice and Bob share using only the correlation data. Specifically, we give two conditions that the Schmidt coefficients must satisfy, which can be tight, and have various applications in quantum tasks. First, one of the characterizations allows us to bound the entanglement between Alice and Bob using Renyi entropies and also to bound the underlying Hilbert space dimension. Second, when the Hilbert space dimension bound is tight, the shared pure quantum state has to be maximally entangled. Third, the second characterization gives a sufficient condition that a Bell correlation cannot be generated by particular quantum states. We also show that our results can be generalized to the case of shared mixed states.Introduction.-In the study of quantum physics, frequently the internal workings of a quantum device are not exactly known. For example, it is often the case that we do not have sufficient knowledge of the internal physical structure, or the precision of the quantum controls is very limited, or even the devices we are using cannot be trusted. In these cases, it could be that the only reliable information available is the measurement statistics from observing the quantum system. However, sometimes we still want to draw nontrivial conclusions on the quantum properties of the involved system. This sounds like a challenging, or even impossible task, but it has been shown to be possible in many cases [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. These kinds of tasks are called device-independent as their application assumes only the correctness of quantum mechanics as a valid description of nature, and is independent of the internal workings of the devices used. Device-independence is a very valuable property in physical implementations of various quantum schemes. Typical examples of its usefulness include the transmission of information safely using untrusted devices, and easy monitoring of the overall performance of vulnerable quantum devices [11][12][13][14].We consider in this paper the setting of a Bell experiment, i.e., two spatially separated parties sharing a quantum state and performing local measurements on their subsystems. The corresponding statistics of the measurement outcomes is called a Bell correlation. It has been shown that the dimension and the entanglement of the underlying quantum state can be quantified in a device-independent way using only the Bell correlation data [5,[8][9][10]. In fact, some quantum states can even be pinned down completely by their violations of particular Bell inequalities, but this is only known to be possible for some special cases [1][2][...

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Device-Independent Entanglement Quantification and Related Applications

Cited by 173 publications

References 59 publications

Analytical characterization of the genuine multiparticle negativity

Analytical characterization of the genuine multiparticle negativity

Quantum randomness extraction for various levels of characterization of the devices

Device-independent characterizations of a shared quantum state independent of any Bell inequalities

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