Finite-size key in the Bennett 1992 quantum-key-distribution protocol for Rényi entropies

Mafu, Mhlambululi; Garapo, Kevin; Petruccione, Francesco

doi:10.1103/physreva.88.062306

Cited by 18 publications

(8 citation statements)

References 21 publications

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“…Many efforts have been made to improve the bounds on the secret key rates for a finite amount of resources [5,16,[53][54][55][56][57][58]. Since the tools for analysing the security under non-asymptotic regime have become available, there is need to provide new security definitions.…”

Section: Finite-length Key Securitymentioning

confidence: 99%

Security of Quantum Key Distribution Protocols

Mafu¹,

Senekane²

2018

Advanced Technologies of Quantum Key Distribution

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Quantum key distribution (QKD), another name for quantum cryptography, is the most advanced subfield of quantum information and communication technology (QICT). The first QKD protocol was proposed in 1984, and since then, more protocols have been proposed. It uses quantum mechanics to enable secure exchange of cryptographic keys. In order to have high confidence in the security of the QKD protocols, such protocols must be proven to be secure against any arbitrary attacks. In this chapter, we discuss and demonstrate security proofs for QKD protocols. Security analysis of QKD protocols can be categorised into two techniques, namely infinite-key and finite-key analyses. Finite-key analysis offers more realistic results than the infinite-key one, while infinite-key analysis provides more simplicity. We briefly provide the background of QKD and also define the basic notion of security in QKD protocols. The cryptographic key is shared between Alice and Bob. Since the key is random and unknown to an eavesdropper, Eve, she is unable to learn anything about the message simply by intercepting the ciphertext. This phenomenon is beyond the ability of classical information processing. We then study some tools that are used in the derivation of security proofs for the infinite-and finite-length key limits.

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Section: Finite-length Key Securitymentioning

confidence: 99%

Security of Quantum Key Distribution Protocols

Mafu¹,

Senekane²

2018

Advanced Technologies of Quantum Key Distribution

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“…Some of them are based on mutually unbiased bases (see, e.g., Refs. [41,42]). We have seen above that the conditional entropies for a pair of successive projective measurements are maximized just in the case of mutual unbiasedness.…”

Section: Bounds For the Second Scenario Of Successive Qubit Measurmentioning

confidence: 99%

Uncertainty and Certainty Relations for Successive Projective Measurements of a Qubit in Terms of Tsallis' Entropies

Rastegin¹

2015

Commun. Theor. Phys.

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We study uncertainty and certainty relations for two successive measurements of two-dimensional observables. Uncertainties in successive measurement are considered within the following two scenarios. In the first scenario, the second measurement is performed on the quantum state generated after the first measurement with completely erased information. In the second scenario, the second measurement is performed on the post-first-measurement state conditioned on the actual measurement outcome. Induced quantum uncertainties are characterized by means of the Tsallis entropies. For two successive projective measurement of a qubit, we obtain minimal and maximal values of related entropic measures of induced uncertainties. Some conclusions found in the second scenario are extended to arbitrary finite dimensionality. In particular, a connection with mutual unbiasedness is emphasized.

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“…Experimental implementations of MUBs have been demonstrated in a wide range of quantum information protocols, e.g. [40,[51][52][53][54][55][56][57], as well as in fairly large dimensional systems [58,59]. The EW approach has the added bonus of requiring at most d + 1 MUBs, measured on each subsystem, while full quantum state reconstruction requires d 2 + 1 MUBs in C d ⊗ C d (or any other informationally complete set of measurements on the full state space), and often suffers from errors, such as the stability of the source over all possible measurements [60,61].…”

Section: Introductionmentioning

confidence: 99%

How many measurements are needed to detect bound entangled states?

Bae¹,

Bera²,

Chruściński³

et al. 2021

Preprint

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From a practical perspective it is advantageous to develop experimental methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of measurements needed to detect bound entanglement in bipartite (d × d)dimensional states, i.e. entangled states that are positive under partial transposition. In particular, we show that a class of entanglement witnesses composed of mutually unbiased bases (MUBs) can detect bound entanglement if the number of measurements is greater than d/2 + 1. This is a substantial improvement over other detection methods, requiring significantly fewer resources than either full quantum state tomography or measuring a complete set of d + 1 MUBs. Our approach is based on a partial characterisation of the (non-)decomposability of entanglement witnesses. We show that non-decomposability is a universal property of MUBs, which holds regardless of the choice of complementary observables, and we find that both the number of measurements and the structure of the witness play an important role in the detection of bound entanglement.

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Finite-size key in the Bennett 1992 quantum-key-distribution protocol for Rényi entropies

Cited by 18 publications

References 21 publications

Security of Quantum Key Distribution Protocols

Security of Quantum Key Distribution Protocols

Uncertainty and Certainty Relations for Successive Projective Measurements of a Qubit in Terms of Tsallis' Entropies

How many measurements are needed to detect bound entangled states?

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