General quantum key distribution in higher dimension

Xiong, Zhaoxi; Shi, Handuo; Wang, Yi Nan; Li, Jing; Jin, Lei; Mu, Liang-Zhu; Fan, Heng

doi:10.1103/physreva.85.012334

Cited by 15 publications

(15 citation statements)

References 28 publications

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“…This cloning machine has been proven to be optimal in the sense that the fidelity between the input qubit and one of the two output qubits is optimal [6]. The UQCM is extended to the higher-dimensional case [5], the case with M identical input states to N equally copies [7], and some other cases [8][9][10][11][12][13][14][15][16], including the recent proposed unified forms [17,18].…”

Section: Introductionmentioning

confidence: 99%

Minimal input sets determining phase-covariant and universal quantum cloning

Wang

Shi

et al. 2012

Phys. Rev. A

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We study the minimal input sets which can determine completely the universal and the phase-covariant quantum cloning machines. We find that the universal quantum cloning machine, which can copy an arbitrary input qubit to two identical copies, however, can be determined completely by only four input states located at the four vertices of a tetrahedron in a Bloch sphere. The phase-covariant quantum cloning machine, which can create two copies from an arbitrary qubit located on the equator of the Bloch sphere, can be determined by three qubits located symmetrically on the equator of the Bloch sphere with equal relative phase. These results sharpen further the well-known results that Bennett-Brassard 1984 protocol (BB84) states and six states used in quantum cryptography can determine completely the phase-covariant and universal quantum cloning machines. This can simplify the testing procedure of whether the quantum clone machines are successful or not; namely, we only need to check that the minimal input sets can be cloned optimally, which can ensure that the quantum clone machines can work well for all input states.

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Section: Introductionmentioning

confidence: 99%

Minimal input sets determining phase-covariant and universal quantum cloning

Wang

Shi

et al. 2012

Phys. Rev. A

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“…[5][6][7][8][9]. By considering that the number of MUBs can be at most d + 1 [9], other than only restricting to 2, it is natural to investigate the uncertainty relation with more than two measurements even for the simplest two-dimensional case, see FIG.…”

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confidence: 99%

“…This uncertainty relation is confirmed experimentally [19,20] and can be applied in studying the security of quantum cryptography. Again, the inequality is only for two measurements while the case of multiple observables is of fundamental interest and of practical applications for quantum key distributions with more than two measurements settings [6,8]. We remark that the uncertainty inequality has been extended to multi-partite systems [21] and can be related with many concepts such as teleportation, entanglement witness in quantum information processing [20,22].…”

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confidence: 99%

Entropic uncertainty relations for multiple measurements

2015

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We present the entropic uncertainty relations for multiple measurement settings in quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory. They take concise forms which can be proven in a unified method and easy to calculate. Our results recover the well known entropic uncertainty relations for two observables, which show the uncertainties about the outcomes of two incompatible measurements. Those uncertainty relations are applicable in both foundations of quantum theory and the security of many quantum cryptographic protocols. Introduction.-Uncertainty principle is one unique feature of quantum mechanics differing from the classical case. Heisenberg [1] formulated the first uncertainty relation which shows that one cannot predict the outcomes with arbitrary precision for two incompatible measurements simultaneously, such as position and momentum, on a particle. As a fundamental property, uncertainty principle is continuously attracting lots of attention and research interests. Variants of uncertainty relations are presented in the past years. One type of best known uncertainty relations today is in the form proposed by Robertson [2]. For arbitrary two observables U and V , the uncertainty relation given by Robertson takes the form, σ U σ V ≥ ψ|

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“…Refs. [37,38] generalized (1) for the case when Alice and Bob use a d-dimensional encoding (d > 2), and g mutually-unbiased measurement bases, 2 ≤ g ≤ d + 1. …”

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confidence: 99%

Rate-loss analysis of an efficient quantum repeater architecture

et al. 2015

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We analyze an entanglement-based quantum key distribution (QKD) architecture that uses a linear chain of quantum repeaters employing photon-pair sources, spectral-multiplexing, linear-optic Bell-state measurements, multi-mode quantum memories and classical-only error correction. Assuming perfect sources, we find an exact expression for the secret-key rate, and an analytical description of how errors propagate through the repeater chain, as a function of various loss and noise parameters of the devices. We show via an explicit analytical calculation, which separately addresses the effects of the principle non-idealities, that this scheme achieves a secret key rate that surpasses the TGW bound-a recently-found fundamental limit to the rate-vs.-loss scaling achievable by any QKD protocol over a direct optical link-thereby providing one of the first rigorous proofs of the efficacy of a repeater protocol. We explicitly calculate the end-to-end shared noisy quantum state generated by the repeater chain, which could be useful for analyzing the performance of other non-QKD quantum protocols that require establishing long-distance entanglement. We evaluate that shared state's fidelity and the achievable entanglement distillation rate, as a function of the number of repeater nodes, total range, and various loss and noise parameters of the system. We extend our theoretical analysis to encompass sources with non-zero two-pair-emission probability, using an efficient exact numerical evaluation of the quantum state propagation and measurements. We expect our results to spur formal rate-loss analysis of other repeater protocols, and also to provide useful abstractions to seed analyses of quantum networks of complex topologies.Shared entanglement underlies many quantum information protocols such as quantum key distribution (QKD) [1], teleportation [2] and dense coding [3], and is a fundamental information resource that can boost reliable classical and quantum communication rates over noisy quantum channels [4,5]. Optical photons are arguably the only candidate for distributing entanglement across long distances. They however are susceptible to loss and noise in the channel, which is the bane of practical realizations of long-distance quantum communication. The maximum entanglement-generation rate over a lossy optical channel with no classical-communication assistance is zero when the total loss exceeds 3 dB [6]. With two-way classical-communication assistance, the rates achievable for entanglement generation, as well as those for reliable quantum communication and secretkey generation (i.e., QKD) over a lossy optical channel must decay linearly with the channel's transmittance (i.e., exponentially with optical fiber length), regardless of the specific protocol used, for loss exceeding ∼ 5 dB [7], while the rate plunges to zero at a maximum loss threshold that is determined by the excess noise in the channel and detectors. In order to generate entanglement over long distances at high rates, intermediate nodes equipped with quant...

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General quantum key distribution in higher dimension

Cited by 15 publications

References 28 publications

Minimal input sets determining phase-covariant and universal quantum cloning

Minimal input sets determining phase-covariant and universal quantum cloning

Entropic uncertainty relations for multiple measurements

Rate-loss analysis of an efficient quantum repeater architecture

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