Practical position-based quantum cryptography

Chakraborty, Kaushik; Leverrier, Anthony

doi:10.1103/physreva.92.052304

Cited by 22 publications

(20 citation statements)

References 31 publications

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“…These include, for instance, quantum bit commitment, [162][163][164] quantum secret sharing, [165][166][167] quantum coin flipping, 168,169 quantum fingerprinting, 170,171 quantum digital signatures, 172,173 blind quantum computing 174,175 and position-based quantum cryptography. [176][177][178] It is known that some of those protocols, such as quantum bit commitment and position-based quantum cryptography, cannot be perfectly achieved with unconditional security. However, other security models exist, such as, for instance, those based on relativistic constraints or on noisy storage assumptions, 179 where by assuming that it is impossible for an eavesdropper to store quantum information for a long time, one can retrieve security for such protocols.…”

Section: Resultsmentioning

confidence: 99%

Practical challenges in quantum key distribution

Diamanti¹,

Lo²,

Qi³

et al. 2016

npj Quantum Inf

597

468

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Quantum key distribution (QKD) promises unconditional security in data communication and is currently being deployed in commercial applications. Nonetheless, before QKD can be widely adopted, it faces a number of important challenges such as secret key rate, distance, size, cost and practical security. Here, we survey those key challenges and the approaches that are currently being taken to address them. For thousands of years, human beings have been using codes to keep secrets. With the rise of the Internet and recent trends to the Internet of Things, our sensitive personal financial and health data as well as commercial and national secrets are routinely being transmitted through the Internet. In this context, communication security is of utmost importance. In conventional symmetric cryptographic algorithms, communication security relies solely on the secrecy of an encryption key. If two users, Alice and Bob, share a long random string of secret bits-the key-then they can achieve unconditional security by encrypting their message using the standard one-time-pad encryption scheme. The central question then is: how do Alice and Bob share a secure key in the first place? This is called the key distribution problem. Unfortunately, all classical methods to distribute a secure key are fundamentally insecure because in classical physics there is nothing preventing an eavesdropper, Eve, from copying the key during its transit from Alice to Bob. On the other hand, standard asymmetric or public-key cryptography solves the key distribution problem by relying on computational assumptions such as the hardness of factoring. Therefore, such schemes do not provide information-theoretic security because they are vulnerable to future advances in hardware and algorithms, including the construction of a large-scale quantum computer.

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Section: Resultsmentioning

confidence: 99%

Practical challenges in quantum key distribution

Diamanti¹,

Lo²,

Qi³

et al. 2016

npj Quantum Inf

597

468

View full text Add to dashboard Cite

show abstract

“…Subsequent work has also been conducted on the instantaneous nonlocal computation of certain families of gates. For gates belonging to the so-called Clifford hierarchy, specialized protocols have been devised by Chakraborty and Leverrier [20]. General LOBC protocols were referred to as fast protocols by Yu et al in Ref.…”

Section: Instantaneous Nonlocal Quantum Computationmentioning

confidence: 99%

Bounds on Instantaneous Nonlocal Quantum Computation

Gonzales

Chitambar

2020

IEEE Trans. Inform. Theory

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Instantaneous nonlocal quantum computation refers to a process in which spacelike separated parties simulate a nonlocal quantum operation on their joint systems through the consumption of pre-shared entanglement. To prevent a violation of causality, this simulation succeeds up to local errors that can only be corrected after the parties communicate classically with one another. However, this communication is non-interactive, and it involves just the broadcasting of local measurement outcomes. We refer to this operational paradigm as local operations and broadcast communication (LOBC) to distinguish it from the standard local operations and (interactive) classical communication (LOCC).In this paper, we show that an arbitrary two-quibt gate can be implemented by LOBC with -error using O(log(1/ )) entangled bits (ebits). This offers an exponential improvement over the best known two-qubit protocols, whose ebit costs behave as O(1/ ). We also consider the family of binary controlled gates on dimensions dA ⊗ dB. We find that any hermitian gate of this form can be implemented by LOBC using a single shared ebit. In sharp contrast, a lower bound of log dB ebits is shown in the case of generic (i.e. non-hermitian) gates from this family, even when dA = 2. This demonstrates an unbounded entanglement cost between LOCC and LOBC gate implementation. Furthermore, whereas previous lower bounds on the entanglement cost for instantaneous nonlocal computation restrict the minimum dimension of the needed entanglement, we bound its entanglement entropy. To our knowledge this is the first such lower bound of its kind.A.G. is with the

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“…Our aim is to extend this procedure to a generic null surface which, of course, will not be a Killing horizon. We shall consider a general null surface and describe it in terms of some suitable null coordinates, called the Gaussian null coordinates (see e.g., [35,36]), defined locally in the vicinity of the surface, and use the spacetime geometry near that surface. Such surfaces, as we shall see below, are much more general than the Killing horizons.…”

Section: The Formalismmentioning

confidence: 99%

“…The most general geometry in the local neighborhood of a null surface can be described using the Gaussian Null Coordinates (see e.g., Ref. [35,36] and references therein), in which the metric takes the form:…”

Section: The Geometrymentioning

confidence: 99%

Entropy of a generic null surface from its associated Virasoro algebra

2016

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Null surfaces act as one-way membranes, blocking information from those observers who do not cross them (e.g., in the black hole and the Rindler spacetimes) and these observers associate an entropy (and temperature) with the null surface. The black hole entropy can be computed from the central charge of an appropriately defined, local, Virasoro algebra on the horizon. We show that one can extend these ideas to a general class of null surfaces, all of which possess a Virasoro algebra and a central charge, leading to an entropy density (i.e., per unit area) which is just $(1/4)$. All the previously known results of associating entropy with horizons arise as special cases of this very general property of null surfaces demonstrated here and we believe this work represents the derivation of the entropy-area law in the most general context. The implications are discussed.Comment: v2, 7pp; added references, discussions and clarifications; improved presentation; published in PL

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Practical position-based quantum cryptography

Cited by 22 publications

References 31 publications

Practical challenges in quantum key distribution

Practical challenges in quantum key distribution

Bounds on Instantaneous Nonlocal Quantum Computation

Entropy of a generic null surface from its associated Virasoro algebra

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