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arXiv:quant-ph/9910072

Quantum secure identification using entanglement and catalysis

Howard Barnum

Published Oct 15, 1999• 24 citations
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Abstract

I consider the use of entanglement between two parties to enable one to authenticate her identity to another over a quantum communication channel. Exploiting the phenomenon of entanglement-catalyzed transformations between pure states gives a potentially reusable entangled identification token. In analyzing this, I consider the independently interesting problem of the best possible approximation to a given pure entangled state realizable using local actions and classical communication by parties sharing a different entangled state.

DOI
10.48550/arxiv.quant-ph/9910072

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I consider the use of entanglement between two parties to enable one to authenticate her identity to another over a quantum communication channel. Exploiting the phenomenon of entanglement-catalyzed transformations between pure states gives a potentially reusable entangled identification token. In analyzing this, I consider the independently interesting problem of the best possible approximation to a given pure entangled state realizable using local actions and classical communication by parties sharing a different entangled state.
We study the mutual catalysis of entanglement transformations, which refers to the fact that each of the two entanglement transformations cannot occur with certainty by local operations and classical communication independently, but both can occur jointly if collective local operations are performed on both of the initial entangled states. We surprisingly find that mutually catalyzed transformations can be realized even in the case when the standard entanglement catalyzed transformations [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999)] are forbidden.
Many applications of the emerging quantum technologies, such as quantum teleportation and quantum key distribution, require singlets, maximally entangled states of two quantum bits. It is thus of utmost importance to develop optimal procedures for establishing singlets between remote parties. As has been shown very recently, singlets can be obtained from other quantum states by using a quantum catalyst, an entangled quantum system which is not changed in the procedure. In this work we take this idea further, investigating properties of entanglement catalysis and its role for quantum communication. For transformations between bipartite pure states, we prove the existence of a universal catalyst, which can enable all possible transformations in this setup. We demonstrate the advantage of catalysis in asymptotic settings, going beyond the typical assumption of independent and identically distributed systems. We further develop methods to estimate the number of singlets which can be established via a noisy quantum channel when assisted by entangled catalysts. For various types of quantum channels our results lead to optimal protocols, allowing to establish the maximal number of singlets with a single use of the channel.
The phenomenon of quantum entanglement is a fundamental feature of quantum mechanics which, as a counterintuitive and inherently ”quantum” phenomenon (with no classical analogue) has been the subject of much study, especially in quantum information theory. One fruitful approach to the description of entanglement has been in its operational description - that is, in the consideration of what can be achieved using entangled states under certain restrictions, typically the regime of local operations and classical communications.\n\nWe present results here related to the operational characterisation of entanglement in the resource model, in both bipartite and multipartite cases. First, we consider the conversion between pure bipartite entangled states in terms of an often-ignored resource - the classical communication cost. Using prior results for more specific conversions, we derive lower bounds on this cost (and the related quantity of the conversion inefficiency) for general bipartite pure states.\n\nWe also consider pure-state conversions of multipartite entanglement, in particular the class of protocols in which multipartite states are converted to states shared between fewer parties. We have found a previously-unconsidered variety of such conversions, in which the target state of the conversion is a state shared between a random subset of the parties. We find that when such post-selection of parties in the protocol is permitted allows for a wider variety of achievable target states; certain states which can not be reliably obtained between predetermined parties (even some where the probability of doing so is arbitrarily small) can be obtained between random parties. We consider a variety of states in which this phenomenon occurs, as well as bounds on such protocols can achieve.\n\nFinally we consider a practical use of entanglement as a resource, in an experimental implementation of a multipartite QKD protocol. This is based on the tripartite GHZ entangled state, but can be implemented using only bipartite entanglement. We adapt existing QKD results for both the bipartite and multipartite case to derive a secure key rate for this implementation, taking into account the ways in which it differs from the idealised theoretical case.
Authentication is one of the security services that assures the system’s adequate security through identification and verification. Additionally, it guarantees that the communication party is who they claim to be. In politics, the economy, banking, daily life, and other areas, quantum identity authentication is essential to guarantee the security of information in communication. The multiphoton strategy is an improved version of the single-photon approach, with higher transmission rates and longer photon travel distances via the Quantum Communication network. Despite the advantages of multiphoton, enforcing authentication on behalf of numerous participants in the quantum channel remains a problem, since existing multiphoton only considers two parties involved in secret message sharing. The issue of scalability arises here when the number of parties involved in the quantum network increases. Furthermore, an eavesdropper might hide her position among other parties and take advantage of the situation to obtain a certain information. Therefore, we require a protocol, that creates a more secure environment in term of authentication in which multiple parties may freely and openly communicate. This paper further identifies research gaps covering critical aspect on how Quantum Identity Authentication (QIA) can be realized and effectively utilized for multiphoton without entanglement based. These include suggestion of future direction to implement multiphoton in multiparty from current protocol.
We analyze approximate transformations of pure entangled quantum states by local operations and classical communication, finding explicit conversion strategies which optimize the fidelity of transformation. These results allow us to determine the most faithful teleportation strategy via an initially shared partially entangled pure state. They also show that procedures for entanglement manipulation such as entanglement catalysis [Jonathan and Plenio, Phys. Rev. Lett. 83, 3566 (1999)] are robust against perturbation of the states involved, and motivate the notion of nonlocal fidelity, which quantifies the difference in the entangled properties of two quantum states.