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Quantum Information and Computation

State-independent quantum key distribution with two-way classical communication

Radha Pyari Sandhir

Published Dec 1, 2019• 1 citation
Publisher

Abstract

A quantum key distribution protocol is proposed that is a variation of BB84 that provides raw key generation from correlations that violate a Bell-type inequality for single qubit systems and not entangled pairs. Additionally, it 1) is state-independent, 2) involves two-way classical communication, and 3) does not require basis matching between the two parties. The Brukner-Taylor-Cheung-Vedral (BTCV) time-like form of the Bell-CHSH inequality by Bruk and by Tay is employed as an eavesdropping check; sequential measurements lead to an inequality identical in form to the Bell-CHSH inequality, which relies only on the measurements performed with no regard for the qubit states. We show that this form manifests naturally from the non-commutativity of observables.

DOI
10.26421/qic19.15-16-2

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A quantum key distribution protocol is proposed that is a variation of BB84 that provides raw key generation from correlations that violate a Bell-type inequality for single qubit systems and not entangled pairs. Additionally, it 1) is state-independent, 2) involves two-way classical communication, and 3) does not require basis matching between the two parties. The Brukner-Taylor-Cheung-Vedral (BTCV) time-like form of the Bell-CHSH inequality by Bruk and by Tay is employed as an eavesdropping check; sequential measurements lead to an inequality identical in form to the Bell-CHSH inequality, which relies only on the measurements performed with no regard for the qubit states. We show that this form manifests naturally from the non-commutativity of observables.
The traditional security system, which depends on asymmetric and symmetric key exchange protocol, is now under threat due to recent developments in quantum computing. In order to generate the safe key without storing the qubit by the sender or recipient trustworthy parties, a unique Quantum Key Distribution (QKD) protocol was presented. Four random classical bits coupled to generate a pair of bell states in any of the places {(1,2,3,4), (1,3,2,4) and (1,4,2,3)}. "n/2" groups were used to generate the raw key while the remaining groups were used to check for Eve. The flying bell states scatter into four separate bell states as a result of Eve's involvement in choosing the incorrect measurement basis, which causes entanglement swapping and its identification during communication. The sender will alter the key in accordance with the receiver's position preference because, in traditional communication, key receiving parties must announce the position information. Under the intercept-measure-resend attack, the trade-off between the key generating rate and disturbance is computed and security is examined. Circuit simulation is demonstrated graphically in IBM Quantum Lab and the proposed protocol is implemented.
The Ekert quantum key distribution protocol [1] uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The 3DEB protocol [2] uses instead pairs of entangled qutrits to achieve better noise resistance than the Ekert protocol. It performs checks based on a Bell inequality for qutrits named CHSH-3 and found in [3, 4]. In this paper, we present a new protocol, which also uses pairs of entangled qutrits, but gaining advantage of a Bell inequality which achieves better noise resistance than the one used in 3DEB. The latter inequality is called here hCHSH-3 and was discovered in [5]. For each party, the hCHSH-3 inequality involves four observables already used in CHSH-3 but also two products of observables which do not commute. We explain how the parties can measure the observables corresponding to these products and thus are able to check the violation of hCHSH-3. In the presence of noise, this violation guarantees the security against a local Trojan horse attack. We also designed a version of our protocol which is secure against individual attacks.
Recently, the notion of full network nonlocality has emerged as some truly quantum network phenomena that cannot be realized in traditional Bell experiments. Present work manifests the utility of such form of truly network non-classicality in designing a four partite network-based entanglement assisted quantum key distribution protocol. Precisely, validity of the QKD protocol relies upon full network nonlocality detection via violation of some suitable trilocal inequality. Based on the quantum bit error rate and violation of trilocal inequality, arbitrary two qubit entangled states are characterized in accordance with their utility in successfully executing the protocol. The protocol is further analyzed from a restricted Eve-aware perspective by quantifying the Eve`s partial side information and discussing its implications for the corresponding Devetak-Winter 111-way secret key rate. Also, considering Eve's control over the trusted parties' measurement devices, an illustration of the protocol`s resistance to detection loophole is provided. Due to connected structure of entangled sources, any genuine form of network nonlocality may offer advantage over standard Bell nonlocality for designing secure key distribution protocols. To establish such an intuition as a fact, another QKD protocol, relying only upon Bell-CHSH violation, is designed. The former offers more stricter validity checks compared to the latter. Importantly, while the quantum bit error rate can be less than 14.6%14.6\%14.6% exploiting Bell-CHSH nonlocality, it can be reduced below 13.7%13.7\%13.7% by exploiting full network nonlocality.
Quantum Key Distribution is a quantum communication technique in which random numbers are encoded on quantum systems, usually photons, and sent from one party, Alice, to another, Bob. Using the data sent via the quantum signals, supplemented by classical communication, it is possible for Alice and Bob to share an unconditionally secure secret key. This is not possible if only classical signals are sent. While this last statement is a long standing result from quantum information theory it turns out only to be true in a non-relativistic setting. If relativistic quantum field theory is considered we show it is possible to distribute an unconditionally secure secret key without sending a quantum signal, instead harnessing the intrinsic entanglement between different regions of space–time. The protocol is practical in free space given horizon technology and might be testable in principle in the near term using microwave technology.