Quantum key distribution (QKD) is the most explored application of quantum information theory. A central problem in entanglement-based QKD (EB-QKD), is whether every entangled state can be used to extract a key. We observe that entanglement is not sufficient for standard practical EB-QKD protocols where the input choices are announced by the parties that want to share a secure key, such as E91 or entanglement-based BB84 type protocols, when even an arbitrarily small amount of leakage of classical side information occurs. We do this by identifying a class of two-qubit isotropic states that are entangled but cannot be used to distil the key under such protocols for any possible measurement by the parties. Counter-intuitively, this gap persists even when the leakage occurs from the "junk" rounds of the protocol, i.e, rounds that cannot be used to generate any key. We then extend this result to arbitrary dimensions and parties by identifying a class of isotropic states that are not useful to extract a secure key under such protocols, even if they are entangled. Finally, we demonstrate that our approach provides a tool to upper-bound the scalability of repeater-based QKD architectures in a protocol-independent manner. Interestingly, we find that allowing for even a tiny noise in the preparation drastically reduces the scalability of the QKD network.
Quantum key distribution (QKD) is the most explored application of quantum information theory. A central problem in entanglement-based QKD (EB-QKD), is whether every entangled state can be used to extract a key. We observe that entanglement is not sufficient for standard practical EB-QKD protocols where the input choices are announced by the parties that want to share a secure key, such as E91 or entanglement-based BB84 type protocols, when even an arbitrarily small amount of leakage of classical side information occurs. We do this by identifying a class of two-qubit isotropic states that are entangled but cannot be used to distil the key under such protocols for any possible measurement by the parties. Counter-intuitively, this gap persists even when the leakage occurs from the "junk" rounds of the protocol, i.e, rounds that cannot be used to generate any key. We then extend this result to arbitrary dimensions and parties by identifying a class of isotropic states that are not useful to extract a secure key under such protocols, even if they are entangled. Finally, we demonstrate that our approach provides a tool to upper-bound the scalability of repeater-based QKD architectures in a protocol-independent manner. Interestingly, we find that allowing for even a tiny noise in the preparation drastically reduces the scalability of the QKD network.
Every quantum key distribution (QKD) protocol must limit the information available outside the users' laboratories. In device-independent QKD this is essentially the only assumption made on the devices. In a prepare-and-measure setting it cannot be imposed strictly, since the sender's device must emit a signal that depends on her private input. The natural replacement, and a minimal one, is a leakage bound: a bound on how much information about the input leaves the sender's laboratory, through the intended signal or through any side channel. We ask how far this unavoidable requirement can replace a detailed model of the source. We show that this single bound, quantified by the probability of guessing the input from everything the source emits, suffices to prove security against collective attacks. In our analysis, nothing is assumed about the precise form of the emitted states, their dimension, energy or purity, nor about the receiver's measurement device, beyond the standard requirement that it does not leak Bob's data. The standard B92 and BB84 protocols do not certify any key under this minimal leakage bound assumption. But closely related protocols can and, in the ideal limit, achieve one secret bit per key round. For noisy implementations, we compute key rates using semidefinite programming relaxations. Our best protocols tolerate visibilities down to 0.84, corresponding to an 8% quantum bit error rate, compared with the 11% threshold of standard device-dependent BB84.
Quantum key distribution (QKD) is a provably secure way for two distant parties to establish a common secret key, which then can be used in a classical cryptographic scheme. Using quantum entanglement, one can reduce the necessary assumptions that the parties have to make about their devices, giving rise to device-independent QKD (DIQKD). However, in all existing protocols to date the parties need to have an initial (at least partially) random seed as a resource. In this work, we show that this requirement can be dropped. Using recent advances in the fields of randomness amplification and randomness expansion, we demonstrate that it is sufficient for the message the parties want to communicate to be (partially) unknown to the adversaries---an assumption without which any type of cryptography would be pointless to begin with. One party can use her secret message to locally generate a secret sequence of bits, which can then be openly used by herself and the other party in a DIQKD protocol. Hence our work reduces the requirements needed to perform secure DIQKD and establish safe communication.
Conventional Quantum Key Distribution (QKD) requires the transmission of qubits proportional to or exceeding the length of the key, as protocols such as BB84 transmit more qubits than the final key size due to basis sifting and privacy amplification. Since quantum networks are still in their infancy and have limited capacity, this overhead puts significant pressure on network resources. To address this issue, we propose a Multi-Qubit Greenberger--Horne--Zeilinger (GHZ) State-based QKD scheme that reduces the number of qubits transmitted over the quantum channel. The proposed method transmits one GHZ qubit between endpoints and reuses the resulting entanglement to convey multiple classical key bits with the help of Quantum Non-Demolition (QND) measurements. Under the stated assumptions on authenticated classical communication, local reset verification, and bounded-error QND discrimination, one can transfer L classical bits by generating an (L+1)-qubit GHZ state and transferring one qubit to the remote party. We verify correctness using the NetSquid quantum network simulator: the protocol achieves 100\% raw-key fidelity for keys of length up to 12 bits under both ideal conditions and depolarizing noise up to p = 0.005 per round. We further show that the proposed QKD algorithm can be extended to multi-party QKD and server-client deployment. The proposed scheme offers a transmitted-qubit-efficient, noise-tolerant alternative for bandwidth-limited quantum networks.
Quantum cryptography is anticipated to drive substantial advancements in cybersecurity. The impending arrival of quantum cryptography compromises current encryption methods, possibly compromising the effectiveness of traditional key management-based security protocols. One fundamental Quantum Key Distribution (QKD) protocol, BB84, encounters challenges when operating with fewer Quantum bits (Qubits) and bases that only support up to 8 Qubits. This limitation weakens the system’s security, making brute force, intercept, and resend attacks less challenging. Consequently, this study proposes a method to enhance the security of the BB84 protocol, to reduce susceptibility to attacks and eavesdropping. The improved BB84 protocol utilizes 9, 12, and 16 quantum bits along with two, and three bases to significantly bolster security. This allows authorized parties to eliminate the use of compromised keys. Additionally, the study implements the E91 QKD protocol utilizing the Entanglement Pair Generation (EPR) method to produce secure keys. While the existing E91 protocol ensures security through Bell’s theorem and Bell’s inequality, it overlooks the impact of noise, leading to inaccuracies in eavesdropper detection. To address this, the study introduces an additional security measure. Whenever an eavesdropper attempts to measure the quantum state, the proposed E91 protocol collapses its state from$\vert 10\rangle to\vert 11\rangle ,settingthefirstQubitto\vert 1\rangle andtheotherQubitto\vert 0\rangle $, thus providing the eavesdropper with incorrect information, accompanied by a phase angle of$15\pi $/8. This leads to a misconception, preventing eavesdroppers from obtaining useful details about transferred quantum states. Additionally, considering that the proposed E91 protocol relies on entangled particles and utilizes double Qubit gates, which are inherently noisier than single Qubit gates and more susceptible to quantum decoherence, this study employs error mitigation techniques during the final measurement to predict outcomes more efficiently.
We investigate the resilience to noise of single-qubit quantum key distribution (QKD) protocols in the scenario of security against independent eavesdropping attacks and key distillation based on one-way classical communication. To this end, we introduce a noise-based metric that quantifies the efficiency of QKD protocols. Within this framework, we analyze the maximal noise levels that allow Alice and Bob to asymptotically establish a secure secret key. Using this assumption, we compare the noise tolerance of general single-qubit QKD protocols, in particular the BB84, B92, E91, and six-state protocols. Our main result determines the noise level threshold for QKD allowing one to distill an asymptotically secure secret key. Additionally, we demonstrate that the six-state protocol achieves the greatest resistance to noise while simultaneously yielding a higher post-selection efficiency than the other analyzed single-qubit protocols, confirming its robustness within the considered security model. Finally, we perform an analysis of the proposed noise-based metric and the conventional quantum bit error rate (QBER) metric.
Quantum key distribution (QKD) allows two spatially separated parties to securely generate a cryptographic key. The first QKD protocol, published by C. H. Bennett and G. Brassard in 1984 (BB84), describes how this is achieved by transmitting individual qubits and exchanging classical authenticated information. Any attempt to eavesdrop on the protocol introduces errors detectable by the legitimate parties. This Licentiate Thesis studies the recently introduced EEQKD protocol which builds on BB84. In EEQKD, the qubits sent individually in BB84 are entangled and thus not directly available to an eavesdropper who is, in this protocol, provided only one-by-one access to the transmission. The maximal information an eavesdropper can gain using a straightforward intercept-resend (IR) attack, is obtained for a given error rate. The secure key generation rate of EEQKD is estimated in practical scenarios including qubit loss and quantum channel noise. In addition, an exquisite vulnerability is exposed: For a particular setting of qubit entanglement, paradoxically proving most useful in the face of an IR attack, EEQKD reduces to BB84. Part of this research has been published in O. Ahonen et al., Physical Review A 78, 032314 (2008).