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AIP Advances

Quantum key distribution using unknown quantum states

Dawei Guo, Wen‐Hai Zhang

Published Jun 1, 2025• 0 citations
Publisher

Abstract

This paper proposes a version of quantum key distribution (QKD) by leveraging unknown quantum states. The measurement made on the unknown quantum states is independent of them. As the number of copies of the unknown states increases, the key rate increases, and the disturbance caused by an eavesdropper also increases synchronously. If the unknown quantum states are orthogonal to each other, they cannot be completely distinguished. Our scheme is more efficient than the previous scenarios in QKD, where a set of known quantum states are leveraged. Our work offers a theoretical groundwork for constructing a highly effective QKD by exploiting unknown quantum states.

DOI
10.1063/5.0273173

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This paper proposes a version of quantum key distribution (QKD) by leveraging unknown quantum states. The measurement made on the unknown quantum states is independent of them. As the number of copies of the unknown states increases, the key rate increases, and the disturbance caused by an eavesdropper also increases synchronously. If the unknown quantum states are orthogonal to each other, they cannot be completely distinguished. Our scheme is more efficient than the previous scenarios in QKD, where a set of known quantum states are leveraged. Our work offers a theoretical groundwork for constructing a highly effective QKD by exploiting unknown quantum states.
Quantum cryptograph exploits the fundamental laws of quantum mechanics to provide a secure way to exchange private information. Such an exchange requires a common random bit sequence, called a key, to be shared secretly between the sender and the receiver. The basic idea behind quantum key distribution (QKD) has widely been understood as the property that any attempt to distinguish encoded quantum states causes a disturbance in the signal. As a result, implementation of a QKD protocol involves an estimation of the experimental parameters influenced by the eavesdropper’s intervention, which is achieved by randomly sampling the signal. If the estimation of many parameters with high precision is required, the portion of the signal that is sacrificed increases, thus decreasing the efficiency of the protocol. Here we propose a QKD protocol based on an entirely different principle. The sender encodes a bit sequence onto non-orthogonal quantum states and the receiver randomly dictates how a single bit should be calculated from the sequence. The eavesdropper, who is unable to learn the whole of the sequence, cannot guess the bit value correctly. An achievable rate of secure key distribution is calculated by considering complementary choices between quantum measurements of two conjugate observables. We found that a practical implementation using a laser pulse train achieves a key rate comparable to a decoy-state QKD protocol, an often-used technique for lasers. It also has a better tolerance of bit errors and of finite-sized-key effects. We anticipate that this finding will give new insight into how the probabilistic nature of quantum mechanics can be related to secure communication, and will facilitate the simple and efficient use of conventional lasers for QKD.
The general conditions for the orthogonal product states of the multistate systems to be used in quantum key distribution (QKD) are proposed, and a novel QKD scheme with orthogonal product states in the $3\ifmmode\times\else\texttimes\fi{}3$ Hilbert space is presented. We show that this protocol has many distinct features such as great capacity and high efficiency. The generalization to $n\ifmmode\times\else\texttimes\fi{}n$ systems is also discussed and an asymptotic limit of 1/2 for the eavesdropper's success probability is obtained.
A quantum key distribution (QKD) protocol based on constructed nonorthogonal states is proposed. By transmitting the photons from Bell states in random order the sender constructs nonorthogonal states, which can prevent an eavesdropper from extracting the key information. At the destination, the receiver performs Bell measurements and then obtains secure key. Different from previous nonorthogonal-states-based QKD protocols, our protocol exhibits a new feature, that is, the users can also obtain some key bits even when they choose different "bases"! Thus it can reach a higher efficiency in theory. Besides, we present a trade-off between the information that an eavesdropper can elicit and the corresponding error rate he/she would introduce, which shows that our protocol is secure.
By carrying out measurements on entangled states, two parties can generate a secret key which is secure not only against an eavesdropper bound by the laws of quantum mechanics, but also against a hypothetical "post-quantum" eavesdroppers limited by the no-signalling principle only. We introduce a family of quantum key distribution protocols of this type, which are more efficient than previous ones, both in terms of key rate and noise resistance. Interestingly, the best protocols involve large number of measurements. We show that in the absence of noise, these protocols can yield one secret bit per entanglement bit, implying that the key rates in the no-signalling post-quantum scenario are comparable to the key rates in usual quantum key distribution.
By carrying out measurements on entangled states, two parties can generate a secret key which is secure not only against an eavesdropper bound by the laws of quantum mechanics, but also against a hypothetical 'post-quantum' eavesdroppers limited by the no-signalling principle only. We introduce a family of quantum key distribution protocols of this type, which are more efficient than previous ones, both in terms of key rate and noise resistance. Interestingly, the best protocols involve large number of measurements. We show that in the absence of noise, these protocols can yield one secret bit per entanglement bit, implying that the key rates in the no-signalling post-quantum scenario are comparable to the key rates in usual quantum key distribution.
A novel quantum key distribution protocol (QKD) based on all unselected states of a quantum sys- tem that set the alphabet with a continuous set of letters is proposed. Employing all states of the Hilbert space leads to a maximum quantum uncertainty of transmitted states, and, therefore, an eavesdropper receives the minimum amount of information. For the case of a two-dimensional Hilbert space, our protocol allows secure transmission at an error rate better than that for the BB84-protocol and is comparable with the characteristics of the best known QKD protocols. However, with increasing the dimensionality of the Hilbert space, the critical error rate for our protocol increases and, in the limit of infinite-dimensional space, the protocol becomes non- threshold.