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Quantum One-Way State Generators Imply Quantum Commitments


Core Concepts
Quantum one-way state generators (OWSGs) with O(n/log(n)) copies are equivalent to quantum commitments and to polytime-copy OWSGs. The weakest OWSGs from which quantum commitments can be obtained are those with O(n/log(n)) copies.
Abstract
The content discusses the relationship between quantum one-way state generators (OWSGs) and quantum commitments. Key highlights: OWSGs are quantum analogues of classical one-way functions, where the output is a quantum state rather than a classical string. It is shown that O(n/log(n))-copy OWSGs are equivalent to polytime-copy OWSGs and to quantum commitments. This establishes that O(n/log(n))-copy OWSGs are the weakest OWSGs from which quantum commitments can be obtained. The proof follows a construction similar to the classical case of obtaining pseudorandom generators from one-way functions, but with crucial modifications to handle the quantum setting. The construction involves flattening the quantum state, using properties of Rényi entropies, and applying quantum extractors to amplify the statistical difference between the commitment states. The reverse direction, showing that quantum commitments imply polytime-copy OWSGs, is also established. These results connect quantum commitments to the fundamental primitive of OWSGs, and have implications for secure multi-party computation in the quantum setting.
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Key Insights Distilled From

by Rishabh Batr... at arxiv.org 04-05-2024

https://arxiv.org/pdf/2404.03220.pdf
Commitments are equivalent to one-way state generators

Deeper Inquiries

What are the potential applications of the equivalence between quantum one-way state generators and quantum commitments beyond secure multi-party computation

The equivalence between quantum one-way state generators and quantum commitments has significant implications beyond secure multi-party computation. One potential application is in quantum key distribution protocols, where the security of the key exchange relies on the commitment scheme. By leveraging the equivalence, we can enhance the security and efficiency of quantum key distribution systems. Additionally, this equivalence can be utilized in quantum digital signatures, ensuring the integrity and authenticity of digital messages in a quantum communication network. Moreover, the equivalence can be applied in quantum coin flipping protocols, enhancing the fairness and trustworthiness of the outcomes in quantum interactions.

Can the techniques developed in this work be extended to establish equivalences between other quantum cryptographic primitives

The techniques developed in this work can be extended to establish equivalences between various other quantum cryptographic primitives. For example, the equivalence between quantum commitments and one-way state generators can be further explored in the context of quantum zero-knowledge proofs. By investigating the relationships between these primitives, we can enhance the security and efficiency of quantum cryptographic protocols such as quantum secure multiparty computation, quantum homomorphic encryption, and quantum oblivious transfer. Additionally, the insights from this work can be applied to study the connections between quantum commitments and quantum obfuscation, paving the way for advancements in quantum secure computation.

How might the insights from this work inform the design of practical quantum cryptographic protocols and systems

The insights from this work can inform the design of practical quantum cryptographic protocols and systems by providing a foundational understanding of the relationships between different cryptographic primitives. By leveraging the equivalence between quantum one-way state generators and quantum commitments, researchers and practitioners can develop more secure and efficient quantum cryptographic protocols for various applications. This understanding can lead to the development of novel quantum cryptographic schemes with enhanced security guarantees and improved performance. Additionally, the insights can guide the implementation of quantum cryptographic systems in real-world scenarios, ensuring the confidentiality, integrity, and authenticity of quantum communication channels.
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