Certified deletion is a protocol which allows two parties to share information, from Alice to Bob, in such a way that if Bob chooses to delete the information, he can prove to Alice that the deletion has taken place by providing a verification key. It is not possible for Bob to both provide this verification, and gain information about the message that was sent. This type of protocol is unique to quantum information and cannot be done with classical approaches. Here, we expand on previous work to outline a high-dimensional version of certified deletion that can be used to incorporate multiple parties. We also experimentally verify the feasibility of these protocols for the first time, demonstrating the original 2-dimensional proposal, as well as the high-dimensional scenario up to dimension 8.
Given a ciphertext, is it possible to prove the deletion of the underlying plaintext? Since classical ciphertexts can be copied, clearly such a feat is impossible using classical information alone. In stark contrast to this, we show that quantum encodings enable certified deletion. More precisely, we show that it is possible to encrypt classical data into a quantum ciphertext such that the recipient of the ciphertext can produce a classical string which proves to the originator that the recipient has relinquished any chance of recovering the plaintext should the decryption key be revealed. Our…
Academia Sinica（中央研究院）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；National Institute of Advanced Industrial Science and Technology (AIST)（产业技术综合研究所）
Broadbent and Islam (TCC '20) proposed a quantum cryptographic primitive called quantum encryption with certified deletion. In this primitive, a receiver in possession of a quantum ciphertext can generate a classical certificate that the encrypted message is deleted. Although their construction is information-theoretically secure, it is limited to the setting of one-time symmetric key encryption (SKE), where a sender and receiver have to share a common key in advance and the key can be used only once. Moreover, the sender has to generate a quantum state and send it to the receiver over a quant…
Quantum information has the property that measurement is an inherently destructive process. This feature is most apparent in the principle of complementarity, which states that mutually incompatible observables cannot be measured at the same time. Recent work by Broadbent and Islam (TCC 2020) builds on this aspect of quantum mechanics to realize a cryptographic notion called certified deletion. While this remarkable notion enables a classical verifier to be convinced that a (private-key) quantum ciphertext has been deleted by an untrusted party, it offers no additional layer of functionality. …
In known constructions of classical zero-knowledge protocols for NP, either of zero-knowledge or soundness holds only against computationally bounded adversaries. Indeed, achieving both statistical zero-knowledge and statistical soundness at the same time with classical verifier is impossible for NP unless the polynomial-time hierarchy collapses, and it is also believed to be impossible even with a quantum verifier. In this work, we introduce a novel compromise, which we call the certified everlasting zero-knowledge proof for QMA. It is a computational zero-knowledge proof for QMA, but the ver…
The Hilbert space dimension of a quantum system is the most basic quantifier of its information content. Lower bounds on the dimension can be certified in a device-independent way, based only on observed statistics. We highlight that some such "dimension witnesses" capture only the presence of systems of some dimension, which in a sense is trivial, not the capacity of performing information processing on them, which is the point of experimental efforts to control high-dimensional systems. In order to capture this aspect, we introduce the notion of irreducible dimension of a quantum behaviour. …
Metasurface quantum graphs for polarization-independent certified randomness
State Key Laboratory of Optical Quantum Materials, University of Hong Kong（光学量子材料国家重点实验室，香港大学）；Department of Electrical & Electronic Engineering, The University of Hong Kong（电子电气工程学系，香港大学）；Materials Innovation Institute for Life Sciences and Energy (MILES), HKU-SIRI, Shenzhen（生命科学与能源材料创新研究所（MILES），港大-西丽研究院，深圳）；Quantum Science Center of Guangdong-Hong Kong-Macao Great Bay Area（粤港澳大湾区量子科学中心）
High-dimensional encoding of quantum information provides a promising method of transcending current limitations in quantum communication. One of the central challenges in the pursuit of such an approach is the certification of high-dimensional entanglement. In particular, it is desirable to do so without resorting to inefficient full state tomography. Here, we show how carefully constructed measurements in two bases (one of which is not orthonormal) can be used to faithfully and efficiently certify bipartite high-dimensional states and their entanglement for any physical platform. To showcase…
Certification of quantum systems and operations is a central task in quantum information processing. Most current schemes rely on a tomography with fully characterised devices, while this may not be met in real experiments. Device characterisations can be removed with device-independent tests, it is technically challenging at the moment, though. In this letter, we investigate the problem of certifying entangled states and measurements via semi-quantum games, a type of non-local quantum games with well characterised quantum inputs, balancing practicality and device-independence. We first design…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）
Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available numerical methods, in particular those based on variational Monte Carlo simulations, become exponentially more challenging with increasing system size. Recently quantum algorithms implemented as variational models have been proposed to accelerate such simulations. The variational ansatz states are characterized by a polynomial number of parameters devised i…
Being comparable in quantum systems makes it possible for spaces with varying dimensions to attribute each other using special conversions can attribute schrodinger equation with like-hydrogen atom potential in defined dimensions to a schrodinger equation with other certified dimensions with isotropic oscillator potential. Applying special transformation provides a relationship between different dimensions of two quantum systems. The result of the quantized isotropic oscillator can be generalized to like-hydrogen atom problem in different dimensions. The connection between coordinate spaces in…
Fidelity-Based Robustness Margins for Finite-Time Quantum Control
United States Military Academy（美国军事学院）；Cardiff University（卡迪夫大学）；University of Bristol（布里斯托大学）；University of Southern California（南加州大学）；Swansea University（斯旺西大学）
