Efficient Simulation of Random States and Random Unitaries

Alagic, Gorjan; Majenz, Christian; Russell, Alexander

doi:10.1007/978-3-030-45727-3_26

Cited by 11 publications

(5 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently Alagic, Majenz and Russell [AMR19] proposed the notion of random state simulators. Simulators are stateful, and their local state grows with the number of copies t, however, there is no a-priori bound on the number of copies that the simulator can produce, and the guarantee is information-theoretic rather than computational.…”

Section: Our Resultsmentioning

confidence: 99%

Scalable Pseudorandom Quantum States

Brakerski¹,

Shmueli²

2020

Preprint

View full text Add to dashboard Cite

Efficiently sampling a quantum state that is hard to distinguish from a truly random quantum state is an elementary task in quantum information theory that has both computational and physical uses. This is often referred to as pseudorandom (quantum) state generator, or PRS generator for short.In existing constructions of PRS generators, security scales with the number of qubits in the states, i.e. the (statistical) security parameter for an n-qubit PRS is roughly n. Perhaps counter-intuitively, n-qubit PRS are not known to imply k-qubit PRS even for k < n. Therefore the question of scalability for PRS was thus far open: is it possible to construct n-qubit PRS generators with security parameter λ for all n, λ. Indeed, we believe that PRS with tiny (even constant) n and large λ can be quite useful.We resolve the problem in this work, showing that any quantum-secure one-way function implies scalable PRS. We follow the paradigm of first showing a statistically secure construction when given oracle access to a random function, and then replacing the random function with a quantum-secure (classical) pseudorandom function to achieve computational security. However, our methods deviate significantly from prior works since scalable pseudorandom states require randomizing the amplitudes of the quantum state, and not just the phase as in all prior works. We show how to achieve this using Gaussian sampling.

show abstract

Section: Our Resultsmentioning

confidence: 99%

Scalable Pseudorandom Quantum States

Brakerski¹,

Shmueli²

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…This in turn implies that the encoding unitary operation E is a haar random unitary [25]. We note that efficient simulation of E exists as proposed in [48].…”

Section: Protocol Descriptionmentioning

confidence: 99%

Client-Server Identification Protocols with Quantum PUF

Doosti,

Kumar,

Delavar

et al. 2020

Preprint

View full text Add to dashboard Cite

Recently, major progress has been made towards the realisation of the quantum internet to enable a broad range of applications that would be out of reach for classical internet. Most of these applications such as delegated quantum computation require running a secure identification protocol between a low-resource and a high-resource party to provide secure communication. Physical Unclonable Functions (PUFs) have been shown as resource-efficient hardware solutions for providing secure identification schemes in both classical and quantum settings. In this work, we propose two identification protocols based on quantum PUFs (qPUFs) as defined by Arapinis et al. In the first protocol, the low-resource party wishes to prove its identity to the high-resource party and in the second protocol, it is vice versa. Unlike existing identification protocols based on Quantum Read-out PUFs which rely on the security against a specific family of attacks, our protocols provide provable exponential security against any Quantum Polynomial-Time (QPT) adversary with resource-efficient parties. We provide a comprehensive comparison between the two proposed protocols in terms of resources such as quantum memory and computing ability required in both parties as well as the communication overhead between them. A stand-out feature of our second protocol is secure identification of a high-resource party by running a purely classical verification algorithm. This is achieved by delegating quantum operations to the high-resource party and utilising the resulting classical outcomes for identification.

show abstract

“…The columns and rows of Haar random unitaries are Haar random unit vectors and have also found many applications in quantum information theory, e.g. for constructing quantum money schemes [JLS18;AMR19]. However Haar random unitaries are infeasible to even approximate, the randomness and number of gates necessary to sample and implement them being exponential in the number of qubits they act on.…”

Section: Introductionmentioning

confidence: 99%

“…In[Kan15], the existence of exact designs is proven in a much more general context, see[AMR19, Corollary 2] for a straightforward application to the unitary case.Accepted in Quantum 2020-08-24, click title to verify. Published under CC-BY 4.0.…”

mentioning

confidence: 99%

Weak approximate unitary designs and applications to quantum encryption

Lancien

Majenz

2020

Quantum

Self Cite

View full text Add to dashboard Cite

Unitary t-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary t-designs. Building on results by Aubrun (Comm. Math. Phys. 2009), we prove that sampling dtpoly(t,log⁡d,1/ϵ) unitaries from an exact t-design provides with positive probability an ϵ-approximate t-design, if the error is measured in one-to-one norm. As an application, we give a randomized construction of a quantum encryption scheme that has roughly the same key size and security as the quantum one-time pad, but possesses the additional property of being non-malleable against adversaries without quantum side information.

show abstract

Efficient Simulation of Random States and Random Unitaries

Cited by 11 publications

References 23 publications

Scalable Pseudorandom Quantum States

Scalable Pseudorandom Quantum States

Client-Server Identification Protocols with Quantum PUF

Weak approximate unitary designs and applications to quantum encryption

Contact Info

Product

Resources

About