Related papers: Lower Bounds for Unitary Property Testing with Pro…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
In order to assess whether quantum resources can provide an advantage over classical computation, it is necessary to characterize and benchmark the non-classical properties of quantum algorithms in a practical manner. In this paper, we show…
Quantum metric learning enhances machine learning by mapping classical data to a quantum Hilbert space with maximal separation between classes. However, on current NISQ hardware, this mapping process itself is prone to errors and could be…
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
The detection loophole problem arises when quantum devices fail to provide an output for some of the experimental runs. These failures allow for the possibility of a local hidden-variable description of the resulting statistics; even if the…
In this work we are interested the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given $n$ copies of an unknown mixed quantum state $\varrho$ on…
QMA (Quantum Merlin Arthur) is the class of problems which, though potentially hard to solve, have a quantum solution which can be verified efficiently using a quantum computer. It thus forms a natural quantum version of the classical…
The recent development of general quantum resource theories has given a sound basis for the quantification of useful quantum effects. Nevertheless, the evaluation of a resource measure can be highly non-trivial, involving an optimisation…
In this paper we consider a quantum computational variant of nondeterminism based on the notion of a quantum proof, which is a quantum state that plays a role similar to a certificate in an NP-type proof. Specifically, we consider quantum…
The polynomial method and the adversary method are the two main techniques to prove lower bounds on quantum query complexity, and they have so far been considered as unrelated approaches. Here, we show an explicit reduction from the…
We define a general formulation of quantum PCPs, which captures adaptivity and multiple unentangled provers, and give a detailed construction of the quantum reduction to a local Hamiltonian with a constant promise gap. The reduction turns…
Estimating the unitarity of an unknown quantum channel $\mathcal{E}$ provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be…
We study the concurrence of four-qubit quantum states and provide analytical lower bounds of concurrence in terms of the monogamy inequality of concurrence for qubit systems. It is shown that these lower bounds are able to improve the…
We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…
A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device, with comparable time and memory resources, is performing a computation that is impossible for classical computers.…
An $\epsilon$-test for any non-trivial property (one for which there are both satisfying inputs and inputs of large distance from the property) should use a number of queries that is at least inversely proportional in $\epsilon$. However,…
Quantum communication devices, such as quantum repeaters, quantum memories, or quantum channels, are unavoidably exposed to imperfections. However, the presence of imperfections can be tolerated, as long as we can verify such devices retain…
Quantum query complexity is a fundamental model for analyzing the computational power of quantum algorithms. It has played a key role in characterizing quantum speedups, from early breakthroughs such as Grover's and Simon's algorithms to…
The (negative-weighted) quantum adversary bound is a tight characterisation of the quantum query complexity for any partial function. We analyse the extent to which this bound can be generalised. Ambainis et al. [arXiv:1012.2112] and Lee et…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…