Related papers: Quantum Hypothesis Testing with Group Structure
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al.,…
A quantum generalized divergence by definition satisfies the data-processing inequality; as such, the relative decrease in such a divergence under the action of a quantum channel is at most one. This relative decrease is formally known as…
Recently, the projective robustness of quantum states has been introduced in [arXiv:2109.04481(2021)]. It shows that the projective robustness is a useful resource monotone and can comprehensively characterize capabilities and limitations…
We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…
We consider a novel group testing procedure, termed semi-quantitative group testing, motivated by a class of problems arising in genome sequence processing. Semi-quantitative group testing (SQGT) is a non-binary pooling scheme that may be…
With increasing commercial availability of quantum information processing devices the need for testing them efficiently for their specified functionality will arise. Complete quantum channel characterization is out of the question for…
A new proof of the direct part of the quantum channel coding theorem is shown based on a standpoint of quantum hypothesis testing. A packing procedure of mutually noncommutative operators is carried out to derive an upper bound on the error…
We present an alternative framework for quantifying the coherence of quantum channels, which contains three conditions: the faithfulness, nonincreasing under sets of all the incoherent superchannels and the additivity. Based on the…
A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory.…
We describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and…
As research on building scalable quantum computers advances, it is important to be able to certify their correctness. Due to the exponential hardness of classically simulating quantum computation, straight-forward verification through…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
Hoeffding's formulation and solution to the universal hypothesis testing (UHT) problem had a profound impact on many subsequent works dealing with asymmetric hypotheses. In this work, we introduce a quantum universal hypothesis testing…
We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum…
We introduce a protocol addressing the conformance test problem, which consists in determining whether a process under test conforms to a reference one. We consider a process to be characterized by the set of end-product it produces, which…
We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…
In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…
Certifying high-dimensional quantum channels is essential for ensuring the reliability of quantum communication protocols. Existing certification schemes often rely on fully trusted internal devices, which is difficult to achieve in…
A modified Beltrametti-Cassinelli-Lahti model of measurement apparatus that satisfies both the probability reproducibility condition and the objectification requirement is constructed. Only measurements on microsystems are considered. The…