Fundamental limits on quantum cloning from the no-signalling principle

The no-cloning theorem is a cornerstone of quantum cryptography. Here we generalize and rederive under weaker assumptions various upper bounds on the maximum achievable fidelity of probabilistic and deterministic cloning machines. Building on ideas by Gisin [Phys.~Lett.~A, 1998], our results hold even for cloning machines that do not obey the laws of quantum mechanics, as long as remote state preparation is possible and the non-signalling principle holds. We apply our general theorem to several subsets of states that are of interest in quantum cryptography

On the feasibility of detecting quantum delocalization effects on gravitational redshift in optical clocks

We derive the predicted time dilation of delocalized atomic clocks in an optical lattice setup in the presence of a gravitational field to leading order in quantum relativistic corrections. We investigate exotic quantum states of motion whose gravitational time dilation is outside of the realm of classical general relativity, finding a regime where $^{24}\mathrm{Mg}$ optical lattice clocks currently in development would comfortably be able to detect this quantum effect (if the technical challenge of generating such states can be met). We provide a detailed experimental protocol and analyse the effects of noise on our predictions. We also show that the magnitude of our predicted quantum gravitational time dilation effect remains just out of detectable reach for the current generation of $^{87}\mathrm{Sr}$ optical lattice clocks. Our calculations agree with the predicted time dilation of classical general relativity when restricting to Gaussian states

Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption

Quantum homomorphic encryption, which allows computation by a server directly on encrypted data, is a fundamental primitive out of which more complex quantum cryptography protocols can be built. For such constructions to be possible, quantum homomorphic encryption must satisfy two privacy properties: data privacy which ensures that the input data is private from the server, and circuit privacy which ensures that the ciphertext after the computation does not reveal any additional information about the circuit used to perform it, beyond the output of the computation itself. While circuit privacy is well-studied in classical cryptography and many homomorphic encryption schemes can be equipped with it, its quantum analogue has received little attention. Here we establish a definition of circuit privacy for quantum homomorphic encryption with information-theoretic security. Furthermore, we reduce quantum oblivious transfer to quantum homomorphic encryption. By using this reduction, our work unravels fundamental trade-offs between circuit privacy, data privacy and correctness for a broad family of quantum homomorphic encryption protocols, including schemes that allow only the computation of Clifford circuits

COVID-19–Related Glomerulopathy: A Report of 2 Cases of Collapsing Focal Segmental Glomerulosclerosis

Coronavirus disease 19 (COVID-19), an infectious disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has been associated with acute kidney injury, presumably due to acute tubular injury. However, this does not explain proteinuria, sometimes severe, and hematuria often observed. We present 2 African American patients with glomerulopathy demonstrated by kidney biopsy in the setting of acute kidney injury and COVID-19 infection. Kidney biopsy specimens showed a collapsing variant of focal segmental glomerulosclerosis in addition to acute tubular injury. Both patients were homozygous for apolipoprotein L1 (APOL1). COVID-19 infection likely caused the interferon surge as a second hit causing podocyte injury leading to collapsing focal segmental glomerulosclerosis. APOL1 testing should be strongly considered in African American patients with nephrotic-range proteinuria. More data from future kidney biopsies will further elucidate the pathology of kidney injury and glomerular involvement from COVID-19 infections