The Conditional Uncertainty Principle

We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define conditional majorization and, for the case of classical memory, we provide its thorough characterization in terms of monotones, i.e., functions that preserve the partial order under conditional majorization. We demonstrate the application of this framework by deriving two types of memory-assisted uncertainty relations: (1) a monotone-based conditional uncertainty relation, (2) a universal measure-independent conditional uncertainty relation, both of which set a lower bound on the minimal uncertainty that Bob has about Alice's pair of incompatible measurements, conditioned on arbitrary measurement that Bob makes on his own system. We next compare the obtained relations with their existing entropic counterparts and find that they are at least independent.Comment: 5 pages main + 10 pages appendix. Changes since v1: new results demonstrating independence of our results from existing conditional uncertainty relations; significant revision in notation and presentation; expanded bibliograph

Long-distance quantum communication over noisy networks without long-time quantum memory

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension $D$ and transmission of quantum information in a $D+1$-dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) network, even when taking into account that encoding and decoding of a state is exposed to an error. For 3D networks we propose a simple encoding and decoding scheme based solely on syndrome measurements on 2D Kitaev topological quantum memory. Our procedure constitutes an alternative scheme of state injection that can be used for universal quantum computation on 2D Kitaev code. It is shown that the encoding scheme is equivalent to teleporting the state, from a specific node into a whole two-dimensional network, through some virtual EPR pair existing within the rest of network qubits. We present an analytic lower bound on fidelity of the encoding and decoding procedure, using as our main tool a modified metric on space-time lattice, deviating from a taxicab metric at the first and the last time slices.Comment: 15 pages, 10 figures; title modified; appendix included in main text; section IV extended; minor mistakes remove

Measurement uncertainty from no-signaling and nonlocality

One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty principle from two comprehensible assumptions: impossibility of instantaneous messaging at a distance (no-signaling), and violation of Bell inequalities (nonlocality). The uncertainty is established for a pair of observables of one of two spatially separated systems that exhibit nonlocal correlations. To this end, we introduce a gentle form of measurement which acquires partial information about one of the observables. We then bound disturbance of the remaining observables by the amount of information gained from the gentle measurement, minus a correction depending on the degree of nonlocality. The obtained quantitative expression resembles the quantum mechanical formulations, yet it is derived without the quantum formalism and complements the known qualitative effect of disturbance implied by nonlocality and no-signaling.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Spectroscopic Characterization and Biological Activity of Hesperetin Schiff Bases and Their Cu(II) Complexes

The three Schiff base ligands, derivatives of hesperetin, HHSB (N-[2,3-dihydro-5,7-dihydroxy-2-(3-hydroxy-4-methoxyphenyl)chromen-4-ylidene]isonicotinohydrazide), HIN (N-[2,3-dihydro-5,7-dihydroxy-2-(3-hydroxy-4-methoxyphenyl)chromen-4-ylidene]benzhydrazide) and HTSC (N-[2,3-dihydro-5,7-dihydroxy-2-(3-hydroxy-4-methoxyphenyl)chromen-4-ylidene]thiosemicarbazide) and their copper complexes, CuHHSB, CuHIN, and CuHTSC were designed, synthesized and analyzed in terms of their spectral characterization and the genotoxic activity. Their structures were established using several methods: elemental analysis, FT-IR, UV-Vis, EPR, and ESI-MS. Spectral data showed that in the acetate complexes the tested Schiff bases act as neutral tridentate ligand coordinating to the copper ion through two oxygen (or oxygen and sulphur) donor atoms and a nitrogen donor atom. EPR measurements indicate that in solution the complexes keep their structures with the ligands remaining bound to copper(II) in a tridentate fashion with (O–, N, Oket) or (O–, N, S) donor set. The genotoxic activity of the compounds was tested against model tumour (HeLa and Caco-2) and normal (LLC-PK1) cell lines. In HeLa cells the genotoxicity for all tested compounds was noticed, for HHSB and CuHHSB was the highest, for HTSC and CuHTSC–the lowest. Generally, Cu complexes displayed lower genotoxicity to HeLa cells than ligands. In the case of Caco-2 cell line HHSB and HTSC induced the strongest breaks to DNA. On the other side, CuHHSB and CuHTSC induced the highest DNA damage against LLC-PK1