Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous computations. A common pattern underpinning algorithms can be identified when computation is viewed as multi-particle interference. We this approach review (and improve) some existing show how they are related instances phase estimation. provide an explicit algorithm for generating any prescribed with arbitrary precision.

Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on communication channel. Although become if supplemented by classical privacy-amplification techniques, resulting difficult to analyze and have not been proved secure. We introduce concept privacy amplification a scheme incorporating it which is provably secure over noisy The uses an ``entanglement purification'' procedure which, because requires only few controlled-not single-qubit operations,...

The optimal precision of frequency measurements in the presence decoherence is discussed. We analyze different preparations $n$ two-level systems as well measurement procedures. show that standard Ramsey spectroscopy on uncorrelated atoms and maximally entangled states provide same resolution. best resolution achieved using partially with a high degree symmetry.

We analyse the use of entangled states to perform quantum computations non locally among distant nodes in a network. The complexity associated with generation multiparticle is quantified terms concept global cost. This parameter allows us compare physical resources different schemes. show that for ideal channels and sufficiently large number nodes, maximally advantageous over uncorrelated ones. For noisy channels, one has entanglement purification procedures order create high fidelity. under...

We establish the best possible approximation to a perfect quantum cloning machine that produces two clones out of single input. analyze both universal and state-dependent cloners. The maximal fidelity is shown be 5/6 for It can achieved either by special unitary evolution or teleportation scheme. construct optimal cloners operating on any prescribed nonorthogonal states discuss their fidelities use auxiliary physical resources in process cloning. permit us derive an upper bound capacity...

We study optimal eavesdropping in quantum cryptography with three-dimensional systems, and show that this scheme is more secure against symmetric attacks than protocols using two-dimensional states. generalize the according transformation to arbitrary dimensions, discuss connection cloning.

We consider an $\stackrel{\ensuremath{\rightarrow}}{N}M$ quantum cloning transformation acting on pure two-level states lying the equator of Bloch sphere. An upper bound for its fidelity is presented, by establishing a connection between optimal phase-covariant and phase estimation. give explicit form that achieves case $N=1,$ $M=2,$ find link this eavesdropping in cryptographic scheme BB84.

We derive a tight upper bound for the fidelity of universal N to M qubit cloner, valid any \geq N, where output cloner is required be supported on symmetric subspace. Our proof based concatenation two cloners and connection between quantum cloning state estimation. generalise operation mixed and/or entangled input qubits described by density matrix subspace constituent qubits. also extend validity optimal estimation methods inputs this kind.

We introduce a general method for the experimental detection of entanglement by performing only few local measurements, assuming some prior knowledge density matrix. The idea is based on minimal decomposition witness operators into pseudomixture operators. discuss an experimentally relevant case two qubits, and show example how bound can be detected with measurements.

We show how procedures which can correct phase and amplitude errors are in themselves sufficient to due quantum entanglement, generalizing earlier results. specify general criteria for error correction, introduce versions of the Hamming Gilbert-Varshamov bounds, comment on practical implementations codes.

We show that entanglement is a useful resource to enhance the mutual information of depolarizing channel when noise on consecutive uses has some partial correlations. obtain threshold in degree memory above which higher amount classical transmitted with entangled signals.

We propose an alternative method for detecting the density matrix of a radiation field via optical homodyne tomography. The needs no assumption on state, and is recovered directly from averages data. tomographic reconstruction very fast provides reliable statistics line with detection. As test we present numericla results set computer-simulated experiments, corresponding to different quantum states source. Then given experimental data provided by Smithey etal. [Phys. Rev. Lett. 70, 1244 (1993)].

We propose a method for the stabilization of quantum computations (including state storage). The is based on operation projection into $\cal SYM$, symmetric subspace full space R redundant copies computer. describe an efficient algorithm and network effecting SYM$--projection discuss stabilizing effect proposed in context unitary errors generated by hardware imprecision, nonunitary arising from external environmental interaction. Finally, limitations are discussed.

We report on the first experimental realization of an entanglement witness, a method to detect with few local measurements. The present demonstration has been performed polarized photons in Werner states, well-known family mixed states that can be either separable or nonseparable. are generated by novel high brilliance source bipartite entangled which state mixedness easily adjusted.

We introduce a class of multiqubit quantum states which generalizes graph states. These correspond to an underlying mathematical hypergraph, i.e. where edges connecting more than two vertices are considered. derive generalized stabilizer formalism describe this the notion k-uniformity and show that gives rise classes inequivalent under action local Pauli group. Finally we disclose one-to-one correspondence with employed in algorithms, such as Deutsch–Jozsa's Grover's.

The laws of quantum mechanics allow for the distribution a secret random key between two parties. Here we analyse security protocol establishing common N parties (i.e. conference key), using resource states with genuine N-partite entanglement. We compare this to via bipartite entanglement, regarding required resources, achievable rates and threshold qubit error rates. Furthermore discuss networks bottlenecks which our multipartite entanglement-based can benefit from network coding, while...

Abstract Artificial neural networks are the heart of machine learning algorithms and artificial intelligence. Historically, simplest implementation an neuron traces back to classical Rosenblatt’s “perceptron”, but its long term practical applications may be hindered by fast scaling up computational complexity, especially relevant for training multilayered perceptron networks. Here we introduce a quantum information-based algorithm implementing computer version binary-valued perceptron, which...

Abstract Artificial intelligence algorithms largely build on multi-layered neural networks. Coping with their increasing complexity and memory requirements calls for a paradigmatic change in the way these powerful are run. Quantum computing promises to solve certain tasks much more efficiently than any classical machine, actual quantum processors now becoming available through cloud access perform experiments testing also outside of research labs. Here we show practice an experimental...

We introduce the notion of distributed quantum dense coding, i.e., generalization coding to more than one sender and receiver. show that global operations (as compared local operations) senders do not increase information transfer capacity, in case a single For two receivers, using classical communication, nontrivial upper bound for capacity is derived. propose general classification scheme states according their usefulness coding. In bipartite (for any dimensions), entanglement useful this task.

Abstract In this paper we address the problem of detection entanglement using only few local measurements when some knowledge about state is given. The idea based on an optimized decomposition witness operators into operators. We discuss two possible ways optimizing decomposition. present several analytical results and estimates for strategies NPT states 2 × N M systems, entangled in 3 qubit bound 4 systems.

We investigate the entanglement features of quantum states employed in algorithms. In particular, we analyze multipartite properties Deutsch-Jozsa, Grover, and Simon Our results show that for these algorithms most instances involve entanglement.

Entanglement-assisted quantum communication employs preshared entanglement between sender and receiver as a resource. We apply the same framework to metrology, introducing shared probe ancilla in preparation stage allowing entangling operations at measurement stage, i.e., using some entangled ancillary system that does not interact with be sampled. This is known useless noiseless case, but was recently shown useful presence of noise [R. Demkowicz-Dobrzanski L. Maccone, Phys. Rev. Lett. 113,...

Abstract Variational quantum machine learning algorithms have become the focus of recent research on how to utilize near-term devices for tasks. They are considered suitable this as circuits that run can be tailored device, and a big part computation is delegated classical optimizer. It has also been hypothesized they may more robust hardware noise than conventional due their hybrid nature. However, effect training models under influence hardware-induced not yet extensively studied. In work,...

We introduce a new decomposition of the multiqubit states form $\rho^{\otimes N}$ and employ it to construct optimal single qubit purification procedure. The same allows us study quantum cloning state estimation mixed states.