Boson Sampling is a computational task strongly believed to be hard for classical computers, but efficiently solvable by orchestrated bosonic interference in specialised quantum computer. Current experimental schemes, however, are still insufficient convincing demonstration of the advantage over computation. A new variation this task, Scattershot Sampling, leads an exponential increase speed device, using larger number photon sources based on parametric downconversion. This achieved having...

Abstract Weak values and Kirkwood–Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory advantages metrology. We propose simple circuits to measure weak values, KD distributions, spectra of density matrices without the need for post-selection. This is achieved by measuring unitary-invariant, relational properties states, which are functions Bargmann invariants, concept that underpins our unified perspective. Our also...

Abstract The geometrical arrangement of a set quantum states can be completely characterized using relational information only. This is encoded in the pairwise state overlaps, as well Bargmann invariants higher degree written traces products density matrices. We describe how to measure suitable generalizations SWAP test. allows for complete and robust characterization projective-unitary invariant properties any pure or mixed states. As applications, we basis-independent tests linear...

We analyse nonclassical resources in interference phenomena using generalized noncontextuality inequalities and basis-independent coherence witnesses. use recently proposed that witness both within the same framework. also propose, view of previous contextual advantage results, a systematic way applying these tools to characterize provided by contextuality quantum information protocols. instantiate this methodology for task interrogation, famously introduced paradigmatic bomb-testing...

Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and metrology. In the standard formulation, state said to have "imaginarity" if associated density matrix not real-valued given, fixed basis. If instead we consider set states, it possible devise tests that guarantee some set, independently basis chosen. Here propose such basis-independent...

Gibbons et al., [Phys. Rev. A 70, 062101 (2004)] have recently defined discrete Wigner functions $W$ to represent quantum states in a Hilbert space with finite dimension. We show that such class of can be so the only pure having non-negative for all are stabilizer states, as conjectured by Galv\~ao, 71, 042302 (2005)]. also unitaries preserving non-negativity definitions form subgroup Clifford group. This means and their associated unitary dynamics classical sense admitting an efficient...

We perform a comprehensive set of experiments that characterize bosonic bunching up to 3 photons in interferometers 16 modes. Our verify two rules govern bunching. The first rule, obtained recently [1,2], predicts the average behavior probability and is known as birthday paradox. second rule new, establishes n!-factor quantum enhancement for all n bosons bunch single output mode, with respect case distinguishable bosons. Besides its fundamental importance phenomena such Bose-Einstein...

It is possible to prepare classical optical beams which cannot be characterized by a tensor product of vectors describing each their degrees freedom. Here we report the experimental creation such nonseparable, tripartite GHZ-like state path, polarization, and transverse modes laser beam. We use Mach-Zehnder interferometer with an additional mirror other elements perform measurements that violate Mermin's inequality. This demonstration analogue entanglement paves path novel applications...

Quantum coherence, nonlocality, and contextuality are key resources for quantum advantage in metrology, communication, computation. We introduce a graph-based approach to derive classicality inequalities that bound local, noncontextual, coherence-free models, offering unified description of these seemingly disparate resources. Our generalizes recently proposed basis-independent coherence witnesses, it recovers all noncontextuality the exclusivity graph approach. Moreover, violations certain...

Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] have recently defined a class of discrete Wigner functions $W$ to represent quantum states in finite Hilbert space dimension $d$. I characterize the set ${C}_{d}$ having non-negative simultaneously all definitions this class. For $d\ensuremath{\leqslant}5$ show is convex hull stabilizer states. This supports conjecture that negativity necessary for exponential speedup pure-state computation.

The purpose of this study was to compare melancholic patients rated by the CORE measure observable psychomotor disturbance with nonmelancholic and control subjects across a set biomarkers.Depressed were classified as or using measure. Both groups patients, well subjects, compared for clinical laboratory measures. Serum levels brain-derived neurotrophic factor, two markers oxidative stress (protein carbonyl content [PCC] thiobarbituric acid reactive substances [TBARS]), several immunity...

The significance of anomalous weak values has been a matter great debate in quantum foundations and information. Here, simple proof shows that the weak-value anomaly requires both negativity certain quasiprobability representation coherence pre- postselected states observable's basis.

Quantum superposition of high-dimensional states enables both computational speed-up and security in cryptographic protocols. However, the exponential complexity tomographic processes makes certification these properties a challenging task. In this work, we experimentally certify coherence witnesses tailored for quantum systems increasing dimension using pairwise overlap measurements enabled by six-mode universal photonic processor fabricated with femtosecond laser writing technology....

The Boson sampling problem consists in from the output probability distribution of a bosonic Fock state, after it evolves through linear interferometer. There is strong evidence that computationally hard for classical computers, while can be solved naturally by bosons. This has led to draw increasing attention as possible way provide experimental quantum computational supremacy. Nevertheless, very complexity makes exclude hypothesis data are sampled different distribution. By exploiting...

Bosonic interference is a fundamental physical phenomenon, and it believed to lie at the heart of quantum computational advantage. It thus necessary develop practical tools witness its presence, both for reliable assessment source investigations. Here we describe how linear interferometers can be used unambiguously genuine n-boson indistinguishability. The amount violation proposed witnesses bounds degree multi-boson indistinguishability, which also provide novel intuitive model using set...

We discuss how quantum information distribution can improve the performance of some computation tasks. This be naturally implemented with different types cloning procedures. give two examples tasks for which provides enhancement in performance, and briefly possible extensions idea.

We translate the quantum teleportation protocol into a sequence of coherent operations involving three degrees freedom classical laser beam. The protocol, which we demonstrate experimentally, transfers polarization state input beam to transverse mode output role entanglement is played by non-separable describing path and freedom. Our illustrates possibility new optical applications based on this intriguing analogue entanglement.

Photonic interference is a key quantum resource for optical computation, and in particular so-called boson sampling devices. In interferometers with certain symmetries, genuine multiphoton effectively suppresses sets of events, as the original Hong–Ou–Mandel effect. Recently, it was shown that some classical semi-classical models could be ruled out by identifying such suppressions Fourier interferometers. Here we propose suppression law suitable random-input experiments multimode Sylvester...

Boson Sampling is a task that conjectured to be computationally hard for classical computer, but which can efficiently solved by linear-optical interferometers with Fock state inputs. Significant advances have been reported in the last few years, demonstrations of small- and medium-scale devices, as well implementations variants such Gaussian Sampling. Besides relevance this class computational models quest unambiguous experimental quantum advantage, recent results also proposed first...

Matchgates are a family of two-qubit gates associated with noninteracting fermions. They classically simulatable if acting only on nearest neighbors, but become universal for quantum computation we relax this restriction or use SWAP [Jozsa and Miyake, Proc. R. Soc. A 464, 3089 (2008)]. We generalize result by proving that any nonmatchgate parity-preserving unitary is capable extending the computational power matchgates into computation. identify single local invariant unitaries responsible...

Photon indistinguishability plays a fundamental role in information processing, with applications such as linear-optical quantum computation and metrology. It is then necessary to develop appropriate tools quantify the amount of this resource multiparticle scenario. Here we report four-photon experiment interferometer designed simultaneously estimate degree between three pairs photons. The design dispenses need heralding for parametric down-conversion sources, resulting an efficient reliable...

Suppose we have $N$ quantum systems in unknown states $\left|{\ensuremath{\psi}}_{i}\right\ensuremath{\rangle}$, but know the value of some pairwise overlaps ${\left|\ensuremath{\langle}{\ensuremath{\psi}}_{k}|{\ensuremath{\psi}}_{l}\ensuremath{\rangle}\right|}^{2}$. What can say about values overlaps? We provide a complete answer to this problem for three pure and two given way obtain bounds general case. discuss how contrasts from that classical model featuring only coherence-free,...