We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction Positive-Operator Valued Measure (POVM) describing given device. If device affected only an invertible noise, it possible correct outcome statistics future performed same To support practical applicability this for near-term devices, we...

Standard projective measurements (PMs) represent a subset of all possible in quantum physics, defined by positive-operator-valued measures. We study what are simulable, that is, can be simulated using and classical randomness. first prove every measurement on given system realized randomization the plus an ancilla same dimension. Then, general dimension two or three, we show deciding whether it is PM simulable solved means semidefinite programming. also establish conditions for simulation...

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 study how useful random states are for quantum metrology, i.e., surpass the classical limits imposed on precision in canonical phase estimation scenario. First, we prove that pure drawn from Hilbert space of distinguishable particles typically do not lead to super-classical scaling even when allowing local unitary optimization. Conversely, show symmetric subspace achieve optimal Heisenberg without need Surprisingly, is observed arbitrarily low purity and preserved under finite particle...

We explore the possibility of efficient classical simulation linear optics experiments under effect particle losses. Specifically, we investigate canonical boson sampling scenario in which an $n$-particle Fock input state propagates through a linear-optical network and is subsequently measured by particle-number detectors $m$ output modes. examine two models In first model fixed number particles lost. prove that this statistics can be well approximated simulation, provided photons left grows...

For any resource theory it is essential to identify tasks for which objects offer advantage over free objects. We show that this identification can always be accomplished theories of quantum measurements in form a convex subset on given Hilbert space. To aim we prove every measurement offers some state discrimination task. Moreover, give an operational interpretation robustness, quantifies the minimal amount noise must added make free. Specifically, geometric quantity related maximal...

The superposition principle is one of the landmarks quantum mechanics. importance superpositions provokes questions about limitations that mechanics itself imposes on possibility their generation. In this work, we systematically study problem creation unknown states. First, prove a no-go theorem forbids existence universal probabilistic protocol producing two Second, provide an explicit generating states, each having fixed overlap with known referential pure state. can be applied to generate...

We introduce a correlated measurement noise model that can be efficiently described and characterized, which admits effective noise-mitigation on the level of marginal probability distributions. Noise mitigation performed up to some error for we derive upper bounds. Characterization is done using Diagonal Detector Overlapping Tomography -- generalization recently introduced Quantum problem reconstruction readout with restricted locality. The procedure allows characterize $k$-local cross-talk...

Demonstrating quantum computational advantage with strong hardness guarantees is shown to be possible using fermionic linear optics magic input states, and an experimentally feasible setup proposed.

We introduce the Piquasso quantum programming framework, a full-stack open-source software platform for simulation and of photonic computers. can be programmed via high-level Python interface enabling users to perform efficient computing with discrete continuous variables. Via optional high-performance C++ backends, provides state-of-the-art performance in The framework is supported by an intuitive web-based graphical user where design circuits, run computations, visualize results.

In quantum theory general measurements are described by so-called Positive Operator-Valued Measures (POVMs). We show that in $d$-dimensional systems an application of depolarizing noise with constant (independent $d$) visibility parameter makes any POVM simulable a randomized implementation projective do not require auxiliary to be realized. This result significantly limits the asymptotic advantage POVMs can offer over various information-processing tasks, including state discrimination,...

A bstract We investigate circuit complexity of unitaries generated by time evolution randomly chosen strongly interacting Hamiltonians in finite dimensional Hilbert spaces. Specifically, we focus on two ensembles random generators — the so called Gaussian Unitary Ensemble (GUE) and ensemble diagonal matrices conjugated Haar unitary transformations. In both scenarios prove that exp(– itH ) exhibits following behaviour with high probability it reaches maximal allowed value same scale as needed...

We report an alternative scheme for implementing generalized quantum measurements that does not require the usage of auxiliary system. Our method utilizes solely (a) classical randomness and postprocessing, (b) projective on a relevant system, (c) postselection nonobserving certain outcomes. The implements arbitrary measurement in dimension $d$ with optimal success probability $1/d$. apply our results to bound relative power unambiguous state discrimination. Finally, we test experimentally...

We present a general algorithm for finding all classes of pure multiparticle states equivalent under stochastic local operations and classical communication (SLOCC). parametrize SLOCC by the critical sets total variance function. Our method works arbitrary systems distinguishable indistinguishable particles. also show how to calculate Morse indices points which have interpretation number independent nonlocal perturbations increasing hence entanglement state. illustrate our two examples.

Epsilon-nets and approximate unitary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> -designs are natural notions that capture properties of operations relevant for numerous applications in quantum information computing. In this work we study quantitative connections between these two notions. Specifically, prove that, notation="LaTeX">$d$ dimensional Hilbert space,...

Abstract We propose a scheme to implement general quantum measurements, also known as Positive Operator Valued Measures (POVMs) in dimension d using only classical resources and single ancillary qubit. Our method is based on probabilistic implementation of -outcome measurements which followed by postselection some the received outcomes. conjecture that success probability our larger than constant independent for all POVMs . Crucially, this implies possibility realizing arbitrary nonadaptive...

Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for minimal number invariant polynomials needed solving local unitary (LU) equivalence problem, that is, problem deciding if two can be connected by operations. Interestingly, this is not same every collection spectra. Some require less to solve LU than others. The result obtained using geometric methods, i.e., calculating dimensions spaces, stemming from symplectic reduction procedure.

Fermionic linear optics is a model of quantum computation which efficiently simulable on classical probabilistic computer. We study the problem simulation fermionic augmented with noisy auxiliary states. If state can be expressed as convex combination pure Gaussian states, corresponding scheme classically simulable. present an analytic characterization set convex-Gaussian states in first nontrivial case, Hilbert space ancilla four-mode Fock space. use our result to solve open recently posed...

For numerous applications of quantum theory it is desirable to be able apply arbitrary unitary operations on a given system. However, in particular situations only subset easily accessible. This raises the question what additional gates should added gate set order attain physical universality, i.e., perform transformation relevant Hilbert space. In this work, we study problem for three paradigmatic cases naturally occurring restricted sets: (A) particle-number preserving bosonic linear...

We present a classical algorithm for simulating universal quantum circuits composed of "free" nearest-neighbour matchgates or equivalently fermionic-linear-optical (FLO) gates, and "resourceful" non-Gaussian gates. achieve the promotion efficiently simulable FLO subtheory to computation by gadgetizing controlled phase gates with arbitrary phases employing resource states. Our key contribution is development novel phase-sensitive circuits. This allows us decompose states arising from...

We construct nonlinear multiparty entanglement measures for distinguishable particles, bosons, and fermions. In each case properties of an measure are related to the decomposition suitably chosen representation relevant symmetry group onto irreducible components. particles considered reduces well-known many-particle concurrence. prove that our criterion is sufficient necessary pure states living in both finite infinite dimensional spaces. generalize mixed by convex roof extension give a...

For several types of correlations (mixed-state entanglement in systems distinguishable particles, particle indistinguishable bosons and fermions, non-Gaussian fermionic systems) we estimate the fraction noncorrelated states among density matrices with same spectra. We prove that for purity exceeding some critical value (depending on considered problem) tends to zero exponentially fast dimension relevant Hilbert space. As a consequence, state randomly chosen from set possessing spectra is...

Estimation of expectation values incompatible observables is an essential practical task in quantum computing, especially for approximating energies chemical and other many-body systems. In this Letter, we introduce a method purpose based on performing single joint measurement that can be implemented locally whose marginals yield noisy (unsharp) versions the target set noncommuting Pauli observables. We derive bounds number experimental repetitions required to estimate up certain precision....