Multi-parameter estimation is necessary for force sensing due to simultaneous and nontrivial small changes of position and momentum. Designing quantum probes that allow simultaneous estimation of all parameters is therefore an important task. The optimal methods for estimation of the conjugate changes of position and momentum of quantum harmonic oscillator employ probes in entangled or quantum non-Gaussian states. We show that the same results can be obtained in a significantly more feasible fashion by employing independent sets of differently squeezed Gaussian states classically correlated to position or momentum measurements. This result demonstrates an unexplored power of a classical correlation between the probe states and measurements directly applicable to force sensing
We discuss the problem of when a set of measurements made on an entangled source can be simulated with a classically correlated source. This is discussed in general and some examples are given. The question of which aspects of quantum imaging can be simulated by classically correlated sources is examined.
In this short note we present a new approach to non-classical correlations that is based on the compression rates for bit strings generated by Alice and Bob. We use normalised compression distance introduced by Cilibrasi and Vitanyi to derive information-theoretic inequalities that must be obeyed by classically correlated bit strings and that are violated by PR-boxes. We speculate about a violation of our inequalities by quantum mechanical correlations.
Consider a bipartite quantum system with at least one of its two components being itself a composite system. By tracing over part of one (or both) of these two subsystems it is possible to obtain a reduced (separable) state that exhibits quantum correlations even if the original state of the full system is endowed only with classical correlations. This effect, first pointed out by Li and Luo in (2008), is of considerable interest because there is a growing body of evidence suggesting that quantum correlations in non-entangled, mixed states may constitute a useful resource to implement non triv…
Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $π/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and Knill states that Clifford circuits are efficiently classically simulable. We show that in contrast, "conjugated Clifford circuits" (CCCs) -- where one additionally conjugates every qubit by the same one-qubit gate $U$ -- can perform hard sampling tasks. In particular, we fully classify the computational power of CCCs by showing that essentially any non-Clifford c…
We study the problem of determining the photon number statistics of an unknown quantum state by simultaneously measuring conjugate quadratures with double homodyne detectors. Classically, the sum of the squared outputs of the two homodyne detectors is proportional to the intensity (thus the photon number) of the input light. Quantum mechanically, due to vacuum noise, the above photon number measurement is intrinsically noisy. We quantify the information gain in a single-shot measurement and discuss potential applications of this technology in quantum key distribution. We also show that the pho…
We show that local PT-symmetric evolutions can lead to violation of the no-signaling principle for separable and even classically correlated bipartite shared quantum states. For classically correlated states, specially chosen PT-symmetric operations from a set of zero volume can also preserve the principle. The violations can be removed by using a CPT inner product instead of the traditional one.
In its original formulation, quantum backflow (QB) is an interference effect that manifests itself as a negative probability transfer for free-particle states comprised of plane waves with only positive momenta. Quantum reentry (QR) is another interference effect in which a wave packet expanding from a spatial region of its initial confinement partially returns to the region in the absence of any external forces. Here we show that both QB and QR are special cases of a more general classically-forbidden probability flow for quantum states with certain position-momentum correlations. We further …
Quantum entanglement has been recently demonstrated as a useful resource in conflicting interest games of incomplete information between two players, Alice and Bob [Pappa et al., Phys. Rev. Lett. 114, 020401 (2015)]. General setting for such games is that of correlated strategies where the correlation between competing players is established through a trusted common adviser; however, players need not reveal their input to the adviser. So far, quantum advantage in such games has been revealed in a restricted sense. Given a quantum correlated equilibrium strategy, one of the players can still re…
We characterize the optimal correlative capacity of entangled, separable, and classically correlated states. Introducing the notions of the infimum and supremum within majorization theory, we construct the least disordered separable state compatible with a set of marginals. The maximum separable correlation information supportable by the marginals of a multi-qubit pure state is shown to be an LOCC monotone. The least disordered composite of a pair of qubits is found for the above classes, with classically correlated states defined as diagonal in the product of marginal bases.
Duan, Giedke, Cirac and Zoller (quant-ph/9908056) and, independently, Simon (quant-ph/9909044) have recently found necessary and sufficient conditions for the separability (classical correlation) of the Gaussian two-party (continuous variable) states. Duan et al remark that their criterion is based on a "much stronger bound" on the total variance of a pair of Einstein-Podolsky-Rosen-type operators than is required simply by the uncertainty relation. Here, we seek to formalize and test this particular assertion in both classical and quantum-theoretic frameworks. We first attach to these states …
It is shown that the use of phase conjugation in one arm of a correlated two-photon imaging apparatus allows undistorted ghost imaging through a region with randomly-varying phase shifts. The images are formed from correlated pairs of photons in such a way that turbulence-induced phase shifts gained by the photons during passage through the medium cancel pairwise.
Quantum imaging has been demonstrated since 1995 by using entangled photon pairs. The physics community named these experiments "ghost image", "quantum crypto-FAX", "ghost interference", etc. Recently, Bennink et al. simulated the "ghost" imaging experiment by two co-rotating k-vector correlated lasers. Did the classical simulation simulate the quantum aspect of the "ghost" image? We wish to provide an answer. In fact, the simulation is very similar to a historical model of local realism. The goal of this article is to clarify the different physics behind the two types of experiments and addre…
We analytically show that it is possible to perform coherent imaging by using the classical correlation of two beams obtained by splitting incoherent thermal radiation. The case of such two classically correlated beams is treated in parallel with the configuration based on two entangled beams produced by parametric down-conversion, and a basic analogy is pointed out. The results are compared in a specific numerical example.
Quantum correlation, or entanglement, is now believed to be an indispensable physical resource for certain tasks in quantum information processing, for which classically correlated states cannot be useful. Besides information processing, what kind of physical processes can exploit entanglement? In this paper, we show that there is indeed a more basic relationship between entanglement and its usefulness in thermodynamics. We derive an inequality showing that we can extract more work out of a heat bath via entangled systems than via classically correlated ones. We also analyze the work balance o…
We study characterization of separable (classically correlated) states for composite systems of distinguishable fermions that are represented as CAR algebras.
We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small c…
Quantum systems in mixed states can be unentangled and yet still correlated in a way that is not possible for classical systems. These correlations can be quantified by the quantum discord and might provide a resource for certain mixed-state quantum information processing tasks. Here we report on the generation of discordant states of two trapped atomic ions via Markovian decoherence processes. While entanglement is strictly non-increasing under such operations, discord can be generated in various forms. Firstly we show that, starting from two classically correlated qubits, it is possible to g…
We demonstrate quantum walks of correlated photons in a 2D network of directly laser written waveguides coupled in a 'swiss cross' arrangement. The correlated detection events show high-visibility quantum interference and unique composite behaviour: strong correlation and independence of the quantum walkers, between and within the planes of the cross. Violations of a classically defined inequality, for photons injected in the same plane and in orthogonal planes, reveal non-classical behaviour in a non-planar structure.
We show that the interaction of a pulsed laser light with a mechanical oscillator through the radiation pressure results in an opto-mechanical entangled state in which the photon number is correlated with the oscillator position. Interestingly, the mechanical oscillator can be delocalized over a large range of positions when driven by an intense laser light. This provides a simple yet sensitive method to probe hypothetic post-quantum theories including an explicit wave function collapse model, like the Diosi and Penrose model. We propose an entanglement witness to reveal the quantum nature of …
In this review we discuss intriguing properties of apparently classical optical fields, that go beyond purely classical context and allow us to speak about quantum characteristics of such fields and about their applications in quantum technologies. We briefly define the genuinely quantum concepts of entanglement and steering. We then move to the boarder line between classical and quantum world introducing quantum discord, a more general concept of quantum coherence, and finally a controversial notion of classical entanglement. To unveil the quantum aspects of often classically perceived system…
In previous studies, we have explored the ansatz that the volume elements of the Bures metrics over quantum systems might serve as prior distributions, in analogy to the (classical) Bayesian role of the volume elements ("Jeffreys' priors") of Fisher information metrics. Continuing this work, we obtain exact Bures probabilities that the members of certain low-dimensional subsets of the fifteen-dimensional convex set of 4 x 4 density matrices are separable or classically correlated. The main analytical tools employed are symbolic integration and a formula of Dittmann (quant-ph/9908044) for Bures…
Quantum discord and quantum entanglement are resources in some quantum information processing (QIP) models. However, in recent years, the evidence that separable states or classically correlated states can also accomplish QIP is demonstrated. It provides a useful tool since such states are easier to prepare. Quantum coherence is a measure of non-classical correlation, containing entanglement and discord as a subset. Nowadays, it is of interest whether quantum coherence can act as a resource in QIP independently or not, without the help from quantum discord or entanglement. In this paper, we sh…
It is well known that a quantum correlated probe can yield better precision in estimating an unknown parameter than classically possible. However, how such a quantum probe should be measured remains somewhat elusive. We examine the role of measurements in quantum metrology by considering two types of readout strategies: coherent, where all probes are measured simultaneously in an entangled basis; and adaptive, where probes are measured sequentially, with each measurement one way conditioned on the prior outcomes. Here we firstly show that for classically correlated probes the two readout strat…
Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semi-classical channel \cite{DagmarBruss}. We find the power of any given local channel for producing quantum correlations on an initially classically correlated state. We introduce a computable measure for quantifying the quantum correlations in quantum-classical states, which is based on the non-commutativity of ensemble states in one party of the composite system. Using this measure we show that the amount of quantum correlations produced, is proporti…
We report experimental generation of non-classically correlated photon pairs from collective emission in a room-temperature atomic vapor cell. The nonclassical feature of the emission is demonstrated by observing a violation of the Cauchy-Schwarz inequality. Each pair of correlated photons are separated by a controllable time delay up to 2 microseconds. This experiment demonstrates an important step towards the realization of the Duan-Lukin-Cirac-Zoller scheme for scalable long-distance quantum communication.
We address realistic schemes for the generation of non-Gaussian states of light based on conditional intensity measurements performed on correlated bipartite states. We consider both quantum and classically correlated states and different kind of detection, comparing the resulting non Gaussianity parameters upon varying the input energy and the detection efficiency. We find that quantum correlations generally lead to higher non Gaussianity, at least in the low energy regime. An experimental implementation feasible with current technology is also suggested.
We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive semidefinite while the other one is necessarily entrywise non-negative. We explore basic properties of these matrix pairs and develop several testable necessary and sufficient conditions that help determine whether or not a pair is PCP. We then establish a connection with quantum entanglement by showing that determining whether or not a pair of matrices is pai…
Simulating complex molecules and materials is an anticipated application of quantum devices. With strong quantum advantage demonstrated in artificial tasks, we examine how such advantage translates into modeling physical problems of correlated electronic structure. We simulate static and dynamical electronic structure on a superconducting quantum processor derived from Google's Sycamore architecture for two representative correlated electron problems: the nitrogenase iron-sulfur molecular clusters, and $α$-ruthenium trichloride, a proximate spin-liquid material. To do so, we simplify the elect…
Joint approximate measurement schemes of position and momentum provide us with a means of inferring pieces of complementary information if we allow for the irreducible noise required by quantum theory. One such scheme is given by the Arthurs-Kelly model, where information about a system is extracted via indirect probe measurements. So far, only separable uncorrelated probes have been considered. Here, following Di Lorenzo (PRL 110, 120403 (2013)), we extend this model to both entangled and classically correlated probes, achieving full generality. We find the measured observable of the system u…
We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case.
We analytically show that it is possible to perform coherent imaging by using the classical correlation of two beams obtained by splitting incoherent thermal radiation. A formal analogy is demonstrated between two such classically correlated beams and two entangled beams produced by parametric down-conversion. Because of this analogy, the classical beams can mimic qualitatively all the imaging properties of the entangled beams, even in ways which up to now were not believed possible. A key feature is that these classical beams are spatially correlated both in the near-field and in the far-fiel…
Cluster-Adaptive Sample-Based Quantum Diagonalization for Strongly Correlated Systems
University of Seoul（首尔大学）；Center for Quantum Information Processing, University of Seoul（首尔大学量子信息处理中心）；Department of Chemistry, Sogang University（延世大学化学系）；Singularity Quantum Inc.（奇点量子公司）
Bounding the cost of classically simulating the outcomes of universal quantum circuits to additive error $δ$ is often called weak simulation and is a direct way to determine when they confer a quantum advantage. Weak simulation of the $T$+Clifford gateset is $BQP$-complete and is expected to scale exponentially with the number $t$ of $T$ gates. We constructively tighten the upper bound on the worst-case $L_1$ norm sampling cost to next order in $t$ from $\mathcal O(ξ^t δ^{-2})$ if $δ^2 \gg ξ^{-t}$ to $\mathcal O((ξ^t{-}t) δ^{-2} )$ if $δ^2 \gg (ξ^t -t)^{-1}$, where $ξ^t = 2^{\sim 0.228 t}$ is …
We present a proof-of-principle experimental demonstration of a reconfigurable entanglement distribution scheme utilizing a poled fiber-based source of broadband polarization-entangled photon pairs and dense wavelength-division multiplexing. A large bandwidth (> 90 nm, centered at 1555 nm) and highly spectrally correlated nature of the entangled source can be exploited to allow for the generation of more than 25 frequency-conjugate entangled pairs when aligned to the standard 200 GHz ITU grid. In this work, three frequency-conjugate entangled pairs are used to demonstrate quantum key distribut…
Two mesoscopic SQUID rings which are far from each other, are considered. A source of two-mode nonclassical microwaves irradiates the two rings with correlated photons. The Josephson currents are in this case quantum mechanical operators, and their expectation values with respect to the density matrix of the microwaves, yield the experimentally observed currents. Classically correlated (separable) and quantum mechanically correlated (entangled) microwaves are considered, and their effect on the Josephson currents is quantified. Results for two different examples that involve microwaves in numb…
The regions of independent quantum states, maximally classically correlated states, and purely quantum entangled (supercorrelated) states described in a recent formulation of quantum information theory by Cerf and Adami are explored here numerically in the parameter space of the well-known exactly soluable Jaynes-Cummings model for equilibrium and nonequilibrium time-dependent ensembles.
Nondegenerate four-wave mixing (FWM) process based on a double-$Λ$ scheme in hot alkali metal vapor is a versatile tool in quantum state engineering, quantum imaging, and quantum precision measurements. In this Letter, we investigate the generation of quantum correlated twin beams which carry nonzero orbital angular momentums (OAMs) based on the FWM process in hot cesium vapor. The amplified probe beam and the newly generated conjugate beam in the FWM process have the same and opposite topological charge as the seed beam, respectively. We also explore the FWM process operated in a nonamplifyin…
We provide a complete set of game-theoretic conditions equivalent to the existence of a transformation from one quantum channel into another one, by means of classically correlated pre/post processing maps only. Such conditions naturally induce tests to certify that a quantum memory is capable of storing quantum information, as opposed to memories that can be simulated by measurement and state preparation (corresponding to entanglement-breaking channels). These results are formulated as a resource theory of genuine quantum memories (correlated in time), mirroring the resource theory of entangl…
Motivated by thermodynamic considerations, we analyse the variation of the quantum mutual information on a unitary orbit of a bipartite system's state, with and without global constraints such as energy conservation. We solve the full optimisation problem for the smallest system of two qubits, and explore thoroughly the effect of unitary operations on the space of reduced-state spectra. We then provide applications of these ideas to physical processes within closed quantum systems, such as a generalized collision model approach to thermal equilibrium and a global Maxwell demon playing tricks o…
Quantum discord is a measure of non-classical correlations, which are excess correlations inherent in quantum states that cannot be accessed by classical measurements. For multipartite states, the classically accessible correlations can be defined by the mutual information of the multipartite measurement outcomes. In general the quantum discord of an arbitrary quantum state involves an optimisation of over the classical measurements which is hard to compute. In this paper, we examine the quantum discord in the experimentally relevant case when the quantum states are Gaussian and the measuremen…
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized implementations of Trotter-Suzuki-based product formulas. We show that low-order Trotter methods perform surprisingly well when used with phase estimation to compute relative precision quantities (e.g. energies per unit cell), as is often the goal for condensed-phase systems. In this context, simulations of the Hubbard and plane-wave electronic structure models …
According to the quantum Zeno effect, the frequent observations of a system can dramatically slow down its dynamical evolution. We show that the Zeno dynamics is the result of projective measurements among quantum states which are indistinguishable. The physical time scale of the problem is provided by the Cramer-Rao lower bound, which measure the distinguishability of states along a path in the Hilbert space. We finally show that the Zeno dynamics with particle entangled states might require quite smaller measurement intervals than classically correlated states, and propose a realistic interf…
We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the long term, provide significantly improved initial states for quantum algorithms. The associated wavefunctions can be represented with linear memory requirement which allows classical optimization of the circuits and naturally defines a minimum benchmark for quantum algorithms. In this work, we employ directly determined pair-natural orbitals within a basis-se…
Quantum walks in an elaborately designed graph, is a powerful tool simulating physical and topological phenomena, constructing analog quantum algorithms and realizing universal quantum computing. Integrated photonics technology has emerged as a versatile platform to implement various quantum information tasks and a promising candidate to perform large-scale quantum walks. Both extending physical dimensions and involving more particles will increase the complexity of the evolving systems and the desired quantum resources. Pioneer works have demonstrated single particle walking on two-dimensiona…
Purifying a high-temperature ensemble of quantum particles towards a known state is a key requirement to exploit quantum many-body effects. An alternative to passive cooling, which brings a system to its ground state, is based on feedback to stabilise the system actively around a target state. This alternative, if realised, offers additional control capabilities for the design of quantum states. Here we present a quantum feedback algorithm capable of stabilising the collective state of an ensemble from an infinite-temperature state to the limit of single quanta. We implement this on ~50,000 nu…
