I raise some doubts concerning a protocol recently applied in an experiment (Walborn et al, Nature) to measure entanglement. The protocol is much simpler than other known entanglement-verification methods, but, I argue, needs assumptions (namely that the state generated is known and pure) that are too strong to be allowed and that are not justified in most experiments. An extension of the protocol suggested in quant-ph/0605250 is much harder to implement and still relies on assumptions not justified in entanglement-verification protocols, as demonstrated by an explicit example.
The problem of the experimental determination of the amount of entanglement of a bipartite pure state is addressed. We show that measuring a single observable does not suffice to determine the entanglement of a given unknown pure state of two particles. Possible minimal local measuring strategies are discussed and a comparison is made on the basis of their best achievable precision.
We present an easy implementable algorithm for approximating the geometric measure of entanglement from above. The algorithm can be applied to any multipartite mixed state. It involves only the solution of an eigenproblem and finding a singular value decomposition, no further numerical techniques are needed. To provide examples, the algorithm was applied to the isotropic states of 3 qubits and the 3-qubit XX model with external magnetic field.
Entanglement of formation is an important measure of quantum entanglement. We present an experimental way to measure the entanglement of formation for arbitrary dimensional pure states. The measurement only evolves local quantum mechanical observables.
In this paper, we present a fast quantum algorithm to measure the Hamming distance between two or more Boolean functions provided as black-boxes. The proposed algorithm constructs a new black-box with a certain property which is utilized to solve this problem. The introduced algorithm converts measuring the Hamming distance between Boolean functions to measuring entanglement between qubits, using concurrence entanglement measure.
An intrinsic relation between maximally entangled states and entanglement measures is revealed, which plays a role in establishing connections for different entanglement quantifiers. We exploit the basic idea and propose a framework to construct schemes for directly measuring entanglement of general states. In particular, we demonstrate that rank-1 local factorizable projective measurements, which are achievable with only one copy of entangled state involved at a time in a sequential way, are sufficient to directly determine the concurrence of arbitrary two-qubit entangled state.
A method is proposed to characterize and quantify multipartite entanglement in terms of the probability density function of bipartite entanglement over all possible balanced bipartitions of an ensemble of qubits. The method is tested on a class of random pure states.
Entanglement is a key property in the development of quantum technologies and in the study of quantum many-body simulations. However, entanglement measurement typically requires quantum full-state tomography (FST). Here we present a neural network-assisted protocol for measuring entanglement in equilibrium and non-equilibrium states of local Hamiltonians. Instead of FST, it can learn comprehensive entanglement quantities from single-qubit or two-qubit Pauli measurements, such as Rényi entropy, partially-transposed (PT) moments, and coherence. It is also exciting that our neural network is able…
It is shown that, despite strong nonlinearity, entanglement of formation of two-qubit state can be measured without prior state reconstruction. Collective measurements on small number of copies are provided that allow to determine quantum concurrence {\it via} estimation of only {\it four} parameters. It is also pointed out that another entanglement measure based on so called negativity can also be measured in similar way. The result is related to general problem: what kind of information can be extracted efficiently from unknown quantum state ?
Measuring entanglement is a demanding task that usually requires full tomography of a quantum system, involving a number of observables that grows exponentially with the number of parties. Recently, it was suggested that adding a single ancillary qubit would allow for the efficient measurement of concurrence, and indeed any entanglement monotone associated to antilinear operations. Here, we report on the experimental implementation of such a device---an embedding quantum simulator---in photonics, encoding the entangling dynamics of a bipartite system into a tripartite one. We show that biparti…
We study the entanglement between a certain qubit and the remaining system in rank- 2 mixed states prepared on the quantum computer. The protocol, which we propose for this purpose, is based on the relation of geometric measure of entanglement with correlations between qubits. As a special case, we consider a two-qubit rank-2 mixed state and find the relation of concurrence with the geometric measure of entanglement. On the ibmq-melbourne quantum computer we measure the geometric measure of entanglement in the cases of 2- and 4-qubit mixed quantum states which consist of Schrödinger cat states…
We study local-realistic inequalities, Bell-type inequalities, for bipartite pure states of finite dimensional quantum systems -- qudits. There are a number of proposed Bell-type inequalities for such systems. Our interest is in relating the value of Bell-type inequality function with a measure of entanglement. Interestingly, we find that one of these inequalities, the Son-Lee-Kim inequality, can be used to measure entanglement of a pure bipartite qudit state and a class of mixed two-qudit states. Unlike the majority of earlier schemes in this direction, where number of observables needed to c…
Three-dimensional entanglement of orbital angular momentum states of an atomic qutrit and a single photon qutrit has been observed. Their full state was reconstructed using quantum state tomography. The fidelity to the maximally entangled state of Schmidt rank 3 exceeds the threshold 2/3. This result confirms that the density matrix cannot be decomposed into ensemble of pure states of Schmidt rank 1 or 2. That is, the Schmidt number of the density matrix must be equal to or greater than 3.
We present methods for evaluating the rate of change in quantities during quantum evolution due to coupling to the environment (dissipation hereafter). The protocol is based on repeating a given quantum circuit (or quantum operation) twice, thrice, and so on, and measuring an expectation value after each number of repetitions. We start by applying this method for measuring the rate of purity changes in quantum circuits. This provides direct information on the quality of the circuit. Furthermore, the presented scheme enables to distill the dissipative contribution in the changes of quantities s…
An experimental scheme is proposed to test Bell's inequality by using superconducting nanocircuits. In this scheme, quantum entanglement of a pair of charge qubits separated in a sufficient long distance may be created by cavity quantum electrodynamic techniques; the population of qubits is experimentally measurable by dc currents through the probe junctions, and one measured outcome may be recorded for every experiment. Therefore, both locality and detection efficiency loopholes should be closed in the same experiment. We also propose a useful method to measure the amount of entanglement base…
Given a finite number $N$ of copies of a qubit state we compute the maximum fidelity that can be attained using joint-measurement protocols for estimating its purity. We prove that in the asymptotic $N\to\infty$ limit, separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This in turn shows that the optimal estimation of the entanglement of a two-qubit state can also be achieved asymptotically with fully separable measurements. The relationship between our global Bayesian approach and the quantum Cramer-Rao bound is also di…
Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz \emph{et al}. [Phys. Rev. Lett. \textbf{113}, 140401 (2014)] presented a rigorous framework to quantify coherence from the view of theory of physical resource. Here we propose a new valid quantum coherence measure which is a convex roof measure, for a quantum system of arbitrary dimension, essentially using the generalized Gell-Mann matrices. Rigorous proof shows that the proposed coherence measure fulfills all the requirements dictated by the resource theory of quantum coherence measur…
One of the most widespread methods to determine if a quantum state is entangled, or to quantify its entanglement dimensionality, is by measuring its fidelity with respect to a pure state. In this Letter we find a large class of states whose entanglement cannot be detected in this manner; we call them unfaithful. We find that unfaithful states are ubiquitous in information theory. For small dimensions, we check numerically that most bipartite states are both entangled and unfaithful. Similarly, numerical searches in low dimensions show that most pure entangled states remain entangled but become…
Here I present a method how intersections of a certain density matrix of rank two with the zero-polytope can be calculated exactly. This is a purely geometrical procedure which thereby is applicable to obtaining the zeros of SL- and SU-invariant entanglement measures of arbitrary polynomial degree. I explain this method in detail for a recently unsolved problem. In particular, I show how a three-dimensional view, namely in terms of the Boch-sphere analogy, solves this problem immediately. To this end, I determine the zero-polytope of the three-tangle, which is an exact result up to computer ac…
We show that block entanglement entropies in one-dimensional systems close to a quantum critical point can in principle be measured in terms of the population of low-lying energy levels following a certain type of local quantum quench.
The polarization analysis of quantized probe light transmitted through an atomic ensemble has been used to prepare entangled collective atomic states. In a "balanced" detection configuration, where the difference signal from two detection ports is analyzed, the continuous monitoring of a component of the Stokes field vector provides a means for conditional projective measurements on the atomic system. Here, we make use of classical driving fields, in the pulsed regime, and of an "unbalanced" detection setup (single detector) where the effective photon number of scattered photons is the detecte…
We describe a direct method for experimental determination of the negativity of an arbitrary two-qubit state with 11 measurements performed on multiple copies of the two-qubit system. Our method is based on the experimentally accessible sequences of singlet projections performed on up to four qubit pairs. In particular, our method permits the application of the Peres-Horodecki separability criterion to an arbitrary two-qubit state. We explicitly demonstrate that measuring entanglement in terms of negativity requires three measurements more than detecting two-qubit entanglement. The reported mi…
We show that the Quantum Zeno Effect prevails even if the entanglement with the measuring probe is not complete. The dynamics towards the asymptotic regime as a function of $N$, the number of measurements, reveals surprising results: the transition probability, for some values of the coupling to the measuring probe, may decrease much faster than the normal QZE.
Traditional method for measuring continuous-variable quantum entanglement relies on balanced homodyne detections, which are sensitive to vacuum quantum noise coupled in through losses resulted from many factors such as detector's quantum efficiency and mode mismatching between detected field and local oscillator. In this paper, we propose and analyze a new measurement method, which is realized by assisting the balanced homodyne detections with a high gain phase sensitive parametric amplifier. The employment of the high gain parametric amplifier helps to tackle the vacuum quantum noise originat…
We present optimal measuring strategies for the estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general measuring strategies are considered in both situations, to conclude in the first case that a local, although collective, measurement suffices to estimate entanglement, a non-local property, optimally.
The basic \emph{entanglement swapping protocol} allows to project two qubits, which have never interacted, onto a maximally entangled state. For deterministic swapping, the key ingredient is the maximal entanglement that was initially contained in two pairs of qubits and the capacity of projecting onto a Bell basis. Thus the basic and deterministic entanglement swapping scheme involves three maximal level of entanglement. In this work we propose probabilistic entanglement swapping processes performed with different amounts of initial entanglement. Besides that we suggest a non Bell measuring-b…
Entanglement is the quintessential quantum mechanical phenomenon understood to lie at the heart of future quantum technologies and the subject of fundamental scientific investigations. Mixture, resulting from noise, is often an unwanted result of interaction with an environment, but is also of fundamental interest, and is proposed to play a role in some biological processes. Here we report an integrated waveguide device that can generate and completely characterize pure two-photon states with any amount of entanglement and arbitrary single-photon states with any amount of mixture. The device c…
We show that the use of real measuring rods in quantum mechanics places a fundamental gravitational limit to the level of entanglement that one can ultimately achieve in quantum systems. The result can be seen as a direct consequence of the fundamental gravitational limitations in the measurements of length and time in realistic physical systems. The effect may have implications for long distance teleportation and the measurement problem in quantum mechanics.
It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasi-probability distribution (Wigner function) [Phys Rev Lett 117, 180401]. Such functions take the form of expectation values of an observable that has a direct analogy to displaced parity operators. In this work we give a procedure for the measurement of the Wigner function that should be applicable to any quantum system. We have applied our procedure to IBM's Quantum Experience five-qubit quantum processor to demonstrate that we can measure and generate the Wigner function…
Chemical magnetometers are radical pair systems such as solutions of pyrene and N,N-dimethylaniline (Py-DMA) that show magnetic field effects in their spin dynamics and their fluorescence. We investigate the existence and decay of quantum entanglement in free geminate Py-DMA radical pairs and discuss how entanglement can be assessed in these systems. We provide an entanglement witness and propose possible observables for experimentally estimating entanglement in radical pair systems with isotropic hyperfine couplings. As an application, we analyze how the field dependence of the entanglement l…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that in general, the Shannon entropy of the probability distribution of certain symmetry observables gives a lower bound to the entropy. In some cases this bound is saturated and directly gives the entropy. We also show other cases in which the probability distribution contains enough information to extract the entropy: we show how this is done in several exampl…
We put forward an approach to estimate the amount of bipartite spatial entanglement of down-converted photon states correlated in orbital angular momentum and the magnitude of the transverse (radial) wave vectors. Both degrees of freedom are properly considered in our framework, which only requires azimuthal local linear optical transformations and mode selection analysis with two fiber detectors. The coincidence distributions predicted by our approach give an excellent fit to the distributions measured in a recent experiment aimed to show the very high-dimensional transverse entanglement of t…
Phase modulation has emerged as a technique to create and manipulate high-dimensional frequency-bin entanglement. A necessary step to extending this technique to depolarized channels, such as those in a quantum networking environment, is the ability to perform phase modulation independent of photon polarization. This also necessary to harness hypertanglement in the polarization and frequency degrees of freedom for operations like Bell state discrimination. However, practical phase modulators are generally sensitive to the polarization of light and this makes them unsuited to such applications.…
The recent direct experimental measurement of quantum entanglement paves the way towards a better understanding of many-body quantum systems and their correlations. Nevertheless, the experimental and theoretical advances had so far been predominantly limited to bosonic systems. Here, we study fermionic systems. Using experimental setups where multiple copies of the same state are prepared, arbitrary order Renyi entanglement entropies and entanglement negativities can be extracted by utilizing spatially-uniform beam splitters and on-site occupation measurement. As an example, we simulate the us…
The genuine concurrence is a standard quantifier of multipartite entanglement, detection and quantification of which still remains a difficult problem from both theoretical and experimental point of view. Although many efforts have been devoted toward the detection of multipartite entanglement (e.g., using entanglement witnesses), measuring the degree of multipartite entanglement, in general, requires some knowledge about an exact shape of a density matrix of the quantum state. An experimental reconstruction of such density matrix can be done by full state tomography which amounts to having th…
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is rapidly gaining prominence in diverse fields ranging from condensed matter to quantum gravity. Despite this generality, measuring entanglement remains challenging. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles usi…
We discuss a scheme to measure the many-body entanglement growth during quench dynamics with bosonic atoms in optical lattices. By making use of a 1D or 2D setup in which two copies of the same state are prepared, we show how arbitrary order Renyi entropies can be extracted using tunnel-coupling between the copies and measurement of the parity of on-site occupation numbers, as has been performed in recent experiments. We illustrate these ideas for a Superfluid-Mott insulator quench in the Bose-Hubbard model, and also for hard-core bosons, and show that the scheme is robust against imperfection…
Entanglement is a defining feature of quantum mechanics that can be a resource in engineered and natural systems, but measuring entanglement in experiment remains elusive especially for large chemical systems. Most practical approaches require determining and measuring a suitable entanglement witness which provides some level of information about the entanglement structure of the probed state. A fundamental quantity of quantum metrology is the quantum Fisher information (QFI) which is a rigorous witness of multipartite entanglement that can be evaluated from linear response functions for certa…
We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of entanglement Hamiltonians, whose functional form is available from field theoretical insights. The method is applicable to classical simulations such as quantum Monte Carlo methods, and to experiments that allow for thermodynamic measurements such as the density of states, accessible via quantum quenches. We benchmark our technique on critical quantum spin chains, an…
We consider one-round games between a classical verifier and two provers who share entanglement. We show that when the constraints enforced by the verifier are `unique' constraints (i.e., permutations), the value of the game can be well approximated by a semidefinite program. Essentially the only algorithm known previously was for the special case of binary answers, as follows from the work of Tsirelson in 1980. Among other things, our result implies that the variant of the unique games conjecture where we allow the provers to share entanglement is false. Our proof is based on a novel `quantum…
We propose a scheme for measuring the squeezing, purity, and entanglement of Gaussian states of light that does not require homodyne detection. The suggested setup only needs beam splitters and single-photon detectors. Two-mode entanglement can be detected from coincidences between photodetectors placed on the two beams.
We investigate the possibility of characterizing two-party entanglement by measuring correlations of Stokes operators in polarized bright light beams. We adapt a general separability criterion to such operators. We then show that entanglement purification can only be singled out for a particular protocol.
Entanglement plays a central role in our understanding of quantum many body physics, and is fundamental in characterising quantum phases and quantum phase transitions. Developing protocols to detect and quantify entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, representing a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles via the dynamic susceptibility, i.e., with resources readily available in present cold atomic gas and condensed-matter experiments. This m…
We analyzed how entanglement harvesting is affected by the performance of a measurement on the quantum field. The measurement on the field is modelled as the coupling of a particle detector to the field, followed by a projective measurement performed on the detector. In our analysis, we considered different arrangements for two detectors harvesting entanglement and an ancillary detector used to perform a measurement. We found different regimes for how performing measurements on the field affects the entanglement harvested, depending on the initial and final states of the detector used to measu…
The threshold between classical and nonclassical two-qubit states is drawn at the place when these states can no longer be described by classical correlations, i.e., quantum discord or entanglement appear. However, to check if the correlations are classical (in terms of quantum discord and entanglement) it is sufficient to witness the lack of quantum discord because its zero value implies the lack of entanglement. We explain how the indicator of quantum discord introduced by Girolami and Adesso [Phys. Rev. Lett. 108, 150403 (2012)] can be practically measured in linear-optical systems using st…
We argue that the entanglement entropy offers us a useful coarse-grained entropy in time-dependent AdS/CFT. We show that the total von-Neumann entropy remains vanishing even when a black hole is created in a gravity dual, being consistent with the fact that its corresponding CFT is described by a time-dependent pure state. We analytically calculate the time evolution of entanglement entropy for a free Dirac fermion on a circle following a quantum quench. This is interpreted as a toy holographic dual of black hole creations and annihilations. It is manifestly free from the black hole informatio…
A pulsed source of entangled photons is desirable for some applications. Yet, such a source has intrinsic problems arising from the simultaneous arrival of the signal and noise photons to the detectors. These problems are analyzed and practical methods to calculate the number of accidental (or spurious) coincidences are described in detail, and experimentally checked, for the different regimes of interest. The results are useful not only to measure entanglement, but to all the situations where extracting the number of valid coincidences from noisy data is required. As an example of the use of …
We show how entanglement may be quantified in spin and cold atom many-body systems using standard experimental techniques only. The scheme requires no assumptions on the state in the laboratory and a lower bound to the entanglement can be read off directly from the scattering cross section of Neutrons deflected from solid state samples or the time-of-flight distribution of cold atoms in optical lattices, respectively. This removes a major obstacle which so far has prevented the direct and quantitative experimental study of genuine quantum correlations in many-body systems: The need for a full …
In this paper we develop an approach for detecting entanglement, which is based on measuring quantum correlations and constructing a correlation matrix. The correlation matrix is then used for defining a family of parameters, named Correlation Minor Norms, which allow one to detect entanglement. This approach generalizes the computable cross-norm or realignment (CCNR) criterion, and moreover requires measuring a state-independent set of operators. Furthermore, we illustrate a scheme which yields for each Correlation Minor Norm a separable state that maximizes it. The proposed entanglement dete…
Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are only available in few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition of a mixed state with the minimal average pure-state entanglement, the so-called convex roof. We show that under certain conditions such a problem becomes trivial. Precisely, we prove by a geometric argument that polynomial entanglement measures of degree 2 are independent of the choice of pure-state decomposition of a mixed state, when the latter has only …
Brussels Free University (VUB)（布鲁塞尔自由大学（VUB））；University of British Columbia（不列颠哥伦比亚大学）；Tianjin University（天津大学）
Conceptual entanglement is a crucial phenomenon in quantum cognition because it implies that classical probabilities cannot model non--compositional conceptual phenomena. While several psychological experiments have been developed to test conceptual entanglement, this has not been explored in the context of Natural Language Processing. In this paper, we apply the hypothesis that words of a document are traces of the concepts that a person has in mind when writing the document. Therefore, if these concepts are entangled, we should be able to observe traces of their entanglement in the documents…
Computing entanglement of an arbitrary bipartite or multipartite mixed state is in general not an easy task as it usually involves complex optimization. Here we show that exploiting symmetries of certain mixed states, we can compute a genuine multiparty entanglement measure, the generalized geometric measure for these classes of mixed states. The chosen states have different ranks and consist of an arbitrary number of parties.
