A workflow for evaluation of entanglement source quality is proposed. Based on quantum state density matrices obtained from theoretical models and experimental data, we make an estimate of a potential performance of a quantum entanglement source in quantum key distribution protocols. This workflow is showcased for continuously pumped spontaneous parametric down-conversion (SPDC) source, where it highlights the trade-off between entangled pair generation rate and entanglement quality caused by multiphoton nature of the generated quantum states. We employ this characterization technique to show that secure key rate of down-converted photon pairs is limited to 0.029 bits per detection window due to intrinsic multiphoton contributions. We also report that there exists one optimum gain for continuous-wave down-conversion sources. We find a bound for secure key rate extracted from SPDC sources and make a comparison with perfectly single-pair quantum states, such as those produced by quantum dots.
We describe the experimental implementation of a recently proposed quantum algorithm involving quantum entanglement at the level of two qubits using NMR. The algorithm solves a generalisation of the Deutsch problem and distinguishes between even and odd functions using fewer function calls than is possible classically. The manipulation of entangled states of the two qubits is essential here, unlike the Deutsch-Jozsa algorithm and the Grover's search algorithm for two bits.
We present a protocol for the teleportation of the quantum state of a pulse of light onto the collective spin state of an atomic ensemble. The entangled state of light and atoms employed as a resource in this protocol is created by probing the collective atomic spin, Larmor precessing in an external magnetic field, off resonantly with a coherent pulse of light. We take here for the first time full account of the effects of Larmor precession and show that it gives rise to a qualitatively new type of multimode entangled state of light and atoms. The protocol is shown to be robust against the dom…
In this paper, we present a new approach to study genuine tripartite entanglement existing in $(2\times 2\times n)-$dimensional quantum pure states. By utilizing the approach, we introduce a particular quantity to measure genuine tripartite entanglement. The quantity is shown to be an entanglement monotone in 2-dimensional subsystems (semi-monotone) and reaches zero for separable states and $(2\times 2\times 2)-$dimensional $W$ states, hence is a good criterion to characterize genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case…
We present a quantum key distribution protocol based on four-level particles entanglement. Furthermore, a controlled quantum key distribution protocol is proposed by utilizing three four-level particles. We show that the two protocols are secure.
We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics alone. Due to the basis independence of statistical effects, our protocol requires less knowledge of the initial state than most entanglement concentration schemes. Moreover, no explicit controlled operation is required at any stage.
It is presented a generalization of the von Neumann mutual information in the context of Tsallis' nonextensive statistics. As an example, entanglement between two (two-level) quantum subsystems is discussed. Important changes occur in the generalized mutual information, which measures the degree of entanglement, depending on the entropic index q.
The Hong-Ou-Mandel interference dip is caused by an entangled state, a delocalized bi-photon state. We propose a method of detecting this entanglement by utilizing inverse Hong-Ou-Mandel interference, while taking into account vacuum and multi-photon contaminations, phase noise, and other imperfections. The method uses just linear optics and photodetectors, and for single-mode photodetectors we find a lower bound on the amount of entanglement.
In this paper we investigate the von Neumann entropy in the ground state of one-dimensional anyonic systems with the repulsive interaction. Based on the Bethe-ansatz method, the entanglement properties for the arbitrary statistical parameter ($0\leqκ\leq1$) are obtained from the one-particle reduced density matrix in the full interacting regime. It is shown that the entanglement entropy increases with the increase in the interaction strength and statistical parameter. The statistic parameter affects the entanglement properties from two aspects: renormalizing of the effective interaction streng…
Interpretations of quantum measurement theory have been plagued by two questions, one concerning the role of observer consciousness and the other the entanglement phenomenon arising from the superposition of quantum states. We emphasize here the remarkable role of quantum statistics in describing the entanglement problem correctly and discuss the relationship to issues arising from current discussions of intelligent observers in entangled, decohering quantum worlds.
Both the topics of entanglement and particle statistics have aroused enormous research interest since the advent of quantum mechanics. Using two pairs of entangled particles we show that indistinguishability enforces a transfer of entanglement from the internal to the spatial degrees of freedom without any interaction between these degrees of freedom. Moreover, sub-ensembles selected by local measurements of the path will in general have different amounts of entanglement in the internal degrees of freedom depending on the statistics (either fermionic or bosonic) of the particles involved.
Quantum entanglement is an essential ingredient for the absolute security of quantum communication. Generation of continuous-variable entanglement or two-mode squeezing between light fields based on the effect of electromagnetically induced transparency (EIT) has been systematically investigated in this work. Here, we propose a new scheme to enhance the degree of entanglement between probe and coupling fields of coherent-state light by introducing a two-photon detuning in the EIT system. This proposed scheme is more efficient than the conventional one, utilizing the dephasing rate of ground-st…
Given an arbitrary statistical theory, different from quantum mechanics, how to decide which are the nonclassical correlations? We present a formal framework which allows for a definition of nonclassical correlations in such theories, alternative to the current one. This enables one to formulate extrapolations of some important quantum mechanical features via adequate extensions of reciprocal maps relating states of a system with states of its subsystems. These extended maps permit one to generalize i) separability measures to any arbitrary statistical model as well as ii) previous entanglemen…
We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this notion to describe the amount of entanglement between two quantum systems from a statistical point of view. Our measure is independent of the number of entangled systems and their dimensionality.
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable states. We further study this system using statistical mechanical methods. Finally, we apply our techniques to Werner states of two qubits and obtain a sufficient criterion for separability.
We study the entanglement properties of a pair of two-level atoms going through a cavity one after another. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the cavity photon field result in the final two-atom state being of a mixed entangled type. We consider the field statistics of the Fock state field, and the thermal field, respectively, inside the cavity. The entanglement of formation of the joint two-atom state is calculated for both these cases as a function of the Rabi-angle $gt$. We present a comparitive study of two-atom e…
We focus on characterizing entanglement of high dimensional bipartite states using various statistical correlators for two-qudit mixed states. The salient results obtained are as follows: (a) A scheme for determining the entanglement measure given by Negativity is explored by analytically relating it to the widely used statistical correlators viz. mutual predictability, mutual information and Pearson Correlation coefficient for different types of bipartite arbitrary dimensional mixed states. Importantly, this is demonstrated using only a pair of complementary observables pertaining to the mutu…
Joint measurements of two observables reveal that every state is nonclassical, with the only trivial exception of the state with density matrix proportional to the identity. This naturally includes states considered universally as classical-like, such as SU(2) and Glauber coherent states. We show that this holds because we can always find a joint measurement whose statistics is not separable.
We have investigated high-precision measurements, beyond the standard quantum limit, utilizing non-classical states. Although entanglement has been considered a resource for achieving the Heisenberg limit in measurements, we show that any advantage expected from using entanglement is dependent on the measurement in question. We investigate several measurement scenarios and illustrate the role of entanglement as a resource for quantum high-precision measurement. In particular, we demonstrate that there is a regime wherein entanglement not only does not help, but prevents the achievement of the …
We extend the idea of entanglement concentration for pure states(Phys. Rev. Lett. {\bf 88}, 187903) to the case of mixed states. The scheme works only with particle statistics and local operations, without the need of any other interactions. We show that the maximally entangled state can be distilled out when the initial state is pure, otherwise the entanglement of the final state is less than one. The distillation efficiency is a product of the diagonal elements of the initial state, it takes the maximum 50%, the same as the case for pure states.
A general and an arbitrarily efficient scheme for entangling the spins (or any spin-like degree of freedom) of two independent uncorrelated identical particles by a combination of two particle interferometry and which way detection is formulated. It is shown that the same setup could be used to identify the quantum statistics of the incident particles from either the sign or the magnitude of measured spin correlations. Our setup also exhibits a curious complementarity between particle distinguishability and the amount of generated entanglement.
In this paper, a bidirectional quantum teleportation protocol based on Einstein-Podolsky-Rosen (EPR) pairs and entanglement swapping is proposed. In this scheme, two users can simultaneously transmit an unknown single-qubit state to each other. The implementation of the proposed scheme is easier in experiment as compared to previous work. By utilizing this bidirectional quantum teleportation protocol, a bidirectional quantum secure direct communication scheme without carrying secret message is presented. Therefore, in the case of using perfect quantum channel, the protocol is completely secure…
The authors of the recent paper [1] boldly claim to discover a new fully quantum approach to foundation of statistical mechanics: "Our conceptually novel approach is free of mathematically ambiguous notions such as probability, ensemble, randomness, etc." The aim of this note is to show that this approach is neither specific for quantum systems nor really conceptually different from the standard textbook arguments supporting microcanonical or canonical ensembles in statistical mechanics.
The effects of photon bunching and antibunching correspond to the classical and quantum features of the electromagnetic field, respectively. No direct evidence suggests whether these effects can be potentially related to quantum entanglement. Here we design a cavity quantum electrodynamics model with two atoms trapped in to demonstrate the connections between the steady-state photon statistics and the two-atom entanglement . It is found that within the weak dissipations and to some good approximation, the local maximal two-atom entanglements perfectly correspond to not only the quantum feature…
Simple joint measurements of pairs of observables reveal that states considered universally as classical-like, such as SU(2) spin coherent states, Glauber coherent states, and thermal states are actually nonclassical. We show that this holds because we can find a joint measurement the statistics of which is not separable. Eventually this may be extended to all states different from the maximally mixed state.
We propose an experimental scheme for the measurement of entanglement between two two-level atoms. Our scheme requires one of the two entangled atoms to interact with a cavity field dispersively, and we show that by measuring the zero time-delay second-order coherence function of the cavity field, one can measure the concurrence of an arbitrary Bell-like atomic two-qubit state. As our scheme requires only one of the atoms to interact with the measured cavity, the entanglement quantification becomes independent of the location of the other atom. Therefore, our scheme can have important implicat…
The quantum entanglement is an important feature of many protocols in the field of quantum computing. In this paper we evaluate a level of entanglement in short qutrit chains. This evaluation is carried out with use of the CCNR criterion and the concurrence measure. We also present some explicit formulae describing the values of CCNR criterion and concurrence for exemplary short spin chains. Utilizing the obtained results, we indicate that analyzing the level of entanglement allows to detect the noise or deviation in the transfer process, in comparison to the perfect transfer where only operat…
We study the entanglement and work statistics in a driven two-qubit system. The regulation of periodic driving has much more versatility and universality in contrast to reservoir engineering in static systems. We found the quasi-steady state entanglement can be amplified effectively by the external drive in certain parameter regimes. The drive extends the range of temperatures or temperature differences at which entanglement can emerge. From the view of the effective Hamiltonian, the addition of the driving alters the inter-qubit coupling and system-bath coupling, which are crucial in determin…
A single-particle entangled state can be generated by illuminating a beam splitter with a single photon. Quantum teleportation utilizing such a single-particle entangled state can be successfully achieved with a simple setup consisting only of linear optical devices such as beam splitters and phase shifters. Application of the locality assumption to a single-particle entangled state leads to Bell's inequality, a violation of which signifies the nonlocal nature of a single particle.
With a product state of the form $ρ_{in} = ρ_a\otimes|0>_b_b< 0|$ as input, the output two-mode state $ρ_{\rm out}$, of the beam splitter is shown to be NPT whenever the photon number distribution (PND) statistics $\{p(n_a) \}$ associated with the possibly mixed state $ρ_a$ of the a_mode is antibunched or otherwise nonclassical, i.e., if $\{p(n_a)\}$ fails to respect any one of an infinite of classicality conditions.
We consider the change of entanglement of formation $ΔE$ produced by the Hadamard-CNOT circuit on a general (pure or mixed) state $ρ$ describing a system of two qubits. We study numerically the probabilities of obtaining different values of $ΔE$, assuming that the initial state is randomly distributed in the space of all states according to the product measure recently introduced by Zyczkowski {\it et al.} [Phys. Rev. A {\bf 58} (1998) 883].
We have presented a theoretical extended version of dense coding protocol using entangled position state of two particles shared between two parties. A representation of Bell states and the required unitary operators are shown utilizing symmetric normalized Hadamard matrices. In addition, some explicit and conceivable forms for the unitary operators are presented by using some introduced basic operators. It is shown that, the proposed version is logarithmically efficient than some other multi-qubit dense coding protocols.
Coherent feedback control (CFC) of multipartite optical entangled states produced by a non-degenerate optical parametric amplifier is theoretically studied. The features of the quantum correlations of amplitude and phase quadratures among more than two entangled optical modes can be controlled by tuning the transmissivity of the optical beam splitter in CFC loop. The physical conditions to enhance continuous variable multipartite entanglement of optical fields utilizing CFC loop are obtained. The numeric calculations based on feasible physical parameters of realistic systems provide direct ref…
We present a novel approach to the study of entanglement decay, which focuses on collective properties. As an example, we investigate the entanglement decay of a two-qubit system, produced by local identical reservoirs acting on the qubits, for three experimentally and theoretically relevant cases. We study the probability distributions of disentanglement times, a quantity independent of the measure used to quantify entanglement, and the time-dependent probability distribution of concurrence. Analytical results are obtained for initially uniformly distributed pure states. The calculation of th…
We study the significance of Photon/Phonons bunching and antibunching on the dynamics of the quantum entanglement in the presence of coupled PT-symmetry systems with balanced/unbalanced gain and loss. We suggest a hybrid electromechanical system to realize a strong and tunable coupling between a Coplanar-Waveguide (CPW) microwave cavity and a nanomechanical resonator (NAMR) via a superconducting Transmon qubit. The hybrid electromechanical system consists of a non-hermitian Hamiltonian with balanced/unbalanced gain and loss. The interplay between the quantum entanglement and the -symmetry syst…
Construction of multi-particle entangled states and direct teleportation of N-(spin 1/2) particles are important areas of quantum information processing. A number of different schemes which have been presented already, address the problem through controlled teleportation. In this article, a criterion based on standard quantum statistical correlations employed in the many body virial expansions is used to determine maximum entanglement for a N-particle state. These states remain entangled through proper traces to states for a smaller number of particles and can be generalized for arbitrary numb…
Quantum secret sharing (QSS) schemes without entanglement have huge advantages in scalability and are easier to realize as they only require sequential communications of a single quantum system. However, these schemes often come with drawbacks such as exact ($n, n$) structure, security flaws and absences of effective cheating detections. To address these problems, we propose a verifiable framework by utilizing entanglement-free states to construct ($t, n$)-QSS schemes. Our work is the heuristic step towards information-theoretical security in entanglement-free QSS, and it sheds light on how to…
Quantum entanglement is a crucial resource for a wide variety of quantum technologies. However, the current state-of-art methods to generate quantum entanglement in optomechanical systems are not as efficient as all-optical methods utilizing nonlinear crystals. This article proposes a new scheme in which two single-mode squeezed light fields are injected into an optomechanical cavity. We demonstrate through our numerical simulations that the quantum entanglement can be substantially enhanced with the careful selection of squeezing strength and squeezing angle of the two quadrature squeezed lig…
We propose how to achieve nonreciprocal quantum entanglement of light and motion and reveal its counterintuitive robustness against random losses. We find that by splitting the counterpropagating lights of a spinning resonator via the Sagnac effect, photons and phonons can be entangled strongly in a chosen direction but fully uncorrelated in the other. This makes it possible both to realize quantum nonreciprocity even in the absence of any classical nonreciprocity and also to achieve significant entanglement revival against backscattering losses in practical devices. Our work provides a way to…
We demonstrate the connection between an operator's matrix element distribution and entangling power via numerical simulations of random, pseudo-random, and quantum chaotic operators. Creating operators with a random distribution of matrix elements is more difficult than creating operators that reproduce other statistical properties of random matrices. Thus, operators that fulfill many random matrix statistical properties may not generate states of high multi-partite entanglement. To quantify the randomness of various statistical distributions and, by extension, entangling power, we use proper…
We discuss the possibility of observing quantum nonlocality using the so-called mode entanglement, analyzing the differences between different types of particles in this context. We first discuss the role of coherent states in such experiments, and we comment on the existence of coherent states in nature. The discussion of coherent states naturally raises questions about the role of particle statistics in this problem. Although the Pauli exclusion principle precludes coherent states with a large number of fermionic particles, we find that a large number of fermionic coherent states, each conta…
The distribution of typical bipartite pure states is studied within the framework of state transformation via local operation and classical communication (LOCC). We report the statistics of comparable and incomparable states in different dimensions for single- and multi-copy regimes and establish a connection between state transformation and the difference between the entanglement contents of the initial and the target states. From the analysis of catalyst resources, required to further otherwise impossible LOCC transformations between pairs, we demonstrate a universal pattern in the average a…
We study experimentally the fundamental limits of sensitivity of an atomic radio-frequency magnetometer. First we apply an optimal sequence of state preparation, evolution, and the back-action evading measurement to achieve a nearly projection noise limited sensitivity. We furthermore experimentally demonstrate that Einstein-Podolsky-Rosen (EPR) entanglement of atoms generated by a measurement enhances the sensitivity to pulsed magnetic fields. We demonstrate this quantum limited sensing in a magnetometer utilizing a truly macroscopic ensemble of 1.5*10^12 atoms which allows us to achieve sub-…
We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second Rényi entropy of highly mixed quantum states consisting of up to $10$ qubits in a trapped-ion quantum simulator [Brydges et al., Science 364, 260 (2019)]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in an experime…
