We studied the entangled state for a one-dimensional $S=1/2$ antiferromagnetic quantum spin chain in a transverse field. We calculate the ground state using the density matrix renormalization group and discuss how the entangled state changes around a quantum phase transition (QPT) point. By analyzing concurrence $C(ρ)$ for two-qubit density matrix $ρ$ after the Lewenstein-Sanpera decomposition, $ρ=Λρ_s + (1-Λ) ρ_e $, where $ρ_s$ is a separable density matrix and $ρ_e$ is a pure entangled state obtained by a linear combination of Bell states, we find singular behaviors both in $C(ρ_e)$ and $1-Λ$ at the QPT point.　 $C(ρ_e)$ includes the effects of quantum fluctuations, which manifest the competition between the antiferromagnetic spin fluctuation and the effect of transverse field in the transverse Ising model. The quantum fluctuation shows the singular maximum at the QPT point as expected from the general picture of phase transition. In contrast, $1-Λ$ reveals the singular minimum at QPT point.
Emission of photon pairs by metal-dielectric interface in case of a superluminally propagating laser-induced nonlinear polarization is considered. Using oblique incidence of the laser wave it is possible to tune frequencies of generated photons due to the Doppler effect. For every frequency smaller than frequency of induced polarization there exist an excitation angle when singular enhancement of the emission takes place. Emitted photon pairs are in the polarization entangled state. The yield of emission is estimated.
Photons with complex spatial mode structures open up possibilities for new fundamental high-dimensional quantum experiments and for novel quantum information tasks. Here we show for the first time entanglement of photons with complex vortex and singularity patterns called Ince-Gauss modes. In these modes, the position and number of singularities vary depending on the mode parameters. We verify 2-dimensional and 3-dimensional entanglement of Ince-Gauss modes. By measuring one photon and thereby defining its singularity pattern, we non-locally steer the singularity structure of its entangled par…
We investigate the geometrical and combinatorial structures of multipartite quantum systems based on conifold and toric variety. In particular, we study the relations between resolution of conifold, toric variety, a separable state, and a quantum entangled state for bipartite and multi-qubit states. For example we show that the resolved or deformed conifold is equivalent with the space of a pure entangled two-qubit state. We also generalize this result into multi-qubit states.
For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as a resource for tasks like the teleportation of arbitrarily many qubits. We show that appropriate states cannot be obtained by density operators in an infinite dimensional Hilbert space. However, using techniques for the description of infinitely many degrees of freedom from field theory and statistical mechanics, such states can nevertheless be constructed …
Based on the conception of quantum entanglement of Einstein-Podolsky-Rosen we construct generalized phase space representation associated with the entangled state |Gamma>_{e}, which is endowed with definite physical meaning. The set of states make up a complete and non-orthogonal representation. The Weyl ordered form of |Gamma>_{ee}_<Gamma| is derived which clearly exhibit the statistical behavior of marginal distribution of |Gamma>_{ee}_<Gamma|.The minimum uncertainty relation obeyed by |Gamma>_{e} is also demonstrated.
Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi-composite-boson states. We derive the two-fermion-states that extremize the normalization ratio for a fixed single-fermion purity P, and establish general tight bounds for this indicator. For very small purities, P<1/N^2, the upper and lower bounds converge, which allows to quantify accurately the departure from perfect…
By choosing H nucleus in Carbon-13 labelled trichloroethylene as one qubit environment, and two C nuclei as a two-qubit system, we have simulated quantum decoherence when the system lies in an entangled state using nuclear magnetic resonance (NMR). Decoupling technique is used to trace over the environment degrees of freedom. Experimental results show agreements with the theoretical predictions. Our experiment scheme can be generalized to the case that environment is composed of multiple qubits.
We demonstrate that single-photon as well as biphoton revivals are possible in a new class of dynamic optical systems-the so-called Glauber-Fock oscillator lattices. In these arrays, both Bloch-like oscillations and dynamic delocalization can occur which can be described in closed form. The bunching and anti-bunching response of path-entangled photons can be pre-engineered in such coupled optical arrangements and the possibility of emulating Fermionic behavior in this family of lattices is also considered. We elucidate these effects via pertinent examples and we discuss the prospect of experim…
We consider quantum systems in entangled states post-selected in non-entangled states. Such systems exhibit unusual behavior, in particular when weak measurements are performed at intermediate times.
We apply the theory of optimal control to the dynamics of two "gmon" qubits, with the goal of preparing a desired entangled ground state from an initial unentangled one. Given an initial state, a target state, and a Hamiltonian with a set of permissible controls, can we reach the target state with coherent quantum evolution and, in that case, what is the minimum time required? The adiabatic theorem provides a far from optimal solution in the presence of a spectral gap. Optimal control yields the fastest possible way of reaching the target state and helps identify unreachable states. In the con…
Using the representation introduced in \cite{frame}, an artificial game in quantum strategy space is proposed and studied. Although it has well-known classical correspondence, which has classical mixture strategy Nash Equilibrium states, the equilibrium state of this quantum game is an entangled strategy (operator) state of the two players. By discovering such behavior, it partially shows the independent meaning of the new representation. The idea of entanglement of strategies, instead of quantum states, is proposed, and in some sense, such entangled strategy state can be regarded as a coopera…
We study one-dimensional quantum walk with four internal degrees of freedom resulted from two entangled qubits. We will demonstrate that the entanglement between the qubits and its corresponding coin operator enable one to steer the walker's state from a classical to standard quantum-walk behavior, and a novel one. Additionally, we report on self-trapped behavior and perfect transfer with highest velocity for the walker. We also show that symmetry of probability density distribution, the most probable place to find the walker and evolution of the entropy are subject to initial entanglement bet…
We consider the kinematics of bi-partite quantum states as determined by observable quantities, in particular the Bloch vectors of the subsystems. In examining the simplest case of a pair of two-level systems, there is a remarkable connection between the presence of non-classical correlations and the chirality of the two bases generated by the singular value decomposition of the correlation matrix of the Bloch vectors. We investigate the limits imposed by quantum mechanics of this effect and it relationship with other methods on quantifying the system's non-classical behaviour.
According to Quantum Mechanics, the particles can exhibit either particle properties or wave properties depending on the experimental set up (wave-particle dualism). A special behavior occurs for a system of two entangled particles 1 and 2 that propagate along two different directions in the space. In such a case, the entangled particle 2 should exhibit either the particle behavior or the wave behavior depending on the kind of measurement that is performed on particle 1 whatever is the actual distance between the two particles. The apparently surprising fact is that the "choice" of what kind o…
Light beams having a vectorial field structure - or polarization - that varies over the transverse profile and a central optical singularity are called vector-vortex (VV) beams and may exhibit specific properties, such as focusing into "light needles" or rotation invariance, with applications ranging from microscopy and light trapping to communication and metrology. Individual photons in such beams exhibit a form of single-particle quantum entanglement between different degrees of freedom. On the other hand, the quantum states of two photons can be also entangled with each other. Here we combi…
When two-photon interactions are induced by down-converted light with a bandwidth that exceeds the pump bandwidth, they can obtain a behavior that is pulse-like temporally, yet spectrally narrow. At low photon fluxes this behavior reflects the time and energy entanglement between the down-converted photons. However, two-photon interactions such as two-photon absorption (TPA) and sum-frequency generation (SFG) can exhibit such a behavior even at high power levels, as long as the final state (i.e. the atomic level in TPA, or the generated light in SFG) is narrowband enough. This behavior does no…
We propose an experiment to investigate the possibility of long-distance thermodynamic relationships between two entangled particles. We consider a pair of spin 1/2 particles prepared in an entangled singlet state in which one particle is sent to Alice and the other to her distant mate Bob, who are spatially separated. Our proposed experiment consists of three different setups: First, both particles are coupled to two heat baths with various temperatures. In the second setup, only Alice's particle is coupled to a heat bath and finally, in the last setup, only Bob's particle is coupled to a hea…
We address the question of optimality of entangled input states in quantum Gaussian memory channels. For a class of such channels, that can be traced back to the memoryless setting, we state a criterion which relate the optimality of entangled inputs to the symmetry properties of the channels' action. Several examples of channel models belonging to this class are discussed.
These notes are more or less a faithful representation of my talk at the Workshop on ``Quantum Coding and Quantum Computing'' held at the University of Virginia. As such it is an introduction for non-physicists to the topics of the quantum theory of light and entangled states of light. In particular, I discuss the photon concept and what is really entangled in an entangled state of light (it is not the photons). Moreover, I discuss an example that highlights the peculiar behavior of entanglement in an infinite-dimensional Hilbert space.
We utilize IBM's quantum computers to perform a full quantum simulation of the optical quantum eraser (QE) utilizing a Mach-Zehnder interferometer with a variable partially-polarizing beam splitter (VPPBS) at the input. The use of the VPPBS motivates us to introduce the entangled quantum eraser, for which the path information is erased using a Bell-basis measurement. We also investigate the behavior of the wave aspect, i.e., the quantum coherence, as well as the particle character, represented by the predictability and entanglement, as delineated in complete complementarity relations (CCRs). A…
Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction procedures can become prohibitively time-consuming. Compressive sensing, a procedure for solving inverse problems by incorporating prior knowledge about the form of the solution, provides an attractive alternative to the problem of high-dimensional quantum state characterisation. Using a modified version of compressive sensing that incorporates the principles of…
We propose a scheme to investigate the time scale of the wave-function collapse by using polarization-entangled photon pairs. The setup is similar to those employed to investigate quantum correlations, but in the present case, synchronization is essential at all stages. We find that it is possible to discriminate between the scenarios of instantaneous collapse and finite-time reduction via a large number of double measurements of polarization. The quantities to be recorded would present distinct behaviors in each scenario, the deviations being small but distinguishable from pure statistical fl…
The possibility of generating a multi-hops network between different entangled nodes (qubits) via spin Dipolar interaction is examined. The negativity, tangle and the non-local coherent advantage are used as quantifiers of the generated quantum correlations. The phenomena of the sudden death/birth is displayed for the entangled two nodes, while the sudden changes phenomena (increasing/ decreasing) is depicted for all entangled three nodes. The amount of correlations between the different nodes depend on the initial network settings, where the largest amount is predicted if the network is initi…
Recent work has studied entanglement between the spin and momentum components of a single spin-1/2 particle and showed that maximal entanglement is obtained only when boosts approach the speed of light. Here we extend the boost scenario to general geometries and show that, intriguingly, maximal entanglement can be achieved with boosts less than the speed of light. Boosts approaching the speed of light may even decrease entanglement. We also provide a geometric explanation for this behavior.
We investigate how arbitrary number of entangled qubits affects properties of quantum walk. We consider variance, positions with non-zero probability density and entropy as criteria to determine the optimal number of entangled qubits in quantum walk. We show that for a single walker in one-dimensional position space, walk with three entangled qubits show better efficiency in considered criteria comparing to the walks with other number of entangled qubits. We also confirm that increment in number of the entangled qubits results into significant drop in variance of probability density distributi…
Detailed analysis of behavior of spin-entangled particle pairs under arbitrary rotations in their Hilbert space has been performed. It shows a rich range of varieties (faces) of entanglement in different bases. Analytic criteria are obtained for the respective faces of an entangled state. The corresponding conditions generally depend on both the state itself and the chosen basis. The most important result is revealing a deep analogy between a spin-entangled electronic qubit pair and momentum-entangled photon pair. Both cases exhibit coherence transfer from individual particles to nonlocal stat…
A system of cascaded qubits interacting via the oneway exchange of photons is studied. While for general operating conditions the system evolves to a superposition of Bell states (a dark state) in the long-time limit, under a particular resonance condition no steady state is reached within a finite time. We analyze the conditional quantum evolution (quantum trajectories) to characterize the asymptotic behavior under this resonance condition. A distinct bimodality is observed: for perfect qubit coupling, the system either evolves to a maximally entangled Bell state without emitting photons (the…
A theoretical scheme is introduced to generate entangled network via Dzyaloshinskii- Moriya (DM)interaction. The dynamics of entanglement generated between different nodes by direct or indirect interaction is investigated. It is shown that, the direction of (DM) interaction and the location of the nodes have a sensational effect on the degree of entanglement. We quantify the minimum entanglement generated between all the nodes. The upper and lower bound of the entanglement of the generated network depends on the direction of DM interaction and the repetition of the behavior depends on the stre…
Although it is widely accepted that classical information cannot travel faster than the speed of light in vacuum, the behavior of quantum correlations and quantum information propagating through actively-pumped fast-light media has not been studied in detail. To investigate this behavior, we send one half of an entangled state of light through a gain-assisted fast-light medium and detect the remaining quantum correlations. We show that the quantum correlations can be advanced by a small fraction of the correlation time while the entanglement is preserved even in the presence of noise added by …
The entanglement behavior of two classes of multi-qubit system, GHZ and GHZ like states passing through a generalized amplitude damping channel is discussed. Despite this channel causes degradation of the entangled properties and consequently their abilities to perform quantum teleportation, one can always improve the lower values of the entanglement and the fidelity of the teleportrd state by controlling on Bell measurements, analyzer angle and channel's strength. Using GHZ-like state within a generalized amplitude damping channel is much better than using the normal GHZ-state, where the deca…
In tripartite discrete systems, two classes of genuine tripartite entanglement have been discovered, namely, the Greenberger-Horne-Zeilinger (GHZ) class and the W class. To date, much research effort has been concentrated on the polarization entangled three-photon GHZ and W states. Most studies of continuous variable multiparticle entanglement have been focused on Gaussian states. In this Brief Report, we examine two classes of three-photon entangled states in space and time. One class is a three-mode three-photon entangled state and the other is a two-mode triphoton state. These states show b…
We consider the entanglement manipulation capabilities of the universal covariant quantum cloner or quantum processor circuit for quantum bits. We investigate its use for cloning a member of a bipartite or a genuine tripartite entangled state of quantum bits. We find that for bipartite pure entangled states a nontrivial behavior of concurrence appears, while for GHZ entangled states a possibility of the partial extraction of bipartite entanglement can be achieved.
We report experimental studies of the multi-photon quantum interference of a two-mode three-photon entangled Fock state $|2, 1\rangle$ + $|1, 2\rangle$ impinging on a two-port balanced beam splitter. When the distinguishability between the two input paths is increased, we observe a reduction followed by a resurgence of the quantum interference signal. We ascribe this unusual behavior to the competition among contributions from distinct numbers of interfering photons. Our theoretical analysis shows that this phenomenon will occur for any entangled Fock-state input of the form $|N, M\rangle$ + $…
The Two-State-Vector formalism and the Entangled Histories formalism are attempts to better understand quantum correlations in time. The main objective of this paper is to show that, with appropriately defined scalar products, both formalisms can be made isomorphic. We show that they treat operators and states on equal footing leading to the same statistics for all measurements. In particular, we discuss the topic of quantum correlations in time and show how they can be generated and analyzed in a consistent way in these formalisms. Furthermore, we elaborate on a novel behavior of quantum hist…
Investigating a class of models that is familiar in studies of cellular automata, we find that quantum operators can be employed to describe their long distance behavior. These operators span a Hilbert space that appears to turn such a model into a genuine quantum field theory, obeying the usual conditions of locality in terms of its quantum commutators. Entangled states can be constructed exactly as in quantum theories. This raises the question whether such models allow Bell's inequalities to be violated. Being a local, deterministic theory, one would argue that this is impossible, but since …
The quantumness of a generic state is the resource of many applications in quantum information theory and it is interesting to survey the measures which are able to detect its trace in the properties of the state. In this work we study the quantum discord and fully entangled fraction of two classes of bipartite states and compare their behaviors. These classes are complements to the $d\otimes d$ Werner and isotropic states, in the sense that each class possesses the same purification as the corresponding complemental class of states. Our results show that maximally entangled mixed states are a…
Ising interaction between qubits could produce distortion in entangled pairs generated for engineering purposes (as in quantum computation) in presence of parasite magnetic fields, destroying or altering the expected behavior of process in which is projected to be used. Quantum control could be used to correct that situation in several ways. Sometimes the user should be make some measurement upon the system to decide which is the best control scheme; other posibility is try to reconstruct the system using similar procedures without perturbate it. In the complete pictures both schemes are prese…
We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS), for studying the ground-state properties of quantum lattice models. These states extend the pair-correlation basis of projected entangled pair states (PEPS) to a simplex. PESS are an exact representation of the simplex solid states and provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of ten…
We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states appear as singularities in the dynamics of entanglement of smoothly varying quantum states. We illustrate this result by implementing a photonic parametric down conversion experiment. Moreover, this effect is connected to recently discovered singularities in condensed matter models.
Quantum walks in atomic systems, owing to their continuous nature, are especially well-suited for the simulation of many-body physics and can potentially offer an exponential speedup in solving certain black box problems. Photonics offers an alternate route to simulating such nonclassical behavior in a more robust platform. However, in photonic implementations to date, an increase to the depth of a continuous quantum walk requires modifying the footprint of the system. Here we report continuous walks of a two-photon quantum frequency comb with entanglement across multiple dimensions. The coupl…
In the present article, the robustness of entanglement in two qubits maximally entangled mixed states (MEME) have been studied under quantum decoherence channels. Here we consider bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels. To quantify the entanglement, the concurrence has been used as an entanglement measure. During this study interesting results have been found for sudden death and birth of entanglement under bit flip and bit-phase-flip channels. While amplitude damping channel produces entanglement sudden death and does not allow re-bi…
Bridging classical and quantum approaches in optical polarimetry: Predicting polarization-entangled photon behavior in scattering environments
Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学）；University of Oulu（奥卢大学）；Fraunhofer Institute for Applied Optics and Precision Engineering IOF（弗劳恩霍夫应用光学和精密工程研究所IOF）；Aston University（阿斯顿大学）
We consider a scattering set-up with an entangler and beam splitter where the current noise exhibits bunching behavior for electronic singlet states and antibunching behavior for triplet states. We show that the entanglement of two electrons in the double-dot can be detected in mesoscopic transport measurements. In the cotunneling regime the singlet and triplet states lead to phase-coherent current contributions of opposite signs and to Aharonov-Bohm and Berry phase oscillations in response to magnetic fields. We analyze the Fermi liquid effects in the transport of entangled electrons.
The behavior of games repeated in parallel, when played with quantumly entangled players, has received much attention in recent years. Quantum analogues of Raz's classical parallel repetition theorem have been proved for many special classes of games. However, for general entangled games no parallel repetition theorem was known. We prove that the entangled value of a two-player game $G$ repeated $n$ times in parallel is at most $c_G n^{-1/4} \log n$ for a constant $c_G$ depending on $G$, provided that the entangled value of $G$ is less than 1. In particular, this gives the first proof that the…
Adaptive Entangled Neurons in the Brain and Natural Intelligence Simulations for Artificial General Intelligence
Laboratory for Artificial Intelligence in Design（设计人工智能实验室）；Royal College of Art（皇家艺术学院）；University of Science and Technology of China（中国科学技术大学）；Red Horse Investments Group（红马投资集团）；Beijing Shangdafei Science & Technology Co., Ltd（北京尚大飞科技有限公司）
We analyze the dynamics of entanglement in a paradigmatic noninteracting system subject to continuous monitoring of the local excitation densities. Recently, it was conjectured that the evolution of quantum correlations in such system is described by a semi-classical theory, based on entangled pairs of ballistically propagating quasiparticles and inspired by the hydrodynamic approach to unitary (integrable) quantum systems. Here, however, we show that this conjecture does not fully capture the complex behavior of quantum correlations emerging from the interplay between coherent dynamics and co…
We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game $G$ of entangled value 1-eps < 1, the value of the $k$-fold repetition of G goes to zero as O((1-eps^c)^k), for some universal constant c\geq 1. Previously parallel repetition with an exponential decay in $k$ was only known for the case of XOR and unique games. To prove the theorem we extend an analytical framework recently introduced by Dinur and Steurer for the study of the classical value of projection games under parallel repetition. Our proo…
Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is obtained, and conditions for this realization are analyzed.
Human-centered systems of systems such as social networks, Internet of Things, or healthcare systems are growingly becoming major facets of modern life. Realistic models of human behavior in such systems play a significant role in their accurate modeling and prediction. Yet, human behavior under uncertainty often violates the predictions by the conventional probabilistic models. Recently, quantum-like decision theories have shown a considerable potential to explain the contradictions in human behavior by applying quantum probability. But providing a quantum-like decision theory that could pred…
We represent a two-qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the Bloch matrix components, leading to three important inequalities, allowing us to parametrize and visualize the two-qubit state space. Applying the singular value decomposition naturally separates the degrees of freedom to local and nonlocal, and simplifies the positivity inequalities. It also allows us to geometrically represent a state as two entangled Bloch …
