An entangled two-mode coherent state is studied within the framework of $2\times 2$ dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.
In this paper, we study the superposition invariance of unitary operators and maximally entangled state respectively. Furthermore, we discuss the set of orthogonal maximally entangled states. We find that orthogonal basis of maximally entangled states can be divided into k subspaces. It is shown that some entanglement properties of superposed state in every subspace are invariant.
Suppose that we have two entangled states $\ket {ϕ_1}$, $\ket{ψ_1}$ that cannot be converted to any of other two states $\ket{ϕ_2}$, $\ket{ψ_2}$ by local operations and classical communication. We analyze the possibility of locally transforming a superposition of $\ket{ϕ_1}$ and $\ket{ψ_1}$ into a superposition of $\ket{ϕ_2}$ and $\ket{ψ_2}$. By using the Nielsen's theorem we find the necessary and sufficient conditions for this conversion to be performed.
We propose a scheme for the generation and reconstruction of entangled states between the internal and external (motional) degrees of freedom of a trapped electron. Such states also exhibit quantum coherence at a mesoscopic level.
A new entangled quantum state is introduced by applying local coherent superposition (ra^+ +ta) of photon subtraction and addition to each mode of even entangled coherent state (EECS) and the properties of entanglement are investigated. It is found that the Shchukin-Vogel inseparability, the degree of entanglement and the average fidelity of quantum teleportation of the EECS can be improved due to the coherent superposition operation. The effects of improvement by coherent superposition operation are better than those by single (a^+) and two-photon (a^+ b^+) addition operations under a small r…
A multiparticle quantum superposition state has been generated by a novel phase-selective parametric amplifier of an entangled two-photon state. This realization is expected to open a new field of investigations on the persistence of the validity of the standard quantum theory for systems of increasing complexity, in a quasi decoherence-free environment. Because of its nonlocal structure the new system is expected to play a relevant role in the modern endeavor on quantum information and in the basic physics of entanglement.
The entangled state that results when a detector measures a superposed quantum system has spawned decades of concern about the problem of definite outcomes or "Schrodinger's cat." This state seems to describe a detector in an indefinite or "smeared" situation of indicating two macroscopic configurations simultaneously. This would be paradoxical. Since all entangled states are known to have nonlocal properties, and since measurements have obvious nonlocal characteristics, it's natural to turn to nonlocality experiments for insight into this question. Unlike the measurement situation where the p…
We suggest a variant of the recently proposed experiment for the generation of a new kind of Schroedinger-cat states, using two coupled parametric down-converter nonlinear crystals [F. De Martini, Phys. Rev. Lett. 81, 2842 (1998)]. We study the parametric oscillator case and find that an entangled Schroedinger-cat type state of two cavities, whose mirrors are placed along the output beams of the nonlinear crystals, can be realized under suitable conditions.
This paper proposes a scheme for teleporting an arbitrary coherent superposition state of two equal-amplitude and opposite-phase squeezed vacuum states (SVS) via a symmetric 50/50 beam splitter and photodetectors. It is shown that the quantum teleportation scheme has the successful probability 1/4. Maximally entangled SVS's are used as quantum channel for realizing the teleportation scheme. It is shown that if an initial quantum channel is in a pure but not maximally entangled SVS, the quantum channel may be distilled to a maximally entangled SVS through entanglement concentration.
Theory and experiment both demonstrate that an entangled quantum state of two subsystems is neither a superposition of states of its subsystems nor a superposition of composite states but rather a coherent superposition of nonlocal correlations between incoherently mixed local states of the two subsystems. Thus, even if one subsystem happens to be macroscopic as in the entangled "Schrodinger's cat" state resulting from an ideal measurement, this state is not the paradoxical macroscopic superposition it is generally presumed to be. It is, instead, a "macroscopic correlation," a coherent quantum…
We present a scheme for demonstrating violation of Bell's inequalities using a spin-1/2 system entangled with a pair of classically distinguishable wave packets in a harmonic potential. In the optical domain, such wave packets can be represented by coherent states of a single light mode. The proposed scheme involves standard spin-1/2 projections and measurements of the position and the momentum of the harmonic oscillator system, which for a light mode can be realized by means of homodyne detection. We discuss effects of imperfections, including non-unit efficiency of the homodyne detector, and…
We proposed two linear optics based entanglement concentration protocols (ECPs) to obtain maximally entangled 4-mode Cluster-type entangled coherent state (ECS) from less (partially) entangled Cluster-type ECS. The first ECP is designed using a superposition of single-mode coherent state with two unknown parameters, whereas the second ECP is obtained using a superposition of single-mode coherent state and a superposition of two-mode coherent state with four unknown parameters. The success probabilities have been calculated for both the ECPs. Necessary quantum circuits enabling future experimen…
We examine Einstein-Podolsky-Rosen's (EPR) steering nonlocality for two realisable Schrodinger cat-type states where a meso/ macroscopic system (called the "cat"-system) is entangled with a spin-$1/2$ system. For large cat-systems, we show that a local hidden state model is near-satisfied, meaning that the cat-system can be consistent with being in a mixture of "dead" and "alive" states despite that it is entangled with the spin system. We justify that a rigorous signature of the Schrodinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This le…
Two quantum Macro-states and their Macroscopic Quantum Superpositions (MQS) localized in two far apart, space - like separated sites can be non-locally correlated by any entangled couple of single-particles having interacted in the past. This novel Macro - Macro paradigm is investigated on the basis of a recent study on an entangled Micro-Macro system involving N=10^5 particles. Crucial experimental issues as the violation of Bell's inequalities by the Macro - Macro system are considered.
We study the conditions when mixtures of entangled pure states with maximally mixed one-qudit reduced density matrices remain entangled. We found that the resulting mixed state remains entangled when the number of entangled pure states to be mixed is less than or equal to the dimension of the pure states. For the latter case of mixing a number of pure states equal to their dimension, we found that the mixed state is entangled provided that the entangled pure states to be mixed are not equally weighted. We also found that one can restrict the set of pure states that one can mix from in order to…
The multiphoton quantum superposition generated by a quantum-injected optical parametric amplifier (QI-OPA) seeded by a single-photon belonging to an EPR entangled pair is made to interact with a Mirror-BEC shaped as a Bragg interference structure. The effect can be greatly enhanced if the mirror is part of a cavity structure or is used within an optical interferometer. The overall process will realize an Entangled Macroscopic Quantum Superposition involving a ''microscopic'' singe-photon state of polarization and the coherent ''macroscopic'' displacement of the BEC structure acting in space-l…
We study a class of mixed non-Gaussian entangled states that, whilst closely related to Gaussian entangled states, none-the-less exhibit distinct properties previously only associated with more exotic, pure non-Gaussian states.
We present the proposition of an experiment in which the multiphoton quantum superposition consisting of N= 10^5 particles generated by a quantum-injected optical parametric amplifier (QI-OPA), seeded by a single-photon belonging to an EPR entangled pair, is made to interact with a Mirror-BEC shaped as a Bragg interference structure. The overall process will realize a Macroscopic Quantum Superposition (MQS) involving a microscopic single-photon state of polarization entangled with the coherent macroscopic transfer of momentum to the BEC structure, acting in space-like separated distant places.
Quantum entanglement and quantum nonlocality of $N$-photon entangled states $|ψ_{N m}> =\mathcal{N}_{m}[\cosγ|N-m>_{1}|m>_{2} +e^{iθ_{m}}\sinγ|m>_{1}|N-m>_{2}]$ and their superpositions are studied. We indicate that the relative phase $θ_{m}$ affects quantum nonlocality but not quantum entanglement for the state $|ψ_{N m}>$. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of $|ψ_{N m}>$, superposition coefficients, and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal valu…
Quantum information science is driving progress in a vast number of scientific and technological areas that cover molecular spectroscopy and matter-light interactions in general. In these fields, the ability to generate quantum mechanically-entangled photons is opening avenues to explore the interaction of molecules with quantum light. This work considers an alternative way of correlating photons by including energy superpositions. We study how the multichromatic quantum superposition, or color superposition of photon-pair states, influences the optical properties of organic chromophores. This…
Schrodinger's famous cat has long been misunderstood. According to quantum theory and experiments with entangled systems, an entangled state such as the Schrodinger's cat state is neither a superposition of states of either subsystem nor a superposition of compound states of the composite system, but rather a nonlocal superposition of correlations between pairs of states of the two subsystems. The entangled post-measurement state that results from an ideal measurement is not paradoxical, but is merely a coherent superposition of two statistical correlations at "zero phase angle," i.e. at 100% …
We provide a scheme for the generation of entangled number states of Bose-Einstein condensates in multiple wells with cyclic pairwise connectivity. The condensate ground state in a multiple well trap can self-evolve, when phase engineered with specific initial phase differences between the neighboring wells, to a macroscopic superposition state with controllable entanglement -- to multiple well generalization of double well NOON states. We demonstrate through numerical simulations the creation of entangled states in three and four wells and then explore the creation of "larger" entangled state…
In two-mode interferometry, for a given total photon number $N$, entangled Fock state superpositions of the form $(|N-m\rangle_a|m\rangle_b+e^{i (N-2m)ϕ}|m\rangle_a|N-m\rangle_b)/\sqrt{2}$ have been considered for phase estimation. Indeed all such states are maximally mode-entangled and violate a Clauser-Horne-Shimony-Holt (CHSH) inequality. However, they differ in their optimal phase estimation capabilities as given by their quantum Fisher informations. The quantum Fisher information is the largest for the $N00N$ state $(|N\rangle_a|0\rangle_b+e^{i Nϕ}|0\rangle_a|N\rangle_b)/\sqrt{2}$ and dec…
We show that it is possible to achieve maximally entangled mixed states of two qubits from the singlet state via the action of local non-trace-preserving quantum channels. Moreover, we present a simple, feasible linear optical implementation of one of such channels.
In some off-resonant cases, the reduced density matrix of two atoms symmetrically coupled with an optical cavity can very approximately approach to maximally entangled mixed states or maximal Bell violation mixed states in their evolution. The influence of phase decoherence on the generation of maximally entangled mixed state is also discussed. PACS numbers: 03.67.-a, 03.65.Ud
We study the degree of entanglement of arbitrary superpositions of $m,n$ photon-added coherent states (PACS) $|ψ\rangle \propto u |α,m\rangle |β,n \rangle+ v |β,n\rangle |α,m\rangle$ using the concurrence, and obtain the general conditions for maximal entanglement. We show that photon addition process can be identified as an entanglement enhancer operation for superpositions of coherent states (SCS). Specifically for the known bipartite positive SCS: $|ψ\rangle \propto |α\rangle_a |-α\rangle_b + |-α\rangle_a |α\rangle_b $ whose entanglement tends to zero for $α\to 0$, can be maximal if al leas…
We consider the case of a pair of particles initially in a superposition state corresponding to a separated pair of wave packets. We calculate \emph{exactly} the time development of this non-Gaussian state due to interaction with an \emph{arbitrary} heat bath. We find that coherence decays continuously, as expected. We then investigate entanglement and find that at a finite time the system becomes separable (not entangled). Thus, we see that entanglement sudden death is also prevalent in continuous variable systems which should raise concern for the designers of entangled systems.
We investigate entanglement properties of a recently introduced class of macroscopic quantum superpositions in two-mode mixed states. One of the tools we use in order to infer the entanglement in this non-Gaussian class of states is the power to entangle a qubit system. Our study reveals features which are hidden in a standard approach to entanglement investigation based on the uncertainty principle of the quadrature variables. We briefly describe the experimental setup corresponding to our theoretical scenario and a suitable modification of the protocol which makes our proposal realizable wit…
We present a full definition of mixed maximally entangled (MME) states for multipartite systems, generalizing their existing definition for bipartite systems by using multipartite Schmidt decomposition. MME states are a special kind of maximally entangled mixed state (MEMS) for which every pure decomposition state in all decompositions is maximally entangled. Thus, MME states have entanglement 1 by all valid unit-normalized entanglement measures, whereas general MEMS can have entanglement less than 1. Multipartite MME states likely have important applications such as remote state preparation, …
We study the fully entangled fraction of a quantum state. An upper bound is obtained for arbitrary bipartite system. This upper bound only depends on the Frobenius norm of the state.
We study the efficacy of two-qubit mixed entangled states as resources for quantum teleportation. We first consider two maximally entangled mixed states, viz., the Werner state\cite{werner}, and a class of states introduced by Munro {\it et al.} \cite{munro}. We show that the Werner state when used as teleportation channel, gives rise to better average teleportation fidelity compared to the latter class of states for any finite value of mixedness. We then introduce a non-maximally entangled mixed state obtained as a convex combination of a two-qubit entangled mixed state and a two-qubit separa…
Presented is a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a superbraid. The crossing of world lines is purely quantum in nature, most conveniently expressed analytically with ladder-operator-based quantum gates. At a crossing, independent world lines can become entangled. Complicated superbraids are systematically reduced by recursively applying novel quantum skein relations. If the superbraid is closed (e.g. representing quantum circuits with closed-loop feedback, quantum lattice gas …
We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectl…
We report experimental results on mixed-state generation by multiple scattering of polarization-entangled photon pairs created from parametric down-conversion. By using a large variety of scattering optical systems we have experimentally obtained entangled mixed states that lie upon and below the Werner curve in the linear entropy-tangle plane. We have also introduced a simple phenomenological model built on the analogy between classical polarization optics and quantum maps. Theoretical predictions from such model are in full agreement with our experimental findings.
We propose a scheme for preparing arbitrary two photons polarization entangled mixed states via controlled location decoherence. The scheme uses only linear optical devices and single-mode optical fibers, and may be feasible in experiment within current optical technology.
We examine the maximum negative energy density which can be attained in various quantum states of a massless scalar field. We consider states in which either one or two modes are excited, and show that the energy density can be given in terms of a small number of parameters. We calculate these parameters for several examples of superposition states for one mode, and entangled states for two modes, and find the maximum magnitude of the negative energy density in these states. We consider several states which have been, or potentially will be, generated in quantum optics experiments.
We prove that for many ranks r<2m-2, random rank r mixed states in bipartite mxm systems have relatively high Schmidt numbers, which is based on algebraic-geometric separability criterion proved in [1]. This also means that the algebraic-geometric separability criterion can be used to detect all low rank entangled mixed states outside a measure zero set.
We present a general theoretical method to generate maximally entangled mixed states of a pair of photons initially prepared in the singlet polarization state. This method requires only local operations upon a single photon of the pair and exploits spatial degrees of freedom to induce decoherence. We report also experimental confirmation of these theoretical results.
We propose novel mixed states in two qubits, ``maximally entangled mixed states'', which have a property that the amount of entanglement of these states cannot be increased further by applying any unitary operations. The property is proven when the rank of the states is less than 4, and confirmed numerically in the other general cases. The corresponding entanglement of formation specified by its eigenvalues gives an upper bound of that for density matrices with same eigenvalues.
Entangled pure-states, Werner-states and generalized mixed-states of any structure, spanning a 2x2 Hilbert space are created by a novel high-brilliance universal source of polarization-entangled photon pairs. The violation of a Bell inequality has been tested for the first time with a pure-state, indeed a conceptually relevant ideal condition, and with Werner-states. The generalized ''maximally entangled mixed states'' (MEMS) were also synthetized for the first time and their exotic properties investigated by means of a quantum tomographic technique.
We describe a set of measurement protocols for performing non-classicality tests and the verification of entangled superposition states of macroscopic continuous variable systems, such as nanomechanical resonators. Following earlier works, we first consider a setup where a two-level system is used to indirectly probe the motion of the mechanical system via Ramsey measurements and discuss the application of this methods for detecting non-classical mechanical states. We then show that the generalization of this techniques to multiple resonator modes allows the conditioned preparation and the det…
Entanglement of superpositions in zero-energy subspace: insights from stabilizer theory
Faculty of Physics, M.V. Lomonosov Moscow State University（莫斯科国立大学物理系）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Artificial Intelligence Research Institute (AIRI)（人工智能研究院）
Quantum nonlocality is tested for an entangled coherent state, interacting with a dissipative environment. A pure entangled coherent state violates Bell's inequality regardless of its coherent amplitude. The higher the initial nonlocality, the more rapidly quantum nonlocality is lost. The entangled coherent state can also be investigated in the framework of $2\times2$ Hilbert space. The quantum nonlocality persists longer in $2\times2$ Hilbert space. When it decoheres it is found that the entangled coherent state fails the nonlocality test, which contrasts with the fact that the decohered enta…
Three-qubit mixed states are used as a channel for controlled quantum teleportation (CQT) of single-qubit states. The connection between different channel parameters to achieve maximum controlled teleportation fidelity is investigated. We show that for a given multipartite entanglement and mixedness, a class of non-maximally entangled mixed $X$ states ($X-$NMEMS) achieves optimum controlled quantum teleportation fidelity, interestingly a class of maximally entangled mixed $X$ states ($X-$MEMS) fails to do so. This demonstrates, for a given spectrum and mixedness, that $X-$MEMS are not sufficie…
A scheme for generating the maximally entangled mixed state of two atoms on-resonance asymmetrically coupled to a single mode optical cavity field is presented. The part frontier of both maximally entangled mixed states and maximal Bell violating mixed states can be approximately reached by the evolving reduced density matrix of two atoms if the ratio of coupling strengths of two atoms is appropriately controlled. It is also shown that exchange symmetry of global maximal concurrence is broken if and only if coupling strength ratio lies between $\frac{\sqrt{3}}{3}$ and $\sqrt{3}$ for the case o…
Purifying noisy entanglement is a protocol which can increase the entanglement of a mixed state (as a source)at expense of the entanglement of others(as an ancilla)by collective measurement. A protocol with which one can get a pure entangled state from a mixed state is defined as purifying mixed states. We address a basic question: can one get a pure entangled state from a mixed state? We give a necessary and sufficient condition of purifying a mixed state by fit local operations and classical communication and show that for a class of source states and ancilla states in arbitrary bipartite sy…
Many non-classicality indicators are used to measure quantum effects of different systems. Kenfack's and Sadeghi's non-classicality indicators are introduced in terms of the amount of Wigner function's negativities and interferences in phase space quantum mechanics, respectively. They are, effectively, applied for some real distribution functions. In this paper, we compared these non-classicality indicators for the entangled state of photonic number states in the Wigner, Husimi and Rivier representations. It is shown that for a two-level entangled state, Sadeghi's indicator has more benefits w…
We constructed a class of non-maximally entangled mixed states \cite{roy2010} and extensively studied its entanglement properties and also their usefulness as teleportation channels. In this article, we revisited our constructed state and have studied it from three different perspectives. Since every entangled state is associated with an witness operator, we have found a suitable entanglement as well as teleportation witness for our non-maximally entangled mixed states. We considered the noisy channel's effects on our constructed state and to see whether it affects the states' capacity as tele…
The maximally entangled mixed states of Munro, James, White, and Kwiat [Phys. Rev. A {\bf 64} (2001) 030302] are shown to exhibit interesting features vis a vis conditional entropic measures. The same happens with the Ishizaka and Hiroshima states [Phys. Rev. A {\bf 62} 022310 (2000)], whose entanglement-degree can not be increased by acting on them with logic gates. Special types of entangled states that do not violate classical entropic inequalities are seen to exist in the space of two qubits. Special meaning can be assigned to the Munro {\it et al.} special participation ratio of 1.8.
Using a geometric measure of entanglement quantification based on Euclidean distance of the Hermitian matrices, we obtain the minimum distance between a bipartite bound entangled $n$- qudit density matrix and the maximally mixed state.This minimum distance for which entangled density matrices necessarily have positive partial transpose (PPT) is obtained as $\frac{1}{\sqrt{\sqrt{d^n(d^n-1)}+1}}$, which is also a lower limit for the existence of 1-distillable entangled states. The separable states necessarily lie within a minimum distance of $\frac{R}{1+d^{n-1}}$ from the Identity,where R is the…
The ability to teleport entanglement through maximally entangled mixed states as defined by concurrence and linear entropy is studied. We show how the teleported entanglement depends on the quality of the quantum channel used, as defined through its entanglement and mixedness, as well as the form of the target state to be teleported. We present new results based on the fidelity of the teleported state as well as an experimental set-up that is immediately implementable with currently available technology.
We consider mixed states of two qubits and show under which global unitary operations their entanglement is maximized. This leads to a class of states that is a generalization of the Bell states. Three measures of entanglement are considered: entanglement of formation, negativity and relative entropy of entanglement. Surprisingly all states that maximize one measure also maximize the others. We will give a complete characterization of these generalized Bell states and prove that these states for fixed eigenvalues are all equivalent under local unitary transformations. We will furthermore chara…
