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.
We study mutually unbiased bases (MUBs) in which all the bases are unextendible maximally entangled ones. We first present a necessary and sufficient condition of constructing a pair of MUBs in $C^2 \otimes C^4$. Based on this condition, an analytical and necessary condition for constructing MUBs is given. Moreover we illustrate our approach by some detailed examples in $C^2 \otimes C^4$. The results are generalized to $C^2 \otimes C^d$ $(d\geq 3)$ and a concrete example in $C^2 \otimes C^8$ is given.
Highly entangled multipartite states such as k-uniform (k-UNI) and absolutely maximally entangled (AME) states serve as critical resources in quantum networking and other quantum information applications. However, there does not yet exist a complete classification of such states, and much remains unknown about their entanglement structure. Here, we substantially broaden the class of known k-UNI and AME states by introducing a method for explicitly constructing such states that combines classical error correcting codes and qudit graph states. This method in fact constitutes a general recipe for…
A new way of constructing unextendible maximally entangled basis (UMEB) from maximally entangled basis (MEB) is proposed. Consequently, it is shown that if there is an $N$-member UMEB in $\mathbb{C}^d\otimes \mathbb{C}^d$, then there exists a $(qd)^2-q(d^2-N)$-member UMEB in $\mathbb{C}^{qd}\otimes \mathbb{C}^{qd}$ for any $q\in\mathbb{N}$. This improves the results in [Phys. Rev. A 90, 034301(2014)], which shows that there exists a $(qd)^2-(d^2-N)$-member UMEB in $\mathbb{C}^{qd}\otimes \mathbb{C}^{qd}$ provided that an $N$-member UMEB exsits in $\mathbb{C}^d\otimes \mathbb{C}^d$. In addition…
Numerical optimization methods such as hillclimbing and simulated annealing have been applied to search for highly entangled multi-qubit states. Here the genetic algorithm is applied to this optimization problem -- to search not only for highly entangled states, but also for the corresponding quantum circuits creating these states. Simple quantum circuits for maximally (highly) entangled states are discovered for 3, 4, 5, and 6-qubit systems; and extension of the method to systems with more qubits is discussed. Among other results we have found explicit quantum circuits for maximally entangled…
The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and six UPBs of size $9$ in $\cH=\bbC^2\ox\bbC^2\ox\bbC^4$, three UPBs of size $9$ in $\cK=\bbC^4\ox\bbC^4$, and no UPB of size $7$ in $\cH$ and $\cK$. Furthermore we construct a 4-qubit positive-partial-transpose (PPT) entangled state $\r$ of rank seven, and show that it is also a PPT entangled state in $\cH$ and $\cK$, respectively. We analytically derive the geometric measure of entanglement of a spec…
There is a connection between classical codes, highly entangled pure states (called k-uniform or absolutely maximally entangled (AME) states), and quantum error correcting codes (QECCs). This leads to a systematic method to construct stabilizer QECCs by starting from a k-uniform state or the corresponding classical code and tracing out one party at each step. We provide explicit constructions for codewords, encoding procedure and stabilizer formalism of the QECCs by describing the changes that partial traces cause on the corresponding generator matrix of the classical codes. We then modify the…
Entanglement allows for the nonlocality of quantum theory, which is the resource behind device-independent quantum information protocols. However, not all entangled quantum states display nonlocality, and a central question is to determine the precise relation between entanglement and nonlocality. Here we present the first general test to decide whether a quantum state is local, and that can be implemented by semidefinite programming. This method can be applied to any given state and for the construction of new examples of states with local hidden-variable models for both projective and genera…
We introduce orthogonal quantum Latin squares, which restrict to traditional orthogonal Latin squares, and investigate their application in quantum information science. We use quantum Latin squares to build maximally entangled bases, and show how a pair of mutually unbiased maximally entangled bases can be constructed in square dimension from orthogonal quantum Latin squares. We also compare our construction to an existing construction due to Beth and Wocjan and show that ours is strictly more general.
Absolutely maximally entangled (AME) states are pure multi-partite generalizations of the bipartite maximally entangled states with the property that all reduced states of at most half the system size are in the maximally mixed state. AME states are of interest for multipartite teleportation and quantum secret sharing and have recently found new applications in the context of high-energy physics in toy models realizing the AdS/CFT-correspondence. We work out in detail the connection between AME states of minimal support and classical maximum distance separable (MDS) error correcting codes and,…
The effects of the entanglement of the inflaton field which initially entangled with those of another field on observables like power spectrum are known in the context of the Schrödinger field theory. To clarify this effect in Heisenberg picture, there were some attempts to construct the initial entangled state by making use of an entangled transformation (like Bogoliubov transformation) between the Bunch-Davies vacuums and squeezed states. We study the role of the time-dependent entangled transformation in the Schrödinger field theory. We derive the relation between two vacuum states which th…
Genuinely entangled subspaces (GESs) are the class of completely entangled subspaces that contain only genuinely multiparty entangled states. They constitute a particularly useful notion in the theory of entanglement but also have found an application, for instance, in quantum error correction and cryptography. In a recent study (Demianowicz and Augusiak in Phys Rev A 98:012313, 2018), we have shown how GESs can be efficiently constructed in any multiparty scenario from the so-called unextendible product bases. The provided subspaces, however, are not of maximal allowable dimensions, and our a…
Constructing local hidden variable (LHV) models for entangled quantum states is challenging, as the model should reproduce quantum predictions for all possible local measurements. Here we present a simple method for building LHV models, applicable to general entangled states, which consists in verifying that the statistics resulting from a finite set of measurements is local, a much simpler problem. This leads to a sequence of tests which, in the limit, fully capture the set of quantum states admitting a LHV model. Similar methods are developed for constructing local hidden state models. We il…
We present detailed instructions for constructing and operating an apparatus to produce and detect polarization-entangled photons. The source operates by type-I spontaneous parametric downconversion in a two-crystal geometry. Photons are detected in coincidence by single-photon counting modules and show strong angular and polarization correlations. We observe more than 100 entangled photon pairs per second. A test of a Bell inequality can be performed in an afternoon.
We study unextendible maximally entangled basis in arbitrary bipartite spaces. A systematic way of constructing a set of $d^{2}$ orthonormal maximally entangled states in $\mathbb{C}^{d}\bigotimes\mathbb{C}^{d'}(\frac{d'}{2}<d<d')$ is provided. The complementary space of the set of these $d^{2}$ orthonormal maximally entangled states contains no maximally entangled states that are orthogonal to all of them. Furthermore, we investigate mutually unbiased bases in which all the bases are unextendible maximally entangled ones. We present two unextendible maximally entangled bases in $\mathbb{C}^{2…
Recently, Briegel et al. present a quantum repeaters protocol using nest entanglement purification for long distance quantum communication(Physical Review Letters \textbf{81},5932). In this paper we present a modified scheme for constructing an optimal quantum repeater using doubly entangled photon pairs that overcomes the limitations of quantum communication via noisy channels. Based on the imperfect quantum operations and classical communications, the polarization entangled quantum channels can be built with a better efficiency.
We demonstrate a general procedure to construct entanglement witnesses for any entangled state. This procedure is based on the trace inequality and a general form of entanglement witnesses, which is in the form $W=ρ-c_ρ I$, where $ρ$ is a density matrix, $c_ρ$ is a non-negative number related to $ρ$, and $I$ is the identity matrix. The general form of entanglement witnesses is deduced from Choi-Jamiołkowski isomorphism, that can be reinterpreted as that all quantum states can be obtained by a maximally quantum entangled state pass through certain completely positive maps. Furthermore, we provi…
Uniformly accelerated frame mimics a thermal bath whose temperature is proportional to the proper acceleration. Using this phenomenon we give a detailed construction of an Otto cycle between two energy eigenstates of a system, consists of two entangled qubits. In the isochoric stages the thermal bath is being provided via the vacuum fluctuations of the background field for a monopole interaction by accelerating them. We find that making of Otto cycle is possible when one qubit is accelerating in the right Rindler wedge and other one is moving in the left Rindler wedge; i.e. in anti-parallel mo…
It is shown that, every entangled state in an infinite-dimensional composite system has a simple entanglement witness of the form $αI+T$ with $α$ a nonnegative number and $T$ a finite rank self-adjoint operator. We also provide two methods of constructing entanglement witness and apply them to obtain some entangled states that cannot be detected by the PPT criterion and the realignment criterion.
The concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is a new type of multipartite entangled state, which has potential application in future quantum information. In this paper, we propose a protocol of constructing arbitrary C-GHZ entangled state approximatively. Different from the previous protocols, each logic is encoded in the coherent state. This protocol is based on the linear optics, which is feasible in experimental technology. This protocol may be useful in quantum information based on the C-GHZ state.
A hypothesis testing scheme for entanglement has been formulated based on the Poisson distribution framework instead of the POVM framework. Three designs were proposed to test the entangled states in this framework. The designs were evaluated in terms of the asymptotic variance. It has been shown that the optimal time allocation between the coincidence and anti-coincidence measurement bases improves the conventional testing method. The test can be further improved by optimizing the time allocation between the anti-coincidence bases.
The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of $2\times2\times4$ and $2\times2\times2\times4$ UPBs of size eight by using the existing four-qubit and five-qubit UPBs. As an application, we construct novel families of multipartite positive-partial-transpose entangled states, as well as their entanglement properties in terms of the geometric measure of entanglement.
Construction of genuinely entangled multipartite subspaces with certain characteristics has become a relevant task in various branches of quantum information. Here we show that such subspaces can be obtained from an arbitrary collection of bipartite entangled subspaces under joining of their adjacent subsystems. In addition, it is shown that direct sums of such constructions under certain conditions are genuinely entangled. These facts are then used in detecting entanglement of tensor products of mixed states and constructing subspaces that are distillable across every bipartite cut, where for…
The "Lewis-Riesenfeld phases" which plays a crucial role in constructing shortcuts to adiabaticity may be a resource for the implementation of quantum phase gates. By combining "Lewis-Riesenfeld invariant" with "quantum Zeno dynamics", we propose an effective scheme of rapidly implementing $π$ phase gates via constructing shortcuts to adiabatic passage in a two-distant-atom-cavity system. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity is discussed. It is noted that this scheme is insensitive to both two error sources. Additionally, a…
We present a method to certify the entanglement of all bipartite entangled quantum states in a device-independent way. This is achieved by placing the state in a quantum network and constructing a correlation inequality based on an entanglement witness for the state. Our method is device-independent, in the sense that entanglement can be certified from the observed statistics alone, under minimal assumptions on the underlying physics. Conceptually, our results borrow ideas from the field of self-testing to bring the recently introduced measurement-device-independent entanglement witnesses into…
In this work, new types of EWs are introduced. They are constructed by using real skew-symmetric operators defined on a single party subsystem of a bipartite dxd system and a maximal entangled state in that system. A canonical form for these witnesses is proposed which is called canonical EW in corresponding to canonical real skew-symmetric operator. Also for each possible partition of the canonical real skew-symmetric operator corresponding EW is obtained. The method used for dxd case is extended to d1xd2 systems. It is shown that there exist Cd2xd1 distinct possibilities to construct EWs for…
In this work, we present a general non-equilibrium ensemble formalism based on the subdynamic equation (SKE). The constructing procedure is to use a similarity transformation between Gibbsian ensemble formalism and the non-equilibrium ensemble formalism. The obtained density distribution is a projected one that can represent essence part of (irreversible) evolution of the density distribution, by which a generalized reduced density distribution for the quantum canonical ensembles is studied and applications in Cayley tree and spin network are discussed.
Quantum entanglement swapping is one of the most promising ways to realize the quantum connection among local quantum nodes. In this Letter, we present an experimental demonstration of the entanglement swapping between two independent multipartite entangled states, each of which involves a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state of an optical field. The entanglement swapping is implemented deterministically by means of a joint measurement on two optical modes coming from the two multipartite entangled states respectively and the classical feedforward of the measurement res…
By exploiting a system of three distant cavities, we propose a scheme for constructing tripartite entangled coherent GHZ and W states which are robust due to the photon losses in the cavities. Each of cavities is doped with a semiconductor quantum dot. By the dynamics, the excitonic modes of quantum dots are enabled to exhibit entan-gled coherent GHZ and W states. Apart from the exciton losses, the master equation approach shows that when the populations of the field modes in the cavities are negli-gible the destruction of entanglement due to decoherence arises from photon losses, is effective…
Quantum mechanics allows entanglement enhanced measurements to be performed, but loss remains an obstacle in constructing realistic quantum metrology schemes. However, recent work has revealed that entangled coherent states (ECSs) have the potential to perform robust sub-classical measurements [J. Joo et. al., Phys. Rev. Lett. 107, 83601 (2011)]. Up to now no read out scheme has been devised which exploits this robust nature of ECSs, but we present here an experimentally accessible method of achieving precision close to the theoretical bound, even with loss. We show substantial improvements ov…
We develop techniques to analyse the statistics of completion times of non-deterministic elements in quantum entanglement generation, and how they affect the overall performance as measured by the secret key rate. By considering such processes as Markov chains, we show how to obtain exact expressions for the probability distributions over the number of errors that a network acquires, as well as the distribution of entanglement establishment times. We show how results from complex analysis can be used to analyse Markov matrices to extract information with a lower computational complexity than p…
We extend the relation between absolutely maximally entangled (AME) states and quantum maximum distance separable (QMDS) codes by constructing whole families of QMDS codes from their parent AME states. We introduce a reduction-friendly form for the generator set of the stabilizer representation of an AME state, from which the stabilizer form for children codes, all QMDS, can be obtained. We then relate this to optimal codes for one-way quantum repeaters, by minimizing the short-term infrastructure cost as well as the long-term running cost of such quantum repeaters. We establish that AME state…
The unextendible entangled basis with any arbitrarily given Schmidt number $k$ (UEBk) in $\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}$ is proposed in [Phys. Rev. A 90 (2014) 054303], $1<k\leq \min\{d_1,d_2\}$, which is a set of orthonormal entangled states with Schmidt number $k$ in a $d_1\otimes d_2$ system consisting of fewer than $d_1d_2$ vectors which have no additional entangled vectors with Schmidt number $k$ in the complementary space. In this paper, we extend it to multipartite case and a general way of constructing $(m+1)$-partite UEBk from $m$-partite UEBk is proposed ($m\geq 2$). Conseq…
In this paper, we study the fast and noise-resistant population transfer, quantum entangled states preparation, and quantum entangled states' transition by constructing the shortcuts to adiabatic passage (STAP) for multiparticle based on the approach of "Lewis-Riesenfeld invariants" in distant cavity quantum electronic dynamics (QED) system. Numerical simulation demonstrates that all of the schemes are fast and robust against the decoherence caused by atomic spontaneous emission and photon leakage. Moreover, not only the total operation time but also the robustness in each scheme against decoh…
Quantum nonlocality of several four-qubit states is investigated by constructing a new Bell inequality. These include the Greenberger-Zeilinger-Horne (GHZ) state, W state, cluster state, and the state $|χ>$ that has been recently proposed in [PRL, {\bf 96}, 060502 (2006)]. The Bell inequality is optimally violated by $|χ>$ but not violated by the GHZ state. The cluster state also violates the Bell inequality though not optimally. The state $|χ>$ can thus be discriminated from the cluster state by using the inequality. Different aspects of four-partite entanglement are also studied by consideri…
According to usual definitions, entangled states cannot be given a separable decomposition in terms of products of local density operators. If we relax the requirement that the local density operators be positive, then an entangled quantum state may admit a separable decomposition in terms of more general sets of single-system operators. This form of separability can be used to construct classical models and simulation methods when only restricted set of measurements are available. With such motivations in mind, we ask what are the smallest such sets of local operators such that a pure biparti…
The correlations of certain entangled quantum states can be fully reproduced via a local model. We discuss in detail the practical implementation of an algorithm for constructing local models for entangled states, recently introduced by Hirsch et al. [Phys. Rev. Lett. 117, 190402 (2016)] and Cavalcanti et al. [Phys. Rev. Lett. 117, 190401 (2016)]. The method allows one to construct both local hidden state (LHS) and local hidden variable (LHV) models, and can be applied to arbitrary entangled states in principle. Here we develop an improved implementation of the algorithm, discussing the optimi…
A multipartite entanglement measure called the ent is presented and shown to be an entanglement monotone, with the special property of automatic normalization. Necessary and sufficient conditions are developed for constructing maximally entangled states in every multipartite system such that they are true-generalized X states (TGX) states, a generalization of the Bell states, and are extended to general nonTGX states as well. These results are then used to prove the existence of maximally entangled basis (MEB) sets in all systems. A parameterization of general pure states of all ent values is …
We present very simple method for constructing indecomposable entanglement witnesses out of a given pair -- an entanglement witness W and the corresponding state detected by W. This method may be used to produce new classes of atomic witnesses which are able to detect the `weakest' quantum entanglement. Actually, it works perfectly in the multipartite case, too. Moreover, this method provides a powerful tool for constructing new examples of bound entangled states.
In this paper we present reducible representation of the $n^{2}$ braid group representation which is constructed on the tensor product of n-dimensional spaces. By some combining methods we can construct more arbitrary $n^{2}$ dimensional braiding matrix S which satisfy the braid relations, and we get some useful braiding matrix S. By Yang-Baxteraition approach, we derive a $ 9\times9 $ unitary $ \breve{R}$ according to a $ 9\times9 $ braiding S-matrix we have constructed. The entanglement properties of $ \breve{R}$-matrix is investigated, and the arbitrary degree of entanglement for two-qutrit…
We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for checking separability that is based on finding state extensions with appropriate properties and may be implemented as a semidefinite program. The main result of this work is to show that there is a series of tests of this kind such that if a multiparty state is entangled this will eventually be detected by one of the tests. The procedure also provides a means of constructing entanglement witnesses that could in princip…
A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multi-qubits states. In particular, our present results are compared with those recently reported by Brown et al. [J. Phys. A: Math. Gen. 38 (2005) 1119]. The statistical distribution of entanglement values for the aforementioned multi-qubit systems is also explored.
We present two entanglement concentration protocols (ECPs) for arbitrary three-electron W state based on their charges and spins. Different from other ECPs, in both two ECPs, with the help of the electronic polarization beam splitter (PBS) and charge detection, the less-entangled W state can be concentrated into a maximally entangled state only with some single charge qubits. The second ECP is more optimal than the first one, for by constructing the complete parity check gate, the second ECP can be used repeatedly to further concentrate the less-entangled state and obtain a higher success prob…
We argue that the so-called entangled states in quantum theory are not something exceptional, deserving a special attention in our efforts to understand conceptual foundations of quantum world. They appear by constructing the basis states of a compound system via the basis states of entering subsystems and describe it as a wholeness. While a system is considered as a wholeness, the individual members, forming the entangled state, have no physical meaning. In consequence, there is no physical ground for Einstein, Podolsky and Rosen (EPR) correlations arising in a process of decaying the system,…
Semiconductor quantum dots are promising building blocks for quantum communication applications. Although deterministic, efficient, and coherent emission of entangled photons has been realized, implementing a practical quantum repeater remains outstanding. Here we explore the statistical limits for entanglement swapping with sources of polarization-entangled photons from the commonly used biexciton-exciton cascade. We stress the necessity of tuning the exciton fine structure, and explain why the often observed time evolution of photonic entanglement in quantum dots is not applicable for large …
A quantum memristor is a resistive passive circuit element with memory engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system-bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequency-entangled optical fields and …
Quantum-cryptography key distribution (QCKD) experiments have been recently reported using polarization-entangled photons. However, in any practical realization, quantum systems suffer from either unwanted or induced interactions with the environment and the quantum measurement system, showing up as quantum and, ultimately, statistical noise. In this paper, we investigate how ideal polarization entanglement in spontaneous parametric downconversion (SPDC) suffers quantum noise in its practical implementation as a secure quantum system, yielding errors in the transmitted bit sequence. Because al…
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…
Bohmian mechanics reproduces all statistical predictions of quantum mechanics, which ensures that entanglement cannot be used for superluminal signaling. However, individual Bohmian particles can experience superluminal influences. We propose to illustrate this point using a double double-slit setup with path-entangled photons. The Bohmian velocity field for one of the photons can be measured using a recently demonstrated weak-measurement technique. The found velocities strongly depend on the value of a phase shift that is applied to the other photon, potentially at spacelike separation.
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…
The paper discusses technical aspects of constructing a highly versatile multi-photon source. The source is able to generate up to four photons which is sufficient for a large number of quantum communications protocols. It can be set to generate separable, partially-entangled or maximally-entangled photon pairs with tunable amount of purity. Furthermore, the two generated pairs can be prepared in different quantum states. In this paper, we provide all the necessary information needed for construction and alignment of the source. To prove the working principle, we also provide results of thorou…
The generation of series of random numbers is an important and difficult problem. Appropriate measurements on entangled states have been proposed as the definitive solution, based on the impossibility of exploiting quantum non locality to get faster than light signaling. There is a controversy regarding what is preferable to produce series with utilizable randomness in practice, high or low entanglement. We prepare biphotons with three different levels of entanglement, easy entangled, marginally entangled and no entangled. Randomness is evaluated, independently of the quantum non locality argu…
We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)]. Such approximations allow to represent in an optimal way any density operator as a sum of a separable state and an entangled state of a certain form. For two qubit systems (M=N=2) the best separable approximation has a form of a mixture of a separable state and a projector onto a pure entangled state. We formulate a necessary condition that the pure state in t…
Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entanglement, i.e. a curious form of entanglement that can also not be distilled into maximally (free) entangled states. Only a few bound entangled states have been found, typically by constructing dedicated entanglement witnesses, so naturally the question arises how large is the volume of those states. We define a l…
We discuss and generalize multi-particle entanglement based on statistical correlations using Ursell-Mayer type of cluster coefficients. Cluster coefficients are used to distinguish different, independent entangled systems as well as those which are connected through local unitary transformations. We propose a genuinely and maximally entangled five-particle state for efficient information processing. The physical realization of entangled states and information processing protocols are analyzed using quantum gates and circuit diagrams. We show that the direct as well as controlled communication…
