Maximally Entangled Mixed States Research Articles

Postponing the decay of entanglement and quantum coherence for maximally entangled mixed states under the action of correlated noise channels

We investigate the dynamics of a maximally entangled mixed state (MEMS) under the action of correlated noise channels. The channel acts in a way that its successive uses are correlated. We have studied the MEMS properties, including quantum coherence and entanglement. For partially correlated channels, both the entanglement and coherence of MEMS are found to decay much slower than those of the memoryless channels. Moreover, we observe a freezing effect of coherence for phase damping as well as depolarizing channels and freezing of entanglement for phase-damping channels with perfect memory. For amplitude damping and depolarizing channels, memory helps in either delaying the sudden death of entanglement or slowing the decay rate of coherence. These observations suggest that memory channels perform better than memoryless channels in maintaining the integrity of quantum states and have utility in quantum information processing protocols.

Open quantum system dynamics of X-states: Entanglement sudden death and sudden birth

In this paper, the origin of disentanglement for two specific sub-classes of [Formula: see text]-states namely maximally nonlocal mixed states (MNMSs) and maximally entangled mixed states (MEMSs) is investigated analytically for a physical system consisting of two spatially separated qubits interacting with a common vacuum bath. The phenomena of entanglement sudden death (ESD) and the entanglement sudden birth (ESB) are observed, but the characteristics of ESD and ESB are found to be different for the case of two-photon coherence and single photon coherence states. The role played by initial coherence for the underlying entanglement dynamics is investigated. Further, the entanglement dynamics of MNMSs and MEMSs under different environmental noises namely phase damping, amplitude damping and random telegraph noise (RTN) noise with respect to the decay and revival of entanglement is analyzed. It is observed that the single photon coherence states are more robust against the sudden death of entanglement, indicating the usability of such states in the development of technologies for the practical implementation of quantum information processing tasks.

Trade-off between Squashed Entanglement and Concurrence in Bipartite Quantum States

In this article we investigate the unitary dynamics of squashed entanglement and concurrence measures in Werner state and maximally entangled mixed states (MEMS) under two different Hamiltonians. The aim of the present study is two fold. The first part of the study deals with the dynamics under Heisenberg Hamiltonian and the second part deals under bi-linear bi-quadratic Hamiltonian which is the extension of first Hamiltonian. In both the parts we investigate the dynamical trade off and balancing points for squashed entanglement and concurrence. During the study, we also found the results of entanglement sudden death (ESD) with Heisenberg Hamiltonian in Werner state under concurrence measure. In second part, we investigate the special result for bi-linear bi-quadratic Hamiltonian; it does not disturb squashed entanglement and concurrence in both the states and exhibit the robust character for both of the states.

Entanglement Sudden Death and Birth Effects in Two Qubits Maximally Entangled Mixed States Under Quantum Channels

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-birth of entanglement. On the other hand, two qubits MEMS exhibit the robust character against the phase flip, phase damping and depolarization channels. The elegant behavior of all the quantum channels have been investigated with varying parameter of quantum state MEMS in different cases.

Broadcasting of quantum correlations in qubit-qudit systems

Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a task of utmost significance. One such strategy of broadcasting is through the application of cloning machines. In this article, broadcasting of quantum resources beyond $2 \otimes 2$ systems is investigated. In particular, in $2\otimes3$ dimension, a class of states not useful for broadcasting of entanglement is characterized for a choice of optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states (MEMS) and two parameter class of states (TPCS) are obtained to exemplify our protocol. A significant derivative of the protocol is the generation of entangled states with positive partial transpose in $3 \otimes 3$ dimension and states which are absolutely separable in $2 \otimes 2$ dimension. Moving beyond entanglement, in $2 \otimes d$ dimension, the impossibility to optimally broadcast quantum correlations beyond entanglement (QCsbE) (discord) and quantum coherence ($l_{1}$-norm) is established. However, some significant illustrations are provided to highlight that non-optimal broadcasting of QCsbE and coherence are still possible.

Influence of Dzyaloshinshkii–Moriya interaction on quantum correlations in two-qubit Werner states and MEMS

In this paper, we study the influence of Dzyaloshinskii–Moriya (DM) interaction on quantum correlations in two-qubit Werner states and maximally entangled mixed states (MEMS). We consider our system as a closed system of a qubit pair and one auxiliary qubit, which interact with any one of the qubit of the pair through DM interaction. We show that DM interaction, taken along any direction (x or y or z), does not affect two-qubit Werner states. On the other hand, the MEMS are affected by x and z components of DM interaction and remain unaffected by the y component. Further, we find that the state (i.e., probability amplitude) of auxiliary qubit does not affect the quantum correlations in both the states, and only DM interaction strength influences the quantum correlations. So one can avoid the intention to prepare the specific state of auxiliary qubit to manipulate the quantum correlations in both the states. We mention here that avoiding the preparation of state can contribute to cost reduction in quantum information processing. We also observe the phenomenon of entanglement sudden death in the present study.

Relevance of rank for a mixed state quantum teleportation resource

Mixed entangled states are generic resource for quantum teleportation. Optimal teleportation fidelity measures the success of quantum teleportation. The relevance of rank in the teleportation process is investigated by constructing three new maximally entangled mixed states (MEMS) of different ranks. Linear entropy, concurrence, optimal teleportation fidelity and Bell function are obtained for each of these states analytically. It is found that mixed states with higher rank are better resource for teleportation. In order to achieve a fixed value of optimal teleportation fidelity, we find that low rank states must have high concurrence. Further, for each of ranks 2, 3 and 4, we numerically generate 30000 maximally entangled mixed states. The analysis of these states reveals the existence of a rank dependent upper bound on optimal teleportation fidelity for a fixed purity. In order to achieve a fixed optimal teleportation fidelity, we find MEMS exhibit a rank dependent lower bound on concurrence. MEMS are classified in terms of their degree of nonlocality. The results are found to be same with logarithmic negativity used as a measure of entanglement.

Entanglement-induced geometric phase of quantum states

The concept of relative state is used to introduce geometric phases that originate from correlations in states of composite quantum systems. In particular, we identify an entanglement-induced geometric phase in terms of a weighted average of geometric phase factors associated with a decomposition that define the entanglement of formation. An explicit procedure to calculate the entanglement-induced geometric phase for qubit pairs is put forward. We illustrate it for maximally entangled mixed states (MEMS) of two qubits.

Linear optics and quantum maps

We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-\emph{vs}-quantum formalism, we show how two-qubit maximally entangled mixed states (MEMS), can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.

Entanglement, purity, and energy: Two qubits versus two modes

We study the relationship between the entanglement, mixedness and energy of two-qubit and two-mode Gaussian quantum states. We parametrize the set of allowed states of these two fundamentally different physical systems using measures of entanglement, mixedness and energy that allow us to compare and contrast the two systems using a phase diagram. This phase diagram enables one to clearly identify not only the physically allowed states, but the set of states connected under an arbitrary quantum operation. We pay particular attention to the maximally entangled mixed states (MEMS) of each system. Following this we investigate how efficiently one may transfer entanglement from two-mode to two-qubit states.

Concurrence versus purity: Influence of local channels on Bell states of two qubits

We analyze how a maximally entangled state of two-qubits (e.g., the singlet $\psi_s$) is affected by action of local channels described by completely positive maps $\cE$ . We analyze the concurrence and the purity of states $\varrho_\cE=\cE\otimes\cI[\psi_s]$.Using the concurrence-{\it vs}-purity phase diagram we characterize local channels $\cE$ by their action on the singlet state $\psi_s$. We specify a region of the concurrence-{\it vs.}-purity diagram that is achievable from the singlet state via the action of unital channels. We show that even most general (including non-unital) local channels acting just on a single qubit of the original singlet state cannot generate the maximally entangled mixed states (MEMS). We study in detail various time evolutions of the original singlet state induced by local Markovian semigroups. We show that the decoherence process is represented in the concurrence-{\it vs.}-purity diagram by a line that forms the lower bound of the achievable region for unital maps. On the other hand, the depolarization process is represented by a line that forms the upper bound of the region of maps induced by unital maps.

Ground-State Entanglement and Mixture in an XXZ Spin Chain

We study the pairwise entanglement and mixture of a three-qubit XXZspin chain in the ground state in the presence of an external magneticfield B. The effects of the magnetic field, the anisotropy and thetemperature on the entanglement and mixture are considered, andentanglement versus the mixture of all the two-spin states isinvestigated. We find that the maximal entangled mixed state can beobtained in the considered system by controlling the magnetic field. Ourresults provide another way to generate maximally entangled mixed states.

Generation of (2 × 2) and (4 × 4) two‐photon states with tunable degree of entanglement and mixedness

AbstractA parametric source of polarization entangled photon pairs with peculiar spatial characteristics allows to generate any kind of bi‐partite entangled states with tunable dgree of entanglement and mixedness. In particular, maximally entangled mixed states (MEMS) have been created in a reliable way by a “patchwork” technique and investigated by quantum tomography. By the same source, momentum‐polarization hyper‐entangled two‐photon states have been synthesized. The quality of the entanglement in the two degrees of freedom has been tested by multimode Hong‐Ou‐Mandel interferometry.

Maximally entangled mixed states: creation and concentration.

Using correlated photons from parametric down-conversion, we extend the boundaries of experimentally accessible two-qubit Hilbert space. Specifically, we have created and characterized maximally entangled mixed states that lie above the Werner boundary in the linear entropy-tangle plane. In addition, we demonstrate that such states can be efficiently concentrated, simultaneously increasing both the purity and the degree of entanglement. We investigate a previously unsuspected sensitivity imbalance in common state measures, i.e., the tangle, linear entropy, and fidelity.