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Register a new userConditional purity and quantum correlation measures in two qubit mixed states
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We analyze and show experimental results of the conditional purity, the quantum discord and other related measures of quantum correlation in mixed two-qubit states constructed from a pair of photons in identical polarization states. The considered states are relevant for the description of spin pair states in interacting spin chains in a transverse magnetic field. We derive clean analytical expressions for the conditional local purity and other correlation measures obtained as a result of a remote local projective measurement, which are fully verified by the experimental results. A simple exact expression for the quantum discord of these states in terms of the maximum conditional purity is also derived.
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To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fidelity of a teleported state depends on the resource state purity and entanglement, as characterized by concurrence. Concurrence and purity are functions of state parameters. However, it turns out that a state with larger purity and concurrence, may have comparatively smaller fidelity. By computing teleportation fidelity, concurrence and purity for two-qubit X-states, we show it explicitly. We further show that fidelity changes monotonically with respect to functions of parameters - other than concurrence and purity. A state with smaller concurrence and purity, but larger value of one of these functions has larger fidelity. These functions, thus characterize nonlocal classical and/or quantum properties of the state that are not captured by purity and concurrence alone. In particular, concurrence is not enough to characterize the entanglement properties of a two-qubit mixed state.
Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more subtle for the more general case of mixed quantum states often found in practice. A large number of different proposals exist. In this review, we summarize the required properties of a quantum fidelity measure, and compare them, to determine which properties each of the different measures has. We show that there are large classes of measures that satisfy all the required properties of a fidelity measure, just as there are many norms of Hilbert space operators, and many measures of entropy. We compare these fidelities, with detailed proofs of their properties. We also summarize briefly the applications of these measures in teleportation, quantum memories, quantum computers, quantum communications, and quantum phase-space simulations.
It is known that protocols based on weak measurements can be used to steer quantum systems into pre-designated pure states. Here we show that weak-measurement-based steering protocols can be harnessed for on-demand engineering of $textit{mixed}$ states. In particular, through a continuous variation of the protocol parameters, one can guide a classical target state to a discorded one, and further on, towards an entangled target state.
We examine, in correlated mixed states of qudit-qubit systems, the set of all conditional qubit states that can be reached after local measurements at the qudit based on rank-1 projectors. While for a similar measurement at the qubit, the conditional post-measurement qudit states lie on the surface of an ellipsoid, for a measurement at the qudit we show that the set of post-measurement qubit states can form more complex solid regions. In particular, we show the emergence, for some classes of mixed states, of sets which are the convex hull of solid ellipsoids and which may lead to cone-like and triangle-like shapes in limit cases. We also analyze the associated measurement dependent conditional entropy, providing a full analytic determination of its minimum and of the minimizing local measurement at the qudit for the previous states. Separable rank-2 mixtures are also discussed.
The ability to reach a maximally entangled state from a separable one through the use of a two-qubit unitary operator is analyzed for mixed states. This extension from the known case of pure states shows that there are at least two families of gates which are able to give maximum entangling power for all values of purity. It is notable that one of this gates coincides with a maximum discording one. We give analytical proof that such gate is indeed perfect entangler at all purities and give numerical evidence for the existence of the second one. Further, we find that there are other gates, many in fact, which are perfect entanglers for a restricted range of purities. This highlights the fact that many perfect entangler gates could in principle be found if a thorough analysis of the full parameter space is performed.
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