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Register a new userRemote one-qubit state control by pure initial state of two-qubit sender. Selective-region- and eigenvalue-creation
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We study the problem of remote one-qubit mixed state creation using a pure initial state of two-qubit sender and spin-1/2 chain as a connecting line. We express the parameters of creatable states in terms of transition amplitudes. We show that the creation of complete receivers state-space can be achieved only in the chain engineered for the one-qubit perfect state transfer (PST) (for instance, in the fully engineered Ekert chain), the chain can be arbitrarily long in this case. As for the homogeneous chain, the creatable receivers state region decreases quickly with the chain length. Both homogeneous chains and chains engineered for PST can be used for the purpose of selective state creation, when only the restricted part of the whole receivers state space is of interest. Among the parameters of the receivers state, the eigenvalue is the most hard creatable one and therefore deserves the special study. Regarding the homogeneous spin chain, an arbitrary eigenvalue can be created only if the chain is of no more then 34 nodes. Alternating chain allows us to increase this length up to 68 nodes.
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We study the optimization problem for remote one- and two-qubit state creation via a homogeneous spin-1/2 communication line using the local unitary transformations of the multi-qubit sender and extended receiver. We show that the maximal length of a communication line used for the needed state creation (the critical length) increases with an increase in the dimensionality of the sender and extended receiver. The model with the sender and extended receiver consisting of up to 10 nodes is used for the one-qubit state creation and we consider two particular states: the almost pure state and the maximally mixed one. Regarding the two-qubit state creation, we numerically study the dependence of the critical length on a particular triad of independent eigenvalues to be created, the model with four-qubit sender without an extended receiver is used for this purpose.
We consider the problem of $1$-sided device-independent self-testing of any pure entangled two-qubit state based on steering inequalities which certify the presence of quantum steering. In particular, we note that in the $2-2-2$ steering scenario (involving $2$ parties, $2$ measurement settings per party, $2$ outcomes per measurement setting), the maximal violation of a fine-grained steering inequality can be used to witness certain extremal steerable correlations, which certify all pure two-qubit entangled states. We demonstrate that the violation of analogous CHSH inequality of steering or nonvanishing value of a quantity constructed using a correlation function called mutual predictability together with the maximal violation of fine-grained steering inequality can be used to self-test any pure entangled two-qubit state in a $1$-sided device-independent way.
A qubit chosen from equatorial or polar great circles on a Bloch sphere can be remotely prepared with an Einstain-Podolsky-Rosen (EPR) state shared and a cbit communication. We generalize this protocal into an arbitrary longitudinal qubit on the Bloch sphere in which the azimuthal angle phi can be an arbitrary value instead of only being zero. The generalized scheme was experimentally realized using liquid-state nuclear magnetic resonance (NMR) techniques. Also, we have experimentally demonstrated remote state measurement (RSM) on an arbitary qubit proposed by Pati.
We consider a scenario of remote state preparation of qubits where a single copy of an entangled state is shared between Alice and several Bobs who sequentially perform unsharp single-particle measurements. We show that a substantial number of Bobs can optimally and reliably prepare the qubit in Alices lab exceeding the classical realm. There can be at most 16 Bobs in a sequence when the state is chosen from the equatorial circle of the Bloch sphere. In general, depending upon the choice of a circle from the Bloch sphere, the optimum number of Bobs ranges from 12 for the worst choice, to become remarkably very large corresponding to circles in the polar regions, in case of an initially shared maximally entangled state. We further show that the bound on the number of observers successful in implementing remote state preparation is higher for maximally entangled initial states than that for non-maximally entangled initial states.
We study the remote creation of the polarization and intensity of the first-order coherence (or coherence intensity) in long spin-1/2 chains with one qubit sender and receiver. Therewith we use a physically motivated initial condition with the pure state of the sender and the thermodynamical equilibrium state of the other nodes. The main part of the creatable region is a one-to-one map of the initial-state (control) parameters, except the small subregion twice covered by the control parameters, which appears owing to the chosen initial state. The polarization and coherence intensity behave differently in the state creation process. In particular, the coherence intensity can not reach any significant value unless the polarization is large in long chains (unlike the short ones), but the opposite is not true. The coherence intensity vanishes with an increase in the chain length, while the polarization (by absolute value) is not sensitive to this parameter. We represent several characteristics of the creatable polarization and coherence intensity and describe their relation to the parameters of the initial state. The link to the eigenvalue-eigenvector parametrization of the receivers state-space is given.
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