Semiclassical $$ \mathcal{S} $$-matrix and black hole entropy in dilaton gravity

We use complex semiclassical method to compute scattering amplitudes of a point particle in dilaton gravity with a boundary. This model has nonzero minimal black hole mass Mcr. We find that at energies below Mcr the particle trivially scatters off the boundary with unit probability. At higher energies the scattering amplitude is exponentially suppressed. The corresponding semiclassical solution is interpreted as formation of an intermediate black hole decaying into the final-state particle. Relating the suppression of the scattering probability to the number of the intermediate black hole states, we find an expression for the black hole entropy consistent with thermodynamics. In addition, we fix the constant part of the entropy which is left free by the thermodynamic arguments. We rederive this result by modifying the standard Euclidean entropy calculation.

FLEXIBLE DETERMINISTIC JOINT REMOTE STATE PREPARATION OF SOME STATES

We provide a new joint remote preparation scheme for some states. By designing some appropriate measurement bases, two separate parties can jointly prepare a three-qubit state for a remote receiver. The receiver may be assigned during the remote preparation progress. This scheme is extended to M > 2 senders for special two-qubit state. Our scheme succeeds with unit probability and is applicable to a certain realistic situation.

CONTROLLED AND REMOTE IMPLEMENTATION OF A SPLIT QUANTUM ROTATION AND SENDER-ENCODED SECRET SHARING

A quantum rotation can be divided into M pieces and teleported from a sender onto M distant receivers via the control of N agents in a quantum network. We utilize the entanglement property of a (2M + N + 1)-qubit Einstein–Podolsky–Rosen (EPR) — Greenberger–Horne–Zeilinger (GHZ) state to design a theoretical scheme for implementing these rotations remotely with unit fidelity and unit probability. The feature of the scheme is that, apart from a sender and M receivers, N agents are included in the process as controllers. Should any one of the N agents not cooperate, the receivers could not gain the original rotations. This scheme can be used to sender-encoded quantum secret sharing. It definitely has the strong security.

DETERMINISTIC AND EXACT TELEPORTATION OF A SINGLE-QUBIT ROTATION ON REMOTE QUBITS USING TWO PARTIALLY ENTANGLED STATES

Teleportation of quantum gates using partially entangled states is considered. Different from the known probability schemes, we propose and study a method for teleporting a prototypical single-qubit rotation on a remote receiver with unit fidelity and unit probability by using two partially entangled pairs. The method is applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients γ and η are (2γ+2η-2γη-1)≥0. In our scheme, the sender's local generalized measurement described by a positive operator-valued measurement (POVM) lies at the heart. We construct the required POVM. The fact that the controlled teleportation of single-qubit rotation could be realized exactly using two partially entangled pairs is also notable. A sender could teleport a rotation on a remote receiver, an arbitrary one of the two receivers, via the control of the other in a network.

QUANTUM TELEPORTATION OF AN ARBITRARY N-QUBIT STATE VIA NON-MAXIMALLY ENTANGLED STATE

We explicitly present two schemes for quantum teleportation of an arbitrary N-qubit entangled state using, respectively, non-maximally entangled Bell states and GHZ states as the quantum channels, and generalized Bell states as the measurement basis. The scheme succeeds with unit fidelity but less than unit probability. By introducing additional qubit and unitary operations, the success probability of these two schemes can be increased.

REMOTE INTERACTIONS ON DISTRIBUTED QUANTUM SYSTEMS: NON-LOCAL CONDITIONAL OPERATIONS AND PRODUCTION OF MULTIPARTICLE ENTANGLED STATE

We present a systematic simple method for constructing non-local quantum conditional rotation with single target and multiple targets operations. We firstly show how a non-local conditional rotation with single target operation can be implemented with unit fidelity and unit probability by using a maximally entangled pair as quantum channel. We also put forward a scheme for probabilistically implementing the operation with unit fidelity by employing a partially entangled pair as quantum channel. The required physical resources for implementation of the non-local operation in these two cases are discussed. We further consider non-local conditional rotation with multiple targets operations on N spatially distributed systems, and show that the number of possible distinct operations increases here exponentially, with the available number of entangled pairs that are initially distributed between systems. We also point out that the non-local conditional rotation operation can be used to generate multiparticle entanglement between particles belonging to distant users in a communication network and distributed quantum computer.

IMPLEMENTATION OF NON-LOCAL CNOT WITH MULTIPLE TARGETS OPERATION BY GHZ STATE AND ENTANGLED PURIFICATION

We show how a non-local quantum CNOT with (N-1)-target operation can be implemented with unit fidelity and unit probability by using a N-qubit maximally entangled GHZ state as quantum channel. We also put forward two schemes for probabilistic implementing the operation with unit fidelity by employing a partially entangled pure GHZ state as quantum channel. The overall physical resources required for accomplishing these schemes are different, and the successful implementation probabilities are also different. We also point out the non-local CNOT with (N-1)-target operation can be used as a purification protocol to concentrate entanglement from an ensemble of partially entangled GHZ states into a subensemble of maximally entangled ones.

SCHEMES FOR REMOTELY PREPARING MULTIPARTITE EQUATORIAL ENTANGLED STATES IN HIGH DIMENSIONS

In this paper, we present two kinds of schemes for remotely preparing multiparticle d-dimensional equatorial entangled states with unit probability. It is found that the first remote state preparation scheme is realized by a multiparticle projective measurement, while the second scheme is achieved by a single particle orthogonal measurement. Each scheme can be perfectly implemented whatsoever the particle number N and the dimension d are.