Search

Alice and Bob are two remote parties. We propose a probabilistic method which allows Alice to map remotely and conclusively Bob’s set of nonorthogonal symmetric d-level quantum states onto another. The procedure we use is a remote positive operator valued measurement (POVM) in Bob’s (2d-1)-level direct sum space. We construct a quantum network for implementing this (2d-1)-level remote nonunitary POVM with (d-1) two-level remote unitary rotations. The fact that the two-level remote rotation, which is hired to rotate remotely a basis vector, can been implementing rapidly using only one ebit (a two-level Einstein-Podolsky-Rosen (EPR) pair) and one cbit (classical communication) is notable. This scheme is simpler but with less resource, which will make it more feasible and suitable for large-scale quantum network.

We show how a shared and programmable maximum-confidence discrimination (SPMCD) can be implemented by two remote parters Alice and Bob. Here Bob is given a qubit prepared in one of N linearly dependent symmetric equiprobable states. Alice has the knowledge of Bob’s signal states, but Bob has not. We build a quantum network that would be able to perform various desired maximum-confidence discrimination among Bob’s measured (data) states depending on Alice’s auxiliary (program) state. The SPMCD can be thought of as a two-step process, in which a two-outcome shared and programmable probability operator measure (POM) performed on data qubit B is firstly implemented by Alice and Bob followed by a N-outcome local POM on B implemented by Bob. We explicitly construct the required POMs. The fact that the nonlocal data-program conditional evolution, which induces the shared and programmable POM, can be realized deterministically using only two partially entangled qubit pairs is notable. The successful probability of implementing this SPMCD is optimal only for one program setting. However, for a relatively large set of program settings it can be very close to the optimal value in an ordinary, local, maximum-confidence discrimination. This protocol is feasible for current experimental technology.

We show how a remote positive operator valued measurement (POVM) can be implemented deterministically by using partially entangled state(s). Firstly, we present a theoretical scheme for implementing deterministically a remote and controlled POVM onto any one of N qubits via a partially entangled (N + 1)-qubit Greenberger-Horne-Zeilinger (GHZ) state, in which (N − 1) administrators are included. Then, we design another scheme for implementing deterministically a POVM onto N remote qubits via N partially entangled qubit pairs. Our schemes have been designed for obtaining the optimal success probabilities: i.e. they are identical to those in the ordinary, local, POVMs. In these schemes, the POVM dictates the amount of entanglement needed. The fact that such overall treatment can save quantum resources is notable.

We give a scheme for locally implementing an inner product modification onto remote qubit product states using partially entangled states, which is designed for obtaining conclusive result with optimal success probability. We exemplify this remote inner product modification (RIPM) by applying it to two-qubit product states via three partially entangled qubit pairs and, additionally, we construct a quantum network to implement this RIPM. It is interesting that our treatment can save entanglement resources.

We present a scheme for implementing a remote minimum-error discrimination (MD) among N linearly independent nonorthogonal symmetric qudit states. The probability of correct guesses is in agreement with the optimal probability for local MD among the N nonorthogonal states. The procedure we use is a remote probability operator measure (POM). We show that this remote POM can be performed as a remote von Neumann measurement by remote basis transformation. We construct a quantum network for realizing the remote MD using local operations, classical communications and shared entanglement (LOCCSE), and thus provide a feasible physical means to realize the remote MD.

We investigate the local implementation of a nonlocal quantum Toffoli gate via partially entangled states. Firstly, we show how the nonlocal Toffoli gate can be implemented with unit fidelity and a certain probability by employing two partially entangled qubit pairs as quantum channels. The quantum circuit that does this proposed implementation is built entirely of local single-level and two-level gates if the target node harness a three-level qudit as a catalyser. This enables the construction of this key nonlocal quantum gate with existing technology. Then, we put forward a scheme to realize deterministic and exact implementation of this nonlocal gate via more partially entangled pairs. In this scheme, the control nodes’ local positive operator valued measurements (POVMs) lies at the heart. We construct the required POVMs. The fact that the deterministic and exact implementation of a nonlocal multi-qubit gate could be realized by using partially entangled qubit pairs and comparatively fewer resources cost is notable.

Two nonlocal and unknown pure qubit states can, with a certain probability of success, be discriminated unambiguously with the aid of local operations, classical communication, and shared entanglements (LOCCSE). We present a scheme for such kind of nonlocal unambiguous quantum state discrimination. This scheme consists of a nonlocal positive operator valued measurement (POVM). This nonlocal POVM can be realized by performing nonlocal unitary operations on initial system and ancillary qubits, and local von Neumann projective measurements on the ancilla plus initial system. By utilizing the degrees of freedom of the original system Hilbert space, we need far more simpler operations than those required by the original Neumark approach. We construct a quantum logic network to implement the required nonlocal POVM.