Orthogonal Complement State Research Articles

Comment on “Quantum Superimposing Multiple Anti-Cloning Machine”

Recently, Li et al. (Int. J. Theor. Phys. 46, 2599, 2007) has constructed the quantum superimposing multiple anti-cloning machine, moreover established the sufficient and necessary condition of this machine exists. In the proofs given by Li et al. (Int. J. Theor. Phys. 46, 2599, 2007), claimed that the following key fact to hold : Fact For an arbitrary unknown state |ψ〉 belongs to n-dimensional Hilbert space, there exists an antiunitary operator K such that K|ψ〉=|ψ⊥〉 here the state |ψ⊥〉 is an orthogonal complement state of |ψ〉, that is, it satisfies the following two conditions 〈ψ|K|ψ〉=〈ψ|ψ⊥〉=0 and 〈ψ|ψ〉=〈ψ⊥|ψ⊥〉=1 In this Comment, we would like to point out that (a). In 1-dimensional Hilbert space, for an arbitrary unknown state |ψ〉, the antiunitary operator K and the orthogonal complement state both do not exist in general. (b). In 3-dimensional Hilbert space, for an arbitrary unknown state |ψ〉, the antiunitary operator K do not exist in general, there are uncountably many orthogonal complement states that can be constructed through the skew-symmetric operator, but is not unitary one. Which shows that above Fact given by Li et al. [1] is incorrect in general for both 1 and 3-dimensional Hilbert space

Deterministic assisted clone of an unknown four-particle entangled cluster-type state

Two deterministic schemes are proposed to realize the assisted clone of an unknown four-particle entangled cluster-type state. The schemes include two stages. The first stage requires teleportation via maximal entanglement as the quantum channel. In the second stages of the protocols, two novel sets of mutually orthogonal basis vectors are constructed. With the assistance of the preparer through a four-particle or two-step two-particle projective measurement under these bases, the perfect copy of an original state can be produced. Comparing with the previous protocols which produce the unknown state and its orthogonal complement state at the site of the sender, the proposed schemes generate the unknown state deterministically.

Assisted Cloning and Orthogonal Complementing of an Arbitrary Unknown Two-Qubit State with χ-Type Entangled States

We propose a scheme for cloning an arbitrary unknown two-qubit state and its orthogonal complement state with the assistance from the state preparer. Our scheme includes two stages. The first stage requires a quantum teleportation process, in which an arbitrary unknown two-qubit state can be deterministically teleported from the sender to the receiver with χ-type entangled states as the quantum channel. In the second stage, with the assistance of the state preparer, either a perfect copy or an orthogonal complement state of an arbitrary unknown two-qubit state can be obtained with a certain probability.

FAITHFUL CLONE OF AN UNKNOWN TWO-PARTICLE ENTANGLED STATE WITH ASSISTANCE

We propose a deterministic and faithful scheme for realizing the assisted clone of an unknown two-particle entangled state. The first stage of the protocol requires teleportation via maximal entanglement. In the second stage, a novel set of mutually orthogonal basis vectors is constructed. With the assistance of the preparer through a two-particle projective measurement under this basis, a perfect copy of an original state can be produced. Compared with the previous protocols which produce the unknown state and its orthogonal complement state at the site of the sender, our scheme generates the unknown state deterministically. On the other hand, we put forward another assisted clone scheme via nonmaximal entanglement as the quantum channel. A faithful copy of the unknown state can be obtained with a certain probability.

Deterministic Clone of an Unknown N-Qubit Entangled State with Assistance

We propose a deterministic scheme to realize assisted-clone of an unknown N(≥3)-qubit entangled state. The first stage of the protocol requires teleportation via maximal entanglement as the quantum channel. In the second stage of the protocol, a novel set of mutually orthogonal basis vectors are constructed. With the assistance of the preparer through an N-particle projective measurement under this basis, the perfect copy of an original state can be produced. Comparing with the previous protocols which produce the unknown state and its orthogonal complement state at the site of the sender, our scheme generates the unknown state deterministically.

SCHEME FOR IMPLEMENTING ASSISTED CLONING OF AN UNKNOWN TWO-PARTICLE ENTANGLED STATE VIA CLUSTER STATE

We present a scheme that can realize quantum cloning of an unknown two-particle entangled state and its orthogonal-complement state with assistance offered by a state preparer, via entangled cluster state as quantum channel. The first stage of the scheme requires usual teleportation via a maximally four-particle entangled cluster state as quantum channel. In the second stage of the scheme, with the assistance (through a two-particle projective measurement) of the preparer, the perfect copies and complement copies of an unknown two-particle entangled state can be obtained. We also put forward a scheme for the teleportation by using nonmaximally entangled quantum channel. The clones and complement clones of unknown state can be produced with certain probability in the latter scheme.

Scheme for Cloning an Unknown Entangled State with Assistance via Non-maximally Entangled Cluster States

We propose a scheme for cloning unknown two-particle entangled state and its orthogonal complement state with assistance from a state preparer. Two stages were included in this scheme. The first stage requires usual teleportation by using a one-dimensional non-maximally four-particle cluster state as quantum channel, after Alice’s (the state sender) Bell measurement, Bob (the state receiver) can get the original state with certain probability. In the second stage, after having received Victor’s (the state preparer) classical message, the perfect copies and complement copies of an unknown state can be produced in Alice’s place, the probability of Alice to get the original state or its orthogonal complement state are calculated. Assisted cloning of an arbitrary unknown two-particle entangled state is discussed in the latter scheme.

SCHEME FOR QUANTUM CLONING OF AN UNKNOWN N-PARTICLE ENTANGLED STATE WITH ASSISTANCE

In this paper, we present a scheme which can realize quantum cloning of an unknown N-particle entangled state and its orthogonal complement state with assistance offered by a state preparer. The first stage of the scheme requires usual teleportation via N non-maximally entangled particle pairs as quantum channel. In the second stage of the scheme, with the assistance (through a N-particle projective measurement) of the preparer, the perfect copies and complement copies of an unknown N-particle entangled state can be obtained.

Scheme for Implementing Assisted Cloning of an Unknown Tripartite Entangled State

In this paper, we propose a protocol which can realize quantum cloning of an unknown tripartite entangled state and its orthogonal complement state with assistance from a state preparer. The first stage of the protocol requires usual teleportation via three entangled particle pairs as quantum channel. In the second stage of the protocol, the perfect copies and complement copies of an unknown state can be produced with the assistance (through a tripartite projective measurement) of the state preparer. We also present a scheme for the teleportation by using non-maximally entangled quantum channel. It is shown that the clones and complement clones of the unknown state can be obtained with certain probability in the latter scheme.

Quantum Cloning of an Unknown Two-Particle Entangled State with Assistance

We propose a protocol where one can realize quantum cloning of an unknown two-particle entangled state and its orthogonal-complement state with assistance offered by a state preparer. The first stage of the protocol requires usual teleportation using a (or two) four-particle entangled state(s) as quantum channel(s). In the second stage of the protocol, with the assistance (through a two-particle projective measurement) of the preparer, the perfect copies and complement copies of an unknown state can be produced.

Assisted cloning of an unknown two-particle entangled state

We propose a protocol where one can realize quantum cloning of an unknown two-particle entangled state and its orthogonal complement state with assistance offered by a state preparer. The first stage of the protocol requires usual teleportation via two entangled particle pairs as quantum channel. In the second stage of the protocol, with the assistance (through a two-particle projective measurement) of the preparer, the perfect copies and complement copies of an unknown state can be produced. We also put forward a scheme for the teleportation by using non-maximally entangled quantum channel. The clones and complement clones of unknown state can be obtained with certain probability in the latter scheme.

Reestablishment of an Unknown State and Its Orthogonal Complement State with Assistance**The project partially supported by National Natural Science Foundation of China under Grant Nos. 90103026 and 60078023

In this paper, we propose a protocol where one can realize reestablishment of an unknown state and its orthogonal complement state with a certain probability. In the first stage of the protocol, teleportation is performed between Alice (a sender) and Bob (a receiver) through a nonmaximally entangled quantum channel. In the process of teleportation, Alice performs nonmaximally entangled state measurement. In the second stage of the protocol, Victor (a state preparer) disentangles leftover nonmaximally entangled states by a single-particle measurement. With the assistance of Victor Alice can reestablish the original state or produce its orthogonal state.