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Indian Journal of Science and Technology

Formal Conditions on Quantum Teleportation

Agus Purwanto, Heru Sukamto, Lila Yuwana

Published May 1, 2018• 2 citations
Publisher

Abstract

Objectives: To formulate the most elementary requirement to realise quantum teleportation. Methods: By expanding procedure to define the capability of general two qubit quantum states to realise quantum teleportation. Findings: By structuring the general form of two qubit and measurement states, we can exhibit the capabilty both separable two qubit states and entangled two qubit states to realise quantum teleportation. Next, we also show the measurement procedure and the unitary operator required to reconstruct a single qubit delivered into correct state. Application/Improvement: The methods exhibited in this paper have relatively simple procedure and very beneficial to improve our last procedure proposed beforehand. Keywords: Entangled States, Separable States, Quantum Channels, Quantum Teleportation

DOI
10.17485/ijst/2018/v11i18/122371

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Objectives: To formulate the most elementary requirement to realise quantum teleportation. Methods: By expanding procedure to define the capability of general two qubit quantum states to realise quantum teleportation. Findings: By structuring the general form of two qubit and measurement states, we can exhibit the capabilty both separable two qubit states and entangled two qubit states to realise quantum teleportation. Next, we also show the measurement procedure and the unitary operator required to reconstruct a single qubit delivered into correct state. Application/Improvement: The methods exhibited in this paper have relatively simple procedure and very beneficial to improve our last procedure proposed beforehand. Keywords: Entangled States, Separable States, Quantum Channels, Quantum Teleportation
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Teleportation of an arbitrary single-qubit state using two partially entangled states is considered.Firstly,we present a method for realizing probabilistically two-destination teleportation by using two partially entangled pairs as quantum channel.Then,we put forward a scheme for realizing deterministic and exact teleportation by using same quantum channel.In these schemes,the sender's local generalized measurement described by a positive operator valued measurement(POVM) lies at the heart.We construct the required POVM.The methods are applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients μ and v are 2μ+2μv-2v-1≥0.
Quantum mechanics shows superiority than classical mechanics in many aspects and quantum entanglement plays an essential role in information processing and some computational tasks such as quantum teleportation (QT). QT was proposed to transmit the unknown states, in which EPR pairs, the entangled states, can be used as quantum channels. In this paper, we present two simple schemes for teleporting a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state respectively. Alice and Bob have shared an entangle state. Two Bell states are used as quantum channels. Then after Alice measuring her qubits and informing Bob her measurement results, Bob can perfectly reconstruct the original state by performing corresponding unitary operators on his qubits. It shown that a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state can be teleported perfectly, i.e. the success probabilities of our schemes are both 1.
We propose a method to realize the teleportation of an unknown entangled state that consists of many qudits through a partially entangled-qudit quantum channel with the help of 2log 2 d -bit classical communication. The operations used in the teleportation process include a generalized Bell-state measurement and a series of single-qudit π-measurements performed by Alice, a series of generalized qudit-Pauli gates and two-level unitary gates, as well as a qubit measurement performed by Bob. For a maximally entangled quantum channel, the successful probability of the teleportation becomes unit.
Quantum teleportation provides a way to transfer unknown quantum states from one system to another via an entangled state as a quantum channel without physical transmission of the object itself. The entangled channel, measurement performed by the sender (Alice), and classical information sent to the receiver (Bob) are three key ingredients in the procedure, which need to cooperate with each other. To study the relationship among the three parts, we propose a scheme for perfect teleportation of a qubit through a high-dimensional quantum channel in a pure state with two equal largest Schmidt coefficients. The scheme requires less entanglement of Alice's measurement but more classical bits than the original scheme via a Bell state. The two quantities increase with the entanglement of the quantum channel when its dimension is fixed and thereby can be regard as Alice's necessary capabilities to use the quantum channel. And the two capabilities appear complementary to each other.
We explicitly show a protocol in which an arbitrary two qubit state $\ensuremath{\mid}\ensuremath{\phi}⟩=a\ensuremath{\mid}00⟩+b\ensuremath{\mid}01⟩+c\ensuremath{\mid}10⟩+d\ensuremath{\mid}11⟩$ is faithfully and deterministically teleported from Alice to Bob. We construct the 16 orthogonal generalized Bell states that can be used to teleport the two qubits. The local operations Bob must perform on his qubits in order to recover the teleported state are also constructed. They are restricted only to single-qubit gates. This means that a controlled-NOT gate is not necessary to complete the protocol. A generalization where NNN qubits are teleported is also shown. We define a generalized magic basis, which possesses interesting properties. These properties help us to suggest a generalized concurrence from which we construct a measure of entanglement that has a clear physical interpretation: A multipartite state has maximum entanglement if it is a genuine quantum teleportation channel.