How is qubit phase teleported from one point to another?

In Quantum System, the classical way of copying data or transferring data from source to destination is not possible since qubit can’t retrieve complete information of state at the other end and due to short coherence times of quantum state. To transfer quantum information from one system to another, Quantum Teleportation is used.

Before we can understand how Quantum Teleportation works, we must know few things. Let’s look into those few things that cover ups quantum teleportation.

Transiting from Classical to Quantum System

From bits to qubits

• In Classical system, a state can be either “0” or “1” called bit. This means a 64-bit data bus can transfer only 64 bits at a time.
• In Quantum system, a state can be in superposition, i.e. simultaneously in “0” and “1” known as qubit. This means a 64 qubit bus can transfer 2⁶⁴=18,446,744,073,709,551,616 states at a time. In laymen's term, a 64 qubit bus acts as 18,446,744,073,709,551,616 classical bit bus.

Dirac Notation

In Quantum System, Dirac notation(or bra-ket notation) is used to describe quantum states. Let a, b are 2-dimensional vector with complex entries.
So the general representation of Dirac notation is given as,

We define quantum states “0” and “1” as:

Multipartite Quantum States

When multiple states are to be described, tensor product is used. If two states are used, it is known as bipartite state. States of this form are uncorrelated, but there are some bipartite states that cannot be written as the tensor product, these states are correlated and sometimes even entangled.

Quantum Entanglement

Quantum entanglement is a physical phenomenon that occurs when a pair or group of particles is generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the pair or group cannot be described independently of the state of the others, including when the particles are separated by a large distance.

If a pure bipartite state on system A & B cannot be written as the its tensor product, it is entangled.

Bell States

Those bipartite states having very strong correlation that are maximally entangled and build an orthonormal basis are called Bell States. The four so-called Bell states are as follows:

The reverse of Bell State circuit gives Bell Measurement, having classical outcome i, j corresponding to Bell State that is used during Quantum Teleportation.

Quantum Teleportation

Quantum teleportation is a process in which quantum information (e.g. the exact state of an atom or photon) can be transmitted (exactly, in principle) from one location to another, with the help of classical communication and previously shared quantum entanglement between the sending and receiving location.

Quantum Teleportation follows no-cloning rule, this means that the data in source gets eliminated during the teleportation; where the source data is scanned and the extracted information is transmitted somewhere else and used to build the source data out of different materials. Teleportation is done from “A” to “B” by sending two classical bits (result of Bell Measurement) from A — > B, such that both must initially share one entangled state.

1. Both system A and system B initially shares a Bell State (highly entangled bipartite state) generated from EPR Source.
2. System A applies Bell State Measurement and sends the result of the measurement (2 classical bits) to System B through classical channel.
3. System B applies a transformation upon its qubit, according to the two received bits.

<hr><p>Quantum Teleportation Simplified was originally published in Quantum Computing Nepal on Medium, where people are continuing the conversation by highlighting and responding to this story.</p>