Quantum Entanglement

 Entanglement is a phenomenon where two or more quantum particles (qubits) become linked in such a way that the state of one particle cannot be described independently of the other.

In simpler terms, they become a single system. Even if you separate them by billions of miles, measuring one of them instantaneously reveals the state of the other.

Here is an explanation using a simple analogy and a technical example.

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1. The Simple Analogy: The "Magic" Coins

Imagine you and a friend each have a coin. In the classical world (our daily life), if you both flip your coins, your results are independent. You might get Heads while your friend gets Tails.

In the Quantum World (Entanglement):

Imagine these two coins are "entangled."

1. You take one coin to the North Pole.

2. Your friend takes the other coin to the South Pole.

3. Both coins are spinning (in a state of superposition).

When you stop your coin and look at it, if it lands on Heads, your friend’s coin will instantly land on Heads as well. If yours lands on Tails, theirs will be Tails.

There is no signal sent between them; the change happens instantly. They are acting as if they are one single object, despite the distance.

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2. The Computing Example: The Bell Pair

In a quantum computer, we don't use coins; we use Qubits.

Scenario:

You create two entangled qubits, Qubit A and Qubit B. You put them into a specific entangled state known as a Bell State.

Mathematically, this state is written as:

$$|\Phi^+\rangle = \frac{|00\rangle + |11\rangle}{\sqrt{2}}$$

What this means for the computer:

• Superposition: Until you measure them, the system is in a superposition of being 00 (both Zero) and 11 (both One) at the same time.

• Measurement:

  • If you measure Qubit A and find it is 0, Qubit B instantly becomes 0.

  • If you measure Qubit A and find it is 1, Qubit B instantly becomes 1.

Why is this useful?

This "link" allows quantum computers to process information in ways classical computers cannot.

• Superdense Coding: You can send two classical bits of information by sending only one entangled qubit.

• Quantum Teleportation: You can transfer the state of a qubit from one physical location to another without moving the physical particle itself.

what is Quantum State in quantum computing explain with example

 In simple terms, a Quantum State is a mathematical description of a quantum system (like a qubit) at a specific point in time.¹ It contains all the information we can possibly know about that system, such as its energy, position, or spin.²

In classical computing, the "state" of a bit is easy to define: it is either 0 (off) or 1 (on).³ In quantum computing, the state is more complex because of a property called superposition.⁴

Here is an explanation using a simple analogy.

The Coin Analogy

To understand a quantum state, imagine a simple coin.

1. The Classical State (Traditional Computer)

Imagine you place a coin on a table. It will sit there showing either Heads or Tails.5

• State: It is definitely Heads OR definitely Tails.⁶

• Computer Equivalent: A classical bit is definitely a 0 or a 1.⁷

2. The Quantum State (Quantum Computer)

Now, imagine you spin that coin on the table. While it is spinning, what is its state? You cannot say it is just Heads, and you cannot say it is just Tails.8 It is in a dynamic mix of both.

• State: It is in a superposition of both Heads and Tails simultaneously.⁹ This "spinning" motion represents the Quantum State.¹⁰

• Computer Equivalent: A qubit (quantum bit) can represent 0 and 1 at the same time.¹¹ The "Quantum State" describes exactly how it is spinning (e.g., is it leaning more toward Heads or more toward Tails?).

Key Characteristics

• It is Probabilistic: The quantum state does not tell you exactly what you will get. It tells you the probability of getting a specific result.¹² For example, a quantum state might tell you: "If you measure this qubit, there is a 70% chance it will be a 0 and a 30% chance it will be a 1."¹³

• Collapse: Just like stopping the spinning coin with your hand forces it to land on either Heads or Tails, measuring a quantum state forces it to "collapse" into a single, definite value (0 or 1).¹⁴ The complex quantum state disappears, and you are left with a classical result.¹⁵

Visual Representation (The Bloch Sphere)

Scientists often visualize a quantum state using a sphere called the Bloch Sphere.¹⁶

• The North Pole represents the state 0.¹⁷

• The South Pole represents the state 1.¹⁸

• The Quantum State is a point anywhere on the surface of this sphere.¹⁹ It could be at the equator (perfectly between 0 and 1), or closer to the North Pole (mostly 0, but a little bit 1). This arrow pointing to a specific spot on the sphere is the vector representing the quantum state.

Summary Table

Feature	Classical State	Quantum State
Basic Unit	Bit	Qubit
Values	0 OR 1	0 AND 1 (Superposition)
Certainty	100% Deterministic	Probabilistic
Analogy	Coin resting on a table	Coin spinning on a table