The Essential Guide to Quantum Teleportation Protocols and Bell Pairs

In the quantum domain, this everyday concept breaks down. Nature prohibits the cloning of an arbitrary, unknown quantum state. If you cannot copy a quantum file, how can you transmit its exact state to another quantum processor without physically carrying the delicate hardware across the world? You can explore our full library of quantum architecture guides at QuantumUting.com. This puzzle is solved by quantum teleportation protocols. A quantum teleportation protocol is a method that transfers the exact quantum state of a qubit to a distant qubit without moving the physical particle itself. The protocol operates on three indispensable ingredients: Shared Entanglement+Classical Communication+Quantum Operations , This guide explores the mechanics of quantum teleportation, dissects each operational gate step by step, reviews circuit implementations in Qiskit, and explains how this foundational protocol powers future quantum networks.

Table of Contents

What Is Quantum Teleportation?

Quantum teleportation is an established quantum information protocol designed to recreate the unknown quantum state of one qubit inside another qubit situated at a different location.

The protocol involves two primary participants:

Alice (The Sender): Holds an unknown quantum state she wants to transmit.
Bob (The Receiver): Holds a separate qubit that will receive that exact state.
The Unknown Qubit (∣ψ⟩): The specific superposition state carried by Alice.
The Entangled Pair: A pre-shared resource distributed between Alice and Bob before the protocol begins.

+------------------------+      +---------------------+
| Unknown Quantum State  |  +   | Shared Entanglement |
+------------------------+      +---------------------+
                                   │
                                   ▼
                        +----------------------+
                        |   Alice's Circuit    |
                        |     & Measurement    |
                        +----------------------+
                                   │
                                   ▼ [2 Classical Bits]
                        +----------------------+
                        | Classical Channel    |
                        +----------------------+
                                   │
                                   ▼
                        +----------------------+
                        |  Bob's Conditional   |
                        |   Quantum Gates      |
                        +----------------------+
                                   │
                                   ▼
                        +----------------------+
                        | Reconstructed State  |
                        +----------------------+

The original state in Alice’s possession is deliberately dismantled during measurement. Quantum state transfer succeeds not by duplication, but by state relocation.

Why Quantum Teleportation Differs From Classical Communication

Classical systems transmit bits (0 or 1) by directly broadcasting voltage spikes or optical pulses. Quantum states, however, carry continuous complex amplitudes that collapse when observed.

Feature	Classical Information	Quantum Information
Basic Unit	Bit (0 or 1)	Qubit (α∥0⟩+β∥1⟩)
Copying	Trivially copied and duplicated	Prohibited by the No-Cloning Theorem
Measurement	Non-destructive readout	Destructive state collapse
Transmission	Direct signal broadcasting	Entangled resource + classical channel
Entanglement	No classical equivalent	Essential for state transfer
State Reconstruction	Read and rewritten directly	Reconstructed via unitary correction gates

Quantum teleportation does not bypass classical channels. Alice must transmit two standard classical bits to Bob, meaning classical communication remains an absolute requirement.

Quantum Teleportation Does Not Move Matter

Because science fiction often equates teleportation with physical dematerialization, scientific clarity is critical:

It does not transport physical atoms or biological matter.
It does not beam humans or physical objects across space.
It does not allow faster-than-light (FTL) data transmission.
It does not violate relativistic causality.

What moves is exclusively the quantum configuration (the probability amplitudes and phase relationship). Bob supplies his own physical qubit; the protocol simply maps Alice’s original state onto Bob’s local particle.

The Three Main Ingredients

To execute a quantum teleportation protocol, three structural components must align:

1. The Unknown Quantum State

Alice holds an arbitrary qubit in a superposition state:

∣ψ⟩=α∣0⟩+β∣1⟩

Here, α and β represent complex probability amplitudes. The state obeys the normalization condition:

∣α∣2+∣β∣2=1

Alice does not know the values of α and β, nor can she measure them directly without destroying the superposition.

2. Shared Entanglement

Alice and Bob must share a pair of entangled qubits prepared in advance. This quantum link provides the correlation resource necessary to bridge the distance between their systems.

3. Classical Communication

Alice must measure her local qubits and transmit the resulting two classical bits over an everyday network line (such as a fiber-optic cable) to Bob.

What Is Quantum Entanglement?

Quantum entanglement occurs when two or more qubits interact in such a way that the quantum state of each particle cannot be described independently of the state of the others.

Even if separated by vast distances, measurement outcomes on entangled pairs exhibit deterministic correlations that classical physics cannot reproduce.

A standard example is the maximally entangled Bell state:

∣Φ+⟩=2∣00⟩+∣11⟩

If one qubit is measured as ∣0⟩, the other immediately yields ∣0⟩. If the first yields ∣1⟩, the second yields ∣1⟩. Crucially, this correlation cannot be used in isolation to transmit arbitrary data instantly, because individual local measurements yield entirely random results.

What Is a Bell State?

The four Bell states form an orthonormal basis of maximally entangled two-qubit states, often called Einstein-Podolsky-Rosen (EPR) pairs.

Bell State	Mathematical Representation	Description
∣Φ+⟩	21(∣00⟩+∣11⟩)	Correlated states with positive phase
∣Φ−⟩	21(∣00⟩−∣11⟩)	Correlated states with phase flip
∣Ψ+⟩	21(∣01⟩+∣10⟩)	Anti-correlated states with positive phase
∣Ψ−⟩	21(∣01⟩−∣10⟩)	Anti-correlated states with phase flip (Singlet)

These states serve as the baseline fuel for quantum teleportation, quantum key distribution, and superdense coding.

Basic Quantum Teleportation Setup

The standard protocol requires a three-qubit register:

ALICE'S DOMAIN                     BOB'S DOMAIN
┌──────────────────────────────┐   ┌──────────────────────────────┐
│ Qubit 1: Unknown State |ψ⟩    │   │ Qubit 3: Bob's Entangled Qubit│
│                              │   │                              │
│ Qubit 2: Alice's Entangled   │   │                              │
│          Qubit               │   │                              │
└──────────────┬───────────────┘   └──────────────▲───────────────┘
               │                                  │
               └───────── Entangled Pair ─────────┘

Alice controls Qubit 1 (the payload) and Qubit 2 (her half of the Bell pair). Bob controls Qubit 3 (his half of the Bell pair).

Quantum Teleportation Protocol Step by Step

Let us trace the standard teleportation protocol through its complete physical sequence:

Step 1: Prepare the Unknown Qubit

Alice holds the target state: ∣ψ⟩=α∣0⟩+β∣1⟩ on Qubit 1.

Step 2: Prepare an Entangled Pair

An EPR source generates a Bell state ∣Φ+⟩ across Qubit 2 (Alice) and Qubit 3 (Bob). The global state is:

∣Ψ0⟩=(α∣0⟩+β∣1⟩)⊗21(∣00⟩+∣11⟩)

Step 3: Alice Applies a CNOT Gate

Alice applies a Controlled-NOT (CNOT) gate using Qubit 1 as the control and Qubit 2 as the target. This entangles her unknown state with her half of the Bell pair.

Step 4: Alice Applies a Hadamard Gate

Alice applies a Hadamard (H) gate to Qubit 1. This converts her remaining information into a basis ready for projective measurement.

Step 5: Alice Measures Her Two Qubits

Alice performs a projective computational measurement on Qubits 1 and 2. This measurement yields one of four possible classical two-bit outcomes:

00
01
10
11

Step 6: Alice Sends the Two Classical Bits to Bob

Alice transmits her measurement result to Bob using a standard classical communication line.

Step 7: Bob Applies Conditional Gates

Upon receiving the two bits, Bob applies specific unitary corrections to Qubit 3:

If Alice measured 00: Bob applies the Identity gate (I) (no operation).
If Alice measured 01: Bob applies the Pauli-X gate (bit flip).
If Alice measured 10: Bob applies the Pauli-Z gate (phase flip).
If Alice measured 11: Bob applies both X and Z gates (ZX).

Step 8: Bob Obtains the Original Quantum State

Bob’s Qubit 3 is now in the exact state ∣ψ⟩=α∣0⟩+β∣1⟩. Alice’s original state on Qubit 1 has collapsed completely.

Quantum Teleportation Circuit

The standard quantum circuit diagram displays how gates and registers interact:

Qubit 1 (|ψ⟩) ───■──────[ H ]───[ M ]═══════════════════
                 │                ║  (Bit 1)
Qubit 2 (|0⟩) ───┼───[ H ]───■────[ M ]═════════════════
                 │           │     ║  (Bit 0)
Qubit 3 (|0⟩) ───┼───[ X ]───┼─────╫───────[ X ]───[ Z ]─── |ψ⟩
                 │     ▲     │     ║         ▲       ▲
                 └───Entangle┘     ║         ║       ║
                                   ╚═════════╩═══════╝

H (Hadamard): Creates equal superpositions.
CNOT (⊕): Entangles pairs and entangles the payload with Alice’s half.
M (Measurement): Collapses quantum states into classical registers.
Classical Control Lines (\doubleheadrightarrow): Route measurement outcomes to trigger conditional X and Z corrections.

Why Measurement Is Important

In classical computing, checking a memory cell has no effect on its stored charge. In quantum mechanics, measurement forces a superposition to choose a definitive computational state.

When Alice measures her two qubits:

She collapses the three-qubit system into one of four distinct branches.
The quantum payload leaves Alice’s physical possession.
The measurement outcomes generate the precise instructions Bob needs to adjust his qubit.

Before Measurement: Continuous Quantum Information (α, β)
                           │
                           ▼
 After Measurement:  Classical Bits (0 or 1) + Rotated Target Qubit

Why the No-Cloning Theorem Matters

Formulated by Wootters, Zurek, and Dieks in 1982, the No-Cloning Theorem proves that an arbitrary, unknown quantum state cannot be replicated identically:

U(∣ψ⟩∣0⟩)=∣ψ⟩∣ψ⟩

If Alice could copy her qubit, she could send Bob the copy while keeping the original. Teleportation honors this law by requiring measurement on Alice’s side, which irreversibly scrambles the original state before Bob completes reconstruction:

Original State⟶Teleportation⟶State at Receiver (Original Destroyed)

Does Quantum Teleportation Break the Speed of Light?

Quantum entanglement causes instantaneous mathematical state projection across two particles, leading to common assumptions about faster-than-light signaling.

However, Bob holds a completely scrambled density matrix until he learns Alice’s measurement result. Without Alice’s two classical bits, Bob’s qubit reveals only random outcomes when measured.

Because those two classical bits must travel through conventional communication media bounded by the speed of light (c), quantum teleportation strictly obeys relativistic causality.

Mathematics Behind Quantum Teleportation

Let us expand the state mathematically to understand why Bob’s corrections work.

The initial three-qubit state is:

∣Ψ0⟩=(α∣0⟩+β∣1⟩)⊗21(∣00⟩+∣11⟩)

Expanding the tensor product:

∣Ψ0⟩=21[α∣000⟩+α∣011⟩+β∣100⟩+β∣111⟩]

Alice applies a CNOT gate from Qubit 1 to Qubit 2:

∣Ψ1⟩=21[α∣000⟩+α∣011⟩+β∣110⟩+β∣101⟩]

Alice applies a Hadamard gate to Qubit 1:

∣Ψ2⟩=21[∣00⟩(α∣0⟩+β∣1⟩)+∣01⟩(α∣1⟩+β∣0⟩)+∣10⟩(α∣0⟩−β∣1⟩)+∣11⟩(α∣1⟩−β∣0⟩)]

Alice’s two-qubit measurement outcomes determine Bob’s state and correction:

Alice’s Measurement	State on Bob’s Qubit	Required Pauli Correction	Resulting State
`00`	α∥0⟩+β∥1⟩	I (None)	α∥0⟩+β∥1⟩
`01`	α∥1⟩+β∥0⟩	X	α∥0⟩+β∥1⟩
`10`	α∥0⟩−β∥1⟩	Z	α∥0⟩+β∥1⟩
`11`	α∥1⟩−β∥0⟩	ZX	α∥0⟩+β∥1⟩

What Are Pauli X and Z Gates?

To correct his qubit, Bob relies on two single-qubit quantum gates:

The Pauli-X Gate

The quantum equivalent of a classical NOT gate. It flips computational basis states:

X∣0⟩=∣1⟩,X∣1⟩=∣0⟩

The Pauli-Z Gate

A phase-flip gate that preserves ∣0⟩ while reversing the sign of ∣1⟩:

Z∣0⟩=∣0⟩,Z∣1⟩=−∣1⟩

Applying these operations restores both the relative amplitudes and quantum phase of the original state.

Role of the Hadamard Gate

The Hadamard (H) gate creates and resolves superpositions:

H∣0⟩=2∣0⟩+∣1⟩,H∣1⟩=2∣0⟩−∣1⟩

In teleportation, the Hadamard gate rotates Alice’s basis prior to measurement, ensuring that phase information from the original state is preserved in the classical measurement outcomes.

Quantum Teleportation vs Quantum Superdense Coding

Quantum teleportation and superdense coding are complementary protocols that use entanglement in opposite configurations.

Feature	Quantum Teleportation	Superdense Coding
Main Goal	Transmit 1 unknown qubit state	Transmit 2 classical bits
Shared Entanglement	1 Bell pair consumed	1 Bell pair consumed
Communication Channel	2 classical bits sent	1 physical qubit sent
Information Transferred	Quantum state (α∥0⟩+β∥1⟩)	Classical data (`00`, `01`, `10`, `11`)

Quantum Teleportation vs Classical Teleportation

Dimension	Classical Teleportation (Sci-Fi Concept)	Quantum Teleportation (Physics Protocol)
Physical Entity	Macroscopic matter and atoms	Quantum state information
Transmission Method	Dematerialization and physical recreation	Entanglement + Classical transmission
Cloning Status	Implies scanning and duplicating blueprints	Strictly non-cloning compliant
Underlying Physics	Speculative / Non-physical	Experimentally validated quantum mechanics

Practical Applications of Quantum Teleportation

Quantum Key Distribution (QKD) Networks: Relaying cryptographic keys securely across long distances.
Distributed Quantum Computing: Connecting multiple smaller quantum processing units (QPUs) to act as a single modular quantum supercomputer.
Quantum Repeaters: Teleporting states across repeater nodes to overcome photon loss in optical fibers.
Blind Quantum Computing: Enabling clients to send quantum tasks to cloud servers without exposing input states or algorithmic steps.
Connecting Remote Quantum Processors: Moving complex states between isolated cryostats without direct physical interaction.

Quantum Teleportation and Quantum Networks

Direct quantum communication through optical fibers suffers from exponential photon absorption loss over long distances. Because unknown qubits cannot be amplified using traditional classical repeaters (due to the No-Cloning Theorem), networks rely on quantum repeaters.

Node A ──[Entanglement Swapping]── Repeater Node ──[State Teleportation]── Node B

By combining entanglement purification and quantum teleportation across intermediate nodes, quantum networks can transmit state information across continental distances.

Quantum Teleportation and Distributed Quantum Computing

Individual quantum chips face physical constraints on qubit density, thermal control, and cross-talk. Distributed quantum computing addresses this by linking multiple smaller QPUs.

Teleportation serves as the data bus in these architectures, transferring computational states between independent processing modules over optical links.

Challenges of Quantum Teleportation

Decoherence: Environmental noise degrades fragile superposition states during execution.
Entanglement Fidelity: Imperfect Bell pairs introduce errors into Bob’s reconstructed state.
Gate Inaccuracies: Imperfections in physical CNOT, H, and Pauli gates reduce overall fidelity.
Measurement Errors: Inaccurate computational readouts cause Bob to apply incorrect recovery gates.
Photon Loss: Distributing entangled photons over long distances suffers from optical attenuation.
Quantum Memory Limitations: Bob must store his entangled qubit reliably until classical bits arrive.
Classical Latency: Physical distance adds latency while waiting for classical routing bits.
Qubit Connectivity: Limited cross-qubit coupling can require extra SWAP operations on physical chips.
Scaling Overhead: Multi-qubit teleportation scales physical hardware requirements significantly.
Error Correction Demands: Fault-tolerant state transfer requires high physical-to-logical qubit ratios.

Quantum Teleportation and Noise

Simulated teleportation assumes perfect gates and noiseless channels. In contrast, real quantum hardware experiences thermal fluctuations, magnetic interference, and control line drift.

These noise sources lower state fidelity (F), a metric comparing the reconstructed state (ρout) with the original state (∣ψ⟩):

F=⟨ψ∣ρout∣ψ⟩

While ideal simulations yield F=1.0, early-stage NISQ (Noisy Intermediate-Scale Quantum) devices require quantum error mitigation techniques to approach high fidelities.

Quantum Teleportation on a Simulator

Beginners can study teleportation using open-source quantum development kits without needing immediate access to cryogenic systems.

The standard simulation workflow follows these stages:

Initialize Register: Allocate 3 quantum bits and 2 classical bits.
State Preparation: Rotate Qubit 0 into a custom target state.
Entanglement Generation: Apply H and CNOT between Qubit 1 and Qubit 2.
Bell Measurement: Apply CNOT and H across Qubits 0 and 1, then measure both.
Dynamic Correction: Apply conditional X and Z gates on Qubit 2.
Statevector Verification: Verify that the output density matrix matches the initial input.

Popular open-source frameworks include Qiskit and Cirq.

Conceptual Qiskit Implementation

The following example builds a standard teleportation circuit using current Qiskit syntax:

Python

import numpy as np
from qiskit import QuantumCircuit
from qiskit_aer import AerSimulator
from qiskit.quantum_info import Statevector

# Step 1: Create a 3-qubit, 2-classical-bit circuit
qc = QuantumCircuit(3, 2)

# Step 2: Prepare an arbitrary unknown state on Qubit 0
# For demonstration: rotate by specific angles
theta = np.pi / 3
qc.ry(theta, 0)
qc.barrier()

# Step 3: Create a Bell pair between Qubit 1 (Alice) and Qubit 2 (Bob)
qc.h(1)
qc.cx(1, 2)
qc.barrier()

# Step 4: Alice entangles her payload with her Bell qubit
qc.cx(0, 1)
qc.h(0)
qc.barrier()

# Step 5: Alice measures her two qubits
qc.measure(0, 0)
qc.measure(1, 1)
qc.barrier()

# Step 6: Bob applies conditional corrections based on classical bits
# In dynamic circuits: bit 1 controls X, bit 0 controls Z
qc.cx(1, 2)
qc.cz(0, 2)

print("Quantum Teleportation Circuit Constructed Successfully.")

Note: In ideal simulation, the final state of Qubit 2 matches the initial state of Qubit 0 with 100% mathematical fidelity. Physical quantum processors exhibit noise-driven deviations.

Hypothetical Quantum Teleportation Example

Consider a hypothetical setup between two academic laboratories:

[Laboratory Alpha - Alice]
Target state: |ψ⟩ = 0.6|0⟩ + 0.8|1⟩ on Qubit 1
         │
         ├── Shared EPR Pair (Qubits 2 & 3) generated by central source
         │
         ├── Alice executes CNOT(1->2) and H(1)
         │
         ├── Alice measures Qubits 1 and 2 -> Outcome: [1, 0]
         │
         └── Alice sends classical packet "10" over standard Internet
                                 │
                                 ▼
[Laboratory Beta - Bob]
Receives packet "10" ──► Applies Pauli-Z Gate to Qubit 3
                                 │
                                 ▼
Reconstructed State on Qubit 3: |ψ⟩ = 0.6|0⟩ + 0.8|1⟩

Benefits of Understanding Quantum Teleportation

Foundational Mechanics: Clarifies state vectors, operators, and tensor product systems.
Entanglement in Action: Shows how entanglement serves as a practical computational resource.
Measurement Dynamics: Demonstrates how measurement collapses states while extracting usable data.
Hybrid Protocol Design: Illustrates how classical and quantum channels work together.
Circuit Literacy: Introduces essential gates like Hadamard, CNOT, and Pauli operators.
No-Cloning Validation: Demonstrates why quantum information transfer avoids duplication.
Networking Principles: Establishes the building blocks for quantum repeater architectures.
Algorithmic Insight: Prepares students for advanced protocols such as gate teleportation and error-corrected logical operations.

Common Misconceptions About Quantum Teleportation

Misconception 1: It moves physical matter.
- Correction: It transfers quantum states between existing particles; it does not move physical mass.
Misconception 2: It enables faster-than-light communication.
- Correction: Bob cannot decode the state without Alice’s classical bits, which travel at or below light speed.
Misconception 3: Entanglement alone transmits messages.
- Correction: Entanglement provides non-local correlations, but local measurements remain completely random on their own.
Misconception 4: The original qubit state remains intact.
- Correction: Alice’s measurement scrambles the original state, preserving the No-Cloning Theorem.
Misconception 5: It creates a duplicate copy of a qubit.
- Correction: The state is transferred, not duplicated.
Misconception 6: Classical channels are optional.
- Correction: Bob cannot determine which correction gate to apply without the classical measurement outcomes.
Misconception 7: Current hardware runs teleportation flawlessly.
- Correction: Device noise and decoherence lower real-world transfer fidelity compared to ideal theory.
Misconception 8: It can teleport macroscopic everyday objects.
- Correction: The protocol operates exclusively on isolated quantum states (such as single photons or trapped ions).
Misconception 9: It makes quantum repeaters unnecessary.
- Correction: Quantum repeaters depend directly on teleportation protocols to extend network ranges.
Misconception 10: It is purely theoretical and untested.
- Correction: Teleportation has been repeatedly verified across optical fibers, free-space links, and satellite channels.

How to Learn Quantum Teleportation

Step 1: Linear Algebra Basics (Vectors, Inner Products, Matrices)
   │
Step 2: Qubit Representations & The Bloch Sphere
   │
Step 3: Superposition & Single-Qubit Gates (X, Y, Z, H)
   │
Step 4: Quantum Measurement & Probability Amplitudes
   │
Step 5: Multi-Qubit Systems & Tensor Products
   │
Step 6: Entanglement & Bell State Generation
   │
Step 7: The No-Cloning Theorem & State Projection
   │
Step 8: Constructing the 3-Qubit Teleportation Circuit
   │
Step 9: Running Circuit Simulations in Qiskit or Cirq
   │
Step 10: Analyzing Noise & Real Hardware Executions

Role of QuantumUting.com

Mastering quantum computing requires bridging mathematical principles with hands-on circuit implementation. QuantumUting.com provides educational resources across key quantum topics:

Quantum Programming: Step-by-step circuit tutorials using standard frameworks like Qiskit.
Core Algorithms: Accessible explanations of foundational algorithms and protocols.
Hardware Architectures: Guides on superconducting qubits, trapped ions, and photonic platforms.
Quantum Networking: In-depth coverage of entanglement distribution, quantum repeaters, and state transfer protocols.

Future of Quantum Teleportation

Current Research ──► Emerging Technologies ──► Long-Term Possibilities

Current Research: Demonstrating high-fidelity teleportation over metropolitan fiber networks and satellite-to-ground optical links.
Emerging Technologies: Designing functional quantum repeater nodes and deterministic entanglement sources.
Long-Term Possibilities: Building a global Quantum Internet, enabling distributed quantum computation across interconnected supercomputing facilities.

Frequently Asked Questions

What is quantum teleportation?

It is a quantum information protocol that transfers the unknown state of a qubit to another distant qubit using shared entanglement and classical communication.

How does quantum teleportation work?

Alice entangles her unknown state with her half of a shared Bell pair, measures both qubits, and sends the two classical bits to Bob. Bob uses those bits to apply correction gates, reconstructing the state on his qubit.

Does quantum teleportation move matter?

No. It transfers the quantum configuration (superposition and phase), not physical particles.

What is needed for quantum teleportation?

The protocol requires an unknown qubit state, a pre-shared entangled Bell pair, a two-bit classical communication channel, and single-qubit quantum gates.

Why is entanglement important in quantum teleportation?

Entanglement provides the non-local quantum correlation needed to reconstruct the state without directly measuring its continuous amplitudes.

Does quantum teleportation happen faster than light?

No. Bob cannot complete state reconstruction without the classical measurement bits, which travel at or below the speed of light.

What is the role of classical communication?

Classical communication tells Bob which specific unitary operation (I,X,Z, or ZX) he must execute to recover Alice’s original state.

What is the No-Cloning Theorem?

It is a fundamental law of quantum mechanics stating that an arbitrary, unknown quantum state cannot be duplicated identically.

Can quantum teleportation be implemented with Qiskit?

Yes. Qiskit allows users to construct, simulate, and execute quantum teleportation circuits using both statevector simulators and physical quantum hardware.

What are the applications of quantum teleportation?

Key applications include long-range quantum key distribution, quantum repeater nodes, modular distributed quantum computers, and blind cloud quantum computing.

Conclusion

Quantum teleportation unites four central ideas in quantum information science. The protocol demonstrates how quantum information differs fundamentally from classical bits. By transferring unknown quantum states without violating the No-Cloning Theorem or relativistic causality, quantum teleportation provides a foundational building block for future quantum networks and distributed quantum computers.