Quantum State Tomography
In classical physics, if you know an object’s position and velocity, you can describe its state completely. But in quantum mechanics, things are more subtle. A quantum state holds all….
Category: Quantum Computing
Entanglement Measures
Entanglement is one of the most fascinating and non-intuitive features of quantum mechanics. It refers to a situation where two or more quantum systems become so deeply connected that the….
Quantum Fidelity and Distance Measures
In classical systems, comparing two pieces of data—like numbers or text—is straightforward. You can use simple distances like subtraction or Hamming distance. But in quantum systems, the objects we’re comparing….
Quantum Channel Capacities
A quantum channel is a medium or method for transmitting quantum information—like qubits—from one place to another. You can think of it like a telephone line or internet cable, but….
Quantum Data Compression
In the classical world, data compression is everywhere. From zip files to video streaming, compression helps us store and transmit more with less. The idea is simple—remove redundancy and represent….
Holevo Bound
In classical communication, if you send a message—say a letter or a digital bit—the receiver gets the full message. If you send 1 bit, the receiver gets 1 bit of….
Quantum Mutual Information
Let’s begin with the basic idea of mutual information from classical information theory. It tells us how much knowing one variable tells us about another. For example, if you know….
Quantum Entropy Measures
In classical information theory, entropy is used to measure uncertainty or the average information content of a message. This idea is extended in the quantum world through quantum entropy measures,….
Complexity of Quantum Sampling Problems
At a high level, quantum sampling problems ask: Can a quantum computer efficiently sample from a probability distribution that is hard (or impossible) for a classical computer to sample from?….
Quantum PCP Theorem
Before we can understand the Quantum PCP Theorem, we need to review the classical PCP (Probabilistically Checkable Proofs) Theorem. The PCP Theorem (a cornerstone of theoretical computer science) says: Any….