What Is Quantum Information?

In a nutshell

Quantum information as the foundation of quantum computing

Everything You Need to Know About Quantum Information to Understand Quantum Computing

Quantum information processing

The world of quantum bits or qubits

Basis states as the starting point for quantum information

Qubits or quantum states

Scope of quantum information — in this paper

Some tidbits of quantum computing as well, but sparingly

Virtually no math or Greek symbols or obscure or confusing jargon

No confusing diagrams, graphs, or images — just plain and simple text

Simplistic definition for quantum information

Simplistic definition for classical information

Full definition of quantum information

Abbreviated definition for quantum information

Common interpretations of quantum information

Mike and Ike on Quantum Information

My own definition from my Quantum Computing Glossary

What is the unit of quantum information?

What isn’t covered here

Qutrits and qudits — beyond the scope of this paper, but…

Quantum communication and quantum networking — beyond the scope of this paper

Alice and Bob and quantum teleportation — beyond the scope of this paper

Alice and Bob and quantum teleportation for distributed quantum computations — a distant future

Distributed quantum computing — the intersection of quantum computing and quantum networking

Quantum cryptography — beyond the scope of this paper

The overly simplistic answer

Qubit vs. bit is not an accurate comparison

Brief summary of the issues

Information, representations, and storage devices

Yes, a bit is information

Representing, storing, and transmitting classical information

Unlike a classical bit, a qubit is a device

Quantum state represents quantum information

Basis states are the closest things to classic bits on a quantum computer

Vectors, kets, and basis states on a quantum computer

Bra-ket notation for quantum states

Quantum state

Logical quantum state vs. physical quantum state

Probability amplitudes

Phase as information vs. as quantum state

What are all of the two pi’s I see in quantum computing?

Principle of unitarity

The two basis state probability amplitudes are not independent — the probabilities must sum to 1.0

Kets with probability amplitudes

Product states — strings of basis states for entangled qubits

Tensor product states — the fancy name for product states

Exponential product states for entangled qubits and quantum states

Inseparability — Product states cannot be measured or determined from the individual qubits or quantum states

States and quantum systems

State vectors

Dramatic size of state vectors for entangled qubits preclude large classical simulations of quantum computers

Pure and mixed states — the simplistic naive model

Ensembles of qubits vs. collections of qubits or quantum states

Probability density matrix — needed to define pure and mixed states

Pure and mixed states — the technically correct but inscrutable model

No intuitive plain language description for the technically correct definition of pure and mixed states, just the technical mechanics of how to calculate it

Classical states and non-classical states — No name for pure or mixed states in the simple naive case, so maybe just call them classical states and non-classical states

Classical information and non-classical information

Interference

Environmental interference

Interference as a quantum computing technique

Basis states are discrete values while probability amplitudes and phase are continuous values

Beware of quantum algorithms dependent on fine granularity of phase or probability amplitude

Some granularity issues for continuous values of probability amplitudes and phase

Pi is irrational and has an infinity of digits, as do the square roots of 2, 3, and other reasonably small integers

Quantum information represented by the continuous values of probability amplitude and phase vs. probability amplitudes and phase themselves

Ask your quantum hardware vendor how many discrete values they support for phase and probability amplitudes

Quantum uncertainty for continuous values such as probability amplitudes and phase

Linear algebra — beyond the scope of this paper

Hilbert space — beyond the scope of this paper

Vectors — beyond the scope of this paper

Probability and statistics — beyond the scope of this paper

Bloch sphere — beyond the scope of this paper

Wave functions (simplified)

Cat state

|+> and |->

|PHI+>, |PHI->, |PSI+>, and |PSI->

A qubit stores and manipulates quantum state

No, a qubit is not quantum information

Qubits store quantum information but they are not the information itself

But classical bits actually are the information

Yes, it’s odd, but there is no shortened term for quantum information

Quantum information bits?

Registers of qubits or quantum states

Quantum computing — Manipulating quantum state

Quantum computing — Rotations and entanglement

Quantum computing — Rotations of quantum state of a qubit

Quantum state angles — theta and phi

Quantum computing — All operations are relative, no absolute values may be used

Quantum computing — Quantum algorithms, quantum circuits and quantum logic gates

Quantum computing — Unitary transformation matrix

Quantum information science (QIS)

Quantum effects

Classical Information Theory

Quantum Information Theory

Quantum information

Need for the new field of quantum information theory

Quantum information science vs. quantum information theory

Quantum information science and technology (QIST)

Quantum science

Quantum science and technology

Quantum technologies

Measurement of qubits and quantum information — collapse into classical bits

Measurement error

Readout and qubit readout — synonym for qubit measurement

Collapse of the wave function — the inevitable result of measuring qubits

Accessing the quantum state of qubits

Quantum phase estimation (QPE) and quantum amplitude estimation (QAE)

Quantum state tomography

Measurement of qubits is probabilistic, not deterministic

Expectation value — Measurement of qubits as a statistical distribution, not a discrete value

Quantum information is probabilistic by nature rather than deterministic, unlike classical information

Errors in quantum information

Types of errors in quantum information

Undetected errors in quantum information

Response to errors in quantum information

Near-perfect qubits

Quantum Error Correction (QEC)

Error correction for continuous values such as probability amplitudes and phase is an interesting challenge — no solution has been suggested other than redundancy

Coherence time

Computing: Input, processing, and output

Quantum computations cannot read input data — it must be encoded in the gate structure of the quantum circuit

Quantum computations cannot output quantum data — final quantum state must be measured as classical data

No rich data types

No persistent data

No network service access

No Big Data, but a huge solution space

Little data with a big solution space

True random number generation is natural for quantum information

No-cloning theorem

No copying or cloning of quantum information, no read or examine

Photonic quantum information — Continuous-variable (CV) qumodes and squeezed states

Quantum memory and quantum storage

Programming models

Some unresolved or open issues for me

My original proposal for this topic

Summary and conclusions

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Freelance Consultant

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