Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

Free Energy Changes for Nonstandard States

Free Energy Changes for Nonstandard States

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:

BIBO stability of continuous and discrete -time systems

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....

Path Between Thermodynamics States

Path Between Thermodynamics States

Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Adaptively Secure Unitary Designs with Constant Non-Clifford Cost.

Physical review letters·2026

Same authorSame journal

Noise-induced shallow circuits and the absence of barren plateaus.

Nature physics·2026

Same author

Asymptotic quantification of entanglement with a single copy.

Nature physics·2026

Same author

Constant Overhead Entanglement Distillation via Scrambling.

Physical review letters·2026

Same author

Large-scale stochastic simulation of open quantum systems.

Nature communications·2025

Same author

Complexity of quantum tomography from genuine non-Gaussian entanglement.

Nature communications·2025

Same journal

Simple input-output dependencies explain neuronal activity.

Nature physics·2026

Same journal

Scaling and self-similarity in the formation of the embryonic epigenome.

Nature physics·2026

Same journal

Adhesion-driven rigidity transition decoupled from density-driven jamming triggers epithelial organization in embryonic tissues.

Nature physics·2026

Same journal

The local mechanostructural properties of protein cargoes regulate nucleocytoplasmic transport.

Nature physics·2026

Same journal

Squeezing, trisqueezing and quadsqueezing in a hybrid oscillator-spin system.

Nature physics·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jan 8, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Learning quantum states of continuous-variable systems.

Francesco A Mele¹, Antonio A Mele², Lennart Bittel²

¹NEST, Scuola Normale Superiore and Istituto Nanoscienze, Pisa, Italy.

|December 15, 2025

Summary

This summary is machine-generated.

Quantum-state tomography for continuous-variable systems is highly inefficient, requiring exponentially more resources than for qubits. However, efficient methods exist for Gaussian and certain non-Gaussian states.

Keywords:

Imaging and sensing Quantum information Theoretical physics

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Gradient Echo Quantum Memory in Warm Atomic Vapor

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Related Experiment Videos

Last Updated: Jan 8, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Gradient Echo Quantum Memory in Warm Atomic Vapor

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Area of Science:

Quantum physics
Quantum information science
Quantum optics

Background:

Quantum measurements are inherently probabilistic, yielding partial information about quantum states.
Quantum-state tomography reconstructs a full quantum state description from multiple measurements.
Continuous-variable systems (e.g., bosonic, quantum optical) pose unique tomography challenges.

Purpose of the Study:

To analyze the ultimate performance limits of quantum-state tomography for continuous-variable systems.
To compare the efficiency of continuous-variable tomography with finite-dimensional systems.
To identify conditions and methods for efficient tomography of specific quantum states.

Main Methods:

Theoretical analysis of resource scaling in quantum-state tomography.
Derivation of error bounds for state reconstruction.
Investigation of Gaussian and non-Gaussian state preparation and tomography.

Main Results:

Tomography of continuous-variable systems is found to be extremely time-resource inefficient compared to qubits.
The number of required state copies scales exponentially with the number of modes and unfavorably with error.
Efficient tomography protocols are proven for Gaussian states and experimentally feasible for certain non-Gaussian states.

Conclusions:

Continuous-variable quantum-state tomography is generally resource-intensive.
Gaussian states and specific non-Gaussian states offer efficient tomography pathways.
These findings impact the development of quantum technologies relying on state characterization.