# Computing quantum discord is NP-complete

@article{Huang2014ComputingQD, title={Computing quantum discord is NP-complete}, author={Yichen Huang}, journal={New Journal of Physics}, year={2014}, volume={16} }

We study the computational complexity of quantum discord (a measure of quantum correlation beyond entanglement), and prove that computing quantum discord is NP-complete. Therefore, quantum discord is computationally intractable: the running time of any algorithm for computing quantum discord is believed to grow exponentially with the dimension of the Hilbert space so that computing quantum discord in a quantum system of moderate size is not possible in practice. As by-products, some…

## 14 Citations

Cost of quantum entanglement simplified

- PhysicsPhysical review letters
- 2020

This Letter introduces an entanglement measure that has a precise information-theoretic meaning as the exact cost required to prepare an entangled state when two distant parties are allowed to perform quantum operations that completely preserve the positivity of the partial transpose.

Geometric quantum discord under noisy environment

- PhysicsQuantum Inf. Process.
- 2016

The effects of collective dephasing noise and rotating noise to a class of two-qubit X states are analyzed, and it is found that quantum correlation is not altered by the collective noises.

Calculation of quantum discord in higher dimensions for X- and other specialized states

- PhysicsQuantum Inf. Process.
- 2018

This paper focuses on this method that uses unitary operations to describe measurements, reducing them to a compact form so as to minimize the number of variables needed for extremizing the classical correlation, often the most difficult part of the discord calculation.

Coherence, entanglement, and quantumness in closed and open systems with conserved charge, with an application to many-body localization

- PhysicsPhysical Review A
- 2019

While the scaling of entanglement in a quantum system can be used to distinguish many-body quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum…

The Optimization Problem of Quantum Discord and Quantumness in Quantum Information Theory

- Physics
- 2018

A mathematical proof is presented for showing that quantum discord minimizes at the diagonal basis of the reduced density matrices for a general m x n density matrix.

Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations

- Physics, Computer Science
- 2017

It is shown that the violation of recent entropic witnesses of the Einstein-Podolsky-Rosen paradox also provides tight lower bounds to multiple entanglement measures, such as the $\textit{entanglement of formation}$ and the $\ textit{distillableEntanglement}$, among others.

Single-Copies Estimation of Entanglement Negativity.

- PhysicsPhysical review letters
- 2020

A scheme to estimate the entanglement negativity for any bipartition of a composite system based on the random unitary evolution and local measurements on a single-copy quantum state, which is more practical compared to former methods based on collective measurements on many copies of the identical state.

Entanglement properties of a measurement-based entanglement distillation experiment

- Physics, Computer SciencePhysical Review A
- 2019

This work analyzes a continuous-variable measurement-basedEntanglement distillation experiment using a collection of entanglement measures, demonstrating that logarithmic negativity alone is inadequate for assessing the performance of the distillation protocol.

Controlling steady-state entanglement and quantum discord through squeezing angle

- PhysicsChaos, Solitons & Fractals
- 2019

General bounds for quantum discord and discord distance

- MathematicsQuantum Inf. Process.
- 2015

The upper bound of purified quantum discord is studied using the Koashi–Winter relation to find that Luo et al.