Entanglement of a Pair of Quantum Bits
@article{Hill1997EntanglementOA, title={Entanglement of a Pair of Quantum Bits}, author={S H Hill and William K. Wootters}, journal={Physical Review Letters}, year={1997}, volume={78}, pages={5022-5025} }
The ``entanglement of formation'' of a mixed state \ensuremath{\rho} of a bipartite quantum system can be defined as the minimum number of singlets needed to create an ensemble of pure states that represents \ensuremath{\rho}. We find an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two nonzero eigenvalues, and we report evidence suggesting that the formula is valid for all states of this system.
Figures from this paper
1,985 Citations
Entanglement of Formation of an Arbitrary State of Two Qubits
- Physics
- 1998
The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state is defined as the minimum average…
Degree of entanglement for two qubits
- Physics
- 2001
We demonstrate that any pure bipartite state of two qubits may be decomposed into a superposition of a maximally entangled state and an orthogonal factorizable one. Although there are many such…
Entanglement of Formation of an Arbitrary State of Two Rebits
- Physics
- 2000
We consider entanglement for quantum states defined in vector spaces over the real numbers. Such real entanglement is different from entanglement in standard quantum mechanics over the complex…
Note on Entanglement of an Arbitrary State of Two Qubits
- Physics
- 2000
It is shown that the norm of the polarization vector of the reduced density matrix can characterize the entanglement of two qubits and so it is defined as a simple measure of entanglement. It is then…
Geometrical Representation of Entanglement of a Three-Qubit |W> State
- Physics
- 2004
In this paper we study the quantum entanglement properties of a tripartite system of qubits. We use the concept of two‐tangle and three‐tangle to understand the nature of entanglement of |W〉 and…
Entanglement distance for arbitrary M -qudit hybrid systems
- Computer SciencePhysical Review A
- 2020
A measure of entanglement that can be computed for any pure state of an $M$-qubit system, and the analysis of the eigenvalues of $\tilde{g}$ gives information about the robustness ofEntanglement.
A Simplified and Obvious Expression of Concurrence in Wootters' Measure of Entanglement of a Pair of Qubits
- Physics
- 2003
We obtain a simplified and obvious expression of ``concurrence" in Wootters' measure of entanglement of a pair of qubits that have no more than two non-zero eigenvalues in terms of the concurrences…
Correlation between resource-generating powers of quantum gates
- PhysicsPhysical Review A
- 2023
We analyze the optimal basis for generating the maximum relative entropy of quantum coherence by an arbitrary gate on a two-qubit system. The optimal basis is not unique, and the high quantum…
Entanglement of Formation
- Physics
- 2002
At least three distinct information-theoretic measures of quantum entanglement have been proposed in recent years. This paper highlights one of them, the entanglement of formation, as well as a…
References
SHOWING 1-8 OF 8 REFERENCES
Quantifying Entanglement
- Physics
- 1997
We have witnessed great advances in quantum information theory in recent years. There are two distinct directions in which progress is currently being made: quantum computation and error correction…
Trans
- Am. Math. Soc. 135, 199 (1969); A. Uhlmann, Rep. Math. Phys. 9, 273 (1976); R. Jozsa, J. Mod. Optics41, 2315
- 1994
Am. Math. Soc. Uhlmann, Rep. Math. Phys. Jozsa, J. Mod. Optics
- Am. Math. Soc. Uhlmann, Rep. Math. Phys. Jozsa, J. Mod. Optics
- 1969
Science
- Science
- 1995
Some alternatives to the definition we adopt , based on other criteria , are given in
- Phys . Rev . Lett .
- 1996
Phys. Rev. Lett
- Phys. Rev. Lett
- 1991
For a guide to some of the literature
- Am. J. Phys
- 1986