Why Two Qubits Are Special

Abstract

We analyze some special properties of a system of two qubits, and in particular of the so-called Bell basis for this system, which have played an important role in recent papers on entanglement of qubits. In particular, we show which of these properties may be generalized to higher dimension. We give a general construction for bases of maximally entangled vectors in any dimension, but show that none of the properties related to complex conjugation in Bell basis can be realized for higher dimensional analogs.

16 pages, TeX

Cited by in corpus (34)

• Entanglement Measures under Symmetry
• Quantum Correlations in Systems of Indistinguishable Particles
• Bloch vectors for qudits
• Dynamics of quantum entanglement
• Dividing Quantum Channels
• All Teleportation and Dense Coding Schemes
• Quantifying entanglement resources
• The state space for two qutrits has a phase space structure in its core
• Entanglement or separability: The choice of how to factorize the algebra of a density matrix
• The geometry of bipartite qutrits including bound entanglement
• Synthesis of Multivalued Quantum Logic Circuits by Elementary Gates
• The fully entangled fraction as an inclusive measure of entanglement applications
• Entanglement witnesses and geometry of entanglement of two--qutrit states
• Incompatibility breaking quantum channels
• Entangling Power of Permutations
• CP^n, or, entanglement illustrated
• Quantum teleportation with identical particles
• Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries
• Gate simulation and lower bounds on the simulation time
• Constructing Mutually Unbiased Bases from Quantum Latin Squares
• How many orthonormal bases are needed to distinguish all pure quantum states?
• Analysis of Bell inequality violation in superconducting qubits
• On orthogonal bases in the Hilbert-Schmidt space of matrices
• State independent uncertainty relations from eigenvalue minimization
• Multipartite entanglement transfer in spin chains
• Relative volume of separable bipartite states
• On the fidelity of two pure states
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Effects of decoherence and errors on Bell-inequality violation
• Degree of separability of bipartite quantum states
• Rigidity of superdense coding
• Optimal quantum tomography with constrained elementary measurements arising from unitary bases
• Gleason's Theorem for a Qubit as Part of a Composite System
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings