author={Samuel L. Braunstein and Carlton M. Caves and Richard Jozsa and Noah Linden and Sandu Popescu and R{\"u}diger Schack},
  journal={Physical Review Letters},
We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable (unentangled). The construction provides an explicit representation of any such state as a mixture of product states. We give upper and lower bounds on the size of the neighborhood, which show that its extent decreases exponentially with the number of qubits. The bounds show that no entanglement appears in the physical states at any stage of present NMR… 
Upper bound on the region of separable states near the maximally mixed state
A lower bound on the amount of noise that must be added to a GHZ-like entangled state to make it separable (also called the random robustness) is found using the transposition condition. The bound is
Quantum dissonance and deterministic quantum computation with a single qubit
This work provides conclusive evidence that there are instances where quantum entanglement is not present in any part of this model, nevertheless it establishes the fact that quantum dissonance present in fully separable (FS) states provide power to DQC1 model.
Orthogonal measurements are almost sufficient for quantum discord of two qubits
The common use in the literature of orthogonal measurements in obtaining quantum discord for two-qubit states is discussed and compared with more general measurements. We prove the optimality of
Statistical constraints on state preparation for a quantum computer
  • S. Kak
  • Physics, Computer Science
  • 2001
This work considers the practical problem of creating a coherent superposition state of several qubits and shows that the constraints of quantum statistics require that the entropy of the system be brought down when several independent qubits are assembled together.
Quantum computing without entanglement
Good dynamics versus bad kinematics: is entanglement needed for quantum computation?
This work analyzes quantum computational protocols which aim to solve exponential classical problems with polynomial resources and shows that, for a large class of such protocols, including Shor's factorization, entanglement is necessary.
Noise robustness of the nonlocality of entangled quantum states.
This work constructs a local model for the case in which rho is maximally entangled and p is at or below a certain bound, and extends the model to arbitrary rho, providing bounds on the resistance to noise of the nonlocal correlations of entangled states.
Quantum entanglement and classical separability in NMR computing
In the discussion about the quantumness of NMR computation a conclusion is done that computational states are separable and therefore can not be entangled. This conclusion is based on the assumption
Quantum Computing with Separable States
It has been shown recently that all nuclear spin states occuring in cur­ rent NMR (nuclear magnetic resonance) quantum computing experi­ ments are separable, i.e., the spins are unentangled and can
Any two-qubit state has nonzero quantum discord under global unitary operations
Quantum discord is significant in analyzing quantum nonclassicality beyond the paradigm of entanglement. Presently we have explored the effectiveness of global unitary operations in manifesting


Volume of the set of separable states
The question of how many entangled or, respectively, separable states there are in the set of all quantum states is considered. We propose a natural measure in the space of density matrices %
Robustness of entanglement
In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is
Power of One Bit of Quantum Information
In standard quantum computation, the initial state is pure and the answer is determined by making a measurement of some of the bits in the computational basis. What can be accomplished if the initial
Ensemble quantum computing by NMR spectroscopy
A new computational model is presented, which differs from a QC only in that the result of a measurement is the expectation value of the observable, rather than a random eigenvalue thereof, which can solve nondeterministic polynomial-time complete problems inPolynomial time.
Bulk quantum computation with nuclear magnetic resonance: theory and experiment
We show that quantum computation is possible with mixed states instead of pure states as inputs. This is performed by embedding within the mixed state a subspace that transforms like a pure state and
Experimental realization of a quantum algorithm
Quantum computers can in principle exploit quantum-mechanical effects to perform computations (such as factoring large numbers or searching an unsorted database) more rapidly than classical
Purification of noisy entanglement and faithful teleportation via noisy channels.
Upper and lower bounds on the yield of pure singlets ($\ket{\Psi^-}$) distillable from mixed states $M$ are given, showing $D(M)>0$ if $\bra{Psi-}M\ket-}>\half$.
Bulk Spin-Resonance Quantum Computation
A new approach to quantum computing is introduced based on the use of multiple-pulse resonance techniques to manipulate the small deviation from equilibrium of the density matrix of a macroscopic ensemble so that it appears to be the density Matrix of a much lower dimensional pure state.
Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer
This work demonstrates the use of a NMR quantum computer based on the pyrimidine base cytosine, and the implementation of a quantum algorithm to solve Deutsch’s problem (distinguishing between constant and balanced functions).
Bell’s theorem without inequalities
It is demonstrated that the premisses of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that the