Operator-Schmidt decomposition of the quantum Fourier transform on C^N1 tensor C^N2

Operator-Schmidt decompositions of the quantum Fourier transform on C^N1 tensor C^N2 are computed for all N1, N2 > 1. The decomposition is shown to be completely degenerate when N1 is a factor of N2 and when N1>N2. The first known special case, N1=N2=2^n, was computed by Nielsen in his study of the communication cost of computing the quantum Fourier transform of a collection of qubits equally distributed between two parties. [M. A. Nielsen, PhD Thesis, University of New Mexico (1998), Chapter 6, arXiv:quant-ph/0011036.] More generally, the special case N1=2^n1<2^n2=N2 was computed by Nielsen et. al. in their study of strength measures of quantum operations. [M.A. Nielsen et. al, (accepted for publication in Phys Rev A); arXiv:quant-ph/0208077.] Given the Schmidt decompositions presented here, it follows that in all cases the communication cost of exact computation of the quantum Fourier transform is maximal.Comment: 9 pages, LaTeX 2e; No changes in results. References and acknowledgments added. Changes in presentation added to satisfy referees: expanded introduction, inclusion of ommitted algebraic steps in the appendix, addition of clarifying footnote

Continuity bounds for entanglement

This note quantifies the continuity properties of entanglement: how much does entanglement vary if we change the entangled quantum state just a little? This question is studied for the pure state entanglement of a bipartite system and for the entanglement of formation of a bipartite system in a mixed state.Comment: 5 pages, submitted to Physical Review A Brief Reports. Minor typo in equation (25) corrected in resubmissio

Quantum parallelism of the controlled-NOT operation: an experimental criterion for the evaluation of device performance

It is shown that a quantum controlled-NOT gate simultaneously performs the logical functions of three distinct conditional local operations. Each of these local operations can be verified by measuring a corresponding truth table of four local inputs and four local outputs. The quantum parallelism of the gate can then be observed directly in a set of three simple experimental tests, each of which has a clear intuitive interpretation in terms of classical logical operations. Specifically, quantum parallelism is achieved if the average fidelity of the three classical operations exceeds 2/3. It is thus possible to evaluate the essential quantum parallelism of an experimental controlled-NOT gate by testing only three characteristic classical operations performed by the gate.Comment: 6 pages, no figures, added references and discussio

Resources required for exact remote state preparation

It has been shown [M.-Y. Ye, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 69, 022310 (2004)] that it is possible to perform exactly faithful remote state preparation using finite classical communication and any entangled state with maximal Schmidt number. Here we give an explicit procedure for performing this remote state preparation. We show that the classical communication required for this scheme is close to optimal for remote state preparation schemes of this type. In addition we prove that it is necessary that the resource state have maximal Schmidt number.Comment: 7 pages, 1 figur

Analysis of an experimental quantum logic gate by complementary classical operations

Quantum logic gates can perform calculations much more efficiently than their classical counterparts. However, the level of control needed to obtain a reliable quantum operation is correspondingly higher. In order to evaluate the performance of experimental quantum gates, it is therefore necessary to identify the essential features that indicate quantum coherent operation. In this paper, we show that an efficient characterization of an experimental device can be obtained by investigating the classical logic operations on a pair of complementary basis sets. It is then possible to obtain reliable predictions about the quantum coherent operations of the gate such as entanglement generation and Bell state discrimination even without performing these operations directly.Comment: 14 pages, 1 figure, 3 tables, Brief Review for Modern Physics Letters A, includes a more detailed analysis of the experimental data in Phys. Rev. Lett. 95, 210506 (2005) (quant-ph/0506263). v2 has minor corrections in layou

Communication cost of breaking the Bell barrier

Correlations in an Einstein-Podolsky-Rosen-Bohm experiment can be made stronger than quantum correlations by allowing a single bit of classical communication between the two sides of the experiment.Comment: One new reference referring to a maximal algebraic violation of the Clauser-Horne-Shimony-Holt (CHSH) inequalit

Separable states are more disordered globally than locally

A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice (A) and Bob (B), may be more disordered locally than globally. That is, S(A) > S(A,B), where S(.) is the von Neumann entropy. It is known that satisfaction of this inequality implies that a state is non-separable. In this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system AB is majorized by the vector of eigenvalues of the density matrix of system A alone. This gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions. We also investigate the extent to which these conditions are sufficient to characterize separability, exhibiting examples that show separability cannot be characterized solely in terms of the local and global spectra of a state. We apply our conditions to give a simple proof that non-separable states exist sufficiently close to the completely mixed state of $n$ qudits.Comment: 4 page

Resonant purification of mixed states for closed and open quantum systems

Pure states are fundamental for the implementation of quantum technologies, and several methods for the purification of the state of a quantum system S have been developed in the past years. In this letter we present a new approach, based on the interaction of S with an auxiliary system P, having a wide range of applicability. Considering two-level systems S and P and assuming a particular interaction between them, we prove that complete purifications can be obtained under suitable conditions on the parameters characterizing P. Using analytical and numerical tools, we show that the purification process exhibits a resonant behavior in both the cases of system isolated from the external environment or not.Comment: 4 pages, LaTe