The trumping relation and the structure of the bipartite entangled states

The majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two states is not possible, but it becomes possible in the presence of another state (known as a catalyst); this situation is described mathematically by the trumping relation, an extension of majorization. The structure of the trumping relation is not nearly as well understood as that of majorization. We give an introduction to this subject and derive some new results. Most notably, we show that the dimension of the required catalyst is in general unbounded; there is no integer $k$ such that it suffices to consider catalysts of dimension $k$ or less in determining which states can be catalyzed into a given state. We also show that almost all bipartite entangled states are potentially useful as catalysts.Comment: 7 pages, RevTe

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

Linear optics quantum Toffoli and Fredkin gates

We design linear optics multiqubit quantum logic gates. We assume the traditional encoding of a qubit onto state of a single photon in two modes (e.g. spatial or polarization). We suggest schemes allowing direct probabilistic realization of the fundamental Toffoli and Fredkin gates without resorting to a sequence of single- and two-qubit gates. This yields more compact schemes and potentially reduces the number of ancilla photons. The proposed setups involve passive linear optics, sources of auxiliary single photons or maximally entangled pairs of photons, and single-photon detectors. In particular, we propose an interferometric implementation of the Toffoli gate in the coincidence basis, which does not require any ancilla photons and is experimentally feasible with current technology.Comment: 8 pages, 4 figures, RevTeX

Quantum discord between relatively accelerated observers

We calculate the quantum discord between two free modes of a scalar field which start in a maximally entangled state and then undergo a relative, constant acceleration. In a regime where there is no distillable entanglement due to the Unruh effect, we show that there is a finite amount of quantum discord, which is a measure of purely quantum correlations in a state, over and above quantum entanglement. Even in the limit of infinite acceleration of the observer detecting one of the modes, we provide evidence for a non-zero amount of purely quantum correlations, which might be exploited to gain non-trivial quantum advantages.Comment: 4 pages, 2 figure

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

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

Distributed implementation of standard oracle operators

The standard oracle operator corresponding to a function f is a unitary operator that computes this function coherently, i.e. it maintains superpositions. This operator acts on a bipartite system, where the subsystems are the input and output registers. In distributed quantum computation, these subsystems may be spatially separated, in which case we will be interested in its classical and entangling capacities. For an arbitrary function f, we show that the unidirectional classical and entangling capacities of this operator are log_{2}(n_{f}) bits/ebits, where n_{f} is the number of different values this function can take. An optimal procedure for bidirectional classical communication with a standard oracle operator corresponding to a permutation on Z_{M} is given. The bidirectional classical capacity of such an operator is found to be 2log_{2}(M) bits. The proofs of these capacities are facilitated by an optimal distributed protocol for the implementation of an arbitrary standard oracle operator.Comment: 4.4 pages, Revtex 4. Submitted to Physical Review Letter

State Transfer and Spin Measurement

We present a Hamiltonian that can be used for amplifying the signal from a quantum state, enabling the measurement of a macroscopic observable to determine the state of a single spin. We prove a general mapping between this Hamiltonian and an exchange Hamiltonian for arbitrary coupling strengths and local magnetic fields. This facilitates the use of existing schemes for perfect state transfer to give perfect amplification. We further prove a link between the evolution of this fixed Hamiltonian and classical Cellular Automata, thereby unifying previous approaches to this amplification task. Finally, we show how to use the new Hamiltonian for perfect state transfer in the, to date, unique scenario where total spin is not conserved during the evolution, and demonstrate that this yields a significantly different response in the presence of decoherence.Comment: 4 pages, 2 figure

Entanglement detection beyond the CCNR criterion for infinite-dimensions

In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entanglement criterion which is strictly stronger than the computable cross-norm or realignment (CCNR) criterion.Comment: 11 page