We present a simple device based on the controlled-SWAP gate that performs quantum state tomography. It can also be used to determine maximum and minimum eigenvalues, expectation values of arbitrary observables, purity estimation as well as characterizing quantum channels. The advantage of this scheme is that the architecture is fixed and the task performed is determined by the input data.PACS numbers: 03.67. Hk, 03.67.Lx One of the the key issues in quantum information is, given an unknown quantum system, what can we learn about it. In particular, we are concerned not only with the resources needed (number of identical unknown physical systems), but also with the complexity of quantum operations required (number of different devices, networks, etc.), in order to obtain certain information about a quantum state, characterized by its density matrix ̺. There are many interesting parameters of ̺ we can determine, such as its maximum and minimum eigenvalues, its purity or even ̺ itself (state tomography [1]), but we also can use ̺ to determine expectation values of arbitrary observables or to characterize unknown quantum channels. However, this usually involves building separate devices for each task, or even building different devices for different measurements within the same task.In this paper we present a simple, universal device, whose architecture is fixed but whose behaviour is determined by the choice of input data [2] (see also [3] for a quantum optical realization of a similar idea). In fact, with suitable input, we can directly measure all the properties mentioned before.Consider a typical interferometric set-up for a single qubit: Hadamard gate, phase shift ϕ, Hadamard gate, followed by a measurement in the computational basis. Here and in the following, we borrow terminology from quantum information science and describe quantum interferometry in terms of quantum logic gates [4]. We modify the interferometer by inserting a controlled-U operation between the Hadamard gates, with its control on the qubit and with U acting on a quantum system described by some unknown density operator ρ. We do not assume anything about the form of ρ, it can, for example, describe several entangled or separable subsystems. This set-up is shown in Fig. 1. The action of the controlled-U on ρ modifies the interference pattern by the factor,where v is the new visibility and α is the shift of the interference fringes, also known as the Pancharatnam phase [5]. Thus, the observed visibility gives a straightforward way of estimating the average value of unitary operators U in state ρ and has a variety of interesting applications. For example, it can be used to measure some entanglement witnesses W , as long as they are unitary operators and the corresponding controlled-W operations are easy to implement [6]. Here, we focus on the applications related to quantum state state tomography. Clearly the interferometer in Fig. 1 can be used to estimate any d × d

Non-linear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number parameters that specify the state. Here we extract a non-local and a non-linear quantity, namely the Renyi entropy, from local measurements on two pairs of polarization entangled photons. We also introduce a "phase marking" technique which allows to select uncorrupted outcomes even with non-deterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of a non-linear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-CHSH inequalities. PACS numbers:Many interesting properties of composite quantum systems, such as entanglement or entropy, are not measured directly but are inferred, usually from a full specification of a quantum state represented by a density operator. However, it is interesting to note that some of these properties can be measured in the same way we measure and estimate average values of observables. Here we illustrate this by extracting a non-local quantity, the Renyi entropy of the composite system, from local measurements on two pairs of polarization entangled photons. This quantity is a non-linear function of the density operator. We then use our experimental data to demonstrate the violation of entropic inequalities, which can be also interpreted as the experimental demonstration of a non-linear entanglement witness.Consider a source which generates pairs of photons. The photons in each pair fly apart from each other to two distant locations A and B. Let us assume that the polarization of each pair is described by some density operator ̺, which is unknown to us. Following Schrödinger's remarks on relations between the information content of the total system and its sub-systems [1], it has been proven that for separable states global von Neumann entropy is always not less then local ones [2]. Subsequently a number of entropic inequalities have been derived, satisfied by all separable states [3,4,5,6]. The simplest one is based on the Renyi entropy, or the purity measure, Tr (̺ 2 ) and can be rewritten aswhere ̺ A and ̺ B are the reduced density operators pertaining to individual photons. The inequalities (1) involve non-linear functions of density operators and are known to be stronger than all Bell-CHSH inequalities [3,7]. There are entangled states which are not and S2 emit pairs of polarization-entangled photons. The entangled pairs are emitted into spatial modes 1 and 3, and 2 and 4. One photon from each pair is directed into location A and the other into location B. At the two locations photons impinge on beam-splitters and are then detected by photodetectors. There are four possible outcomes in this experiment: coalescence at A and coalescence at B, coalescen...

We present an entanglement generation scheme which allows arbitrary graph states to be efficiently created in a linear quantum register via an auxiliary entangling bus. The dynamics of the entangling bus is described by an effective non-interacting fermionic system undergoing mirror-inversion in which qubits, encoded as local fermionic modes, become entangled purely by Fermi statistics. We discuss a possible implementation using two species of neutral atoms stored in an optical lattice and find that the scheme is realistic in its requirements even in the presence of noise.PACS numbers: 03.67. Mn, 03.67.Lx Bipartite entanglement has long been recognized as a useful physical resource for tasks such as quantum cryptography and quantum teleportation. Similarly, multipartite entanglement is an essential ingredient for more complex quantum information processing (QIP) tasks, and interest in this resource has grown since its controlled generation was demonstrated in several physical systems [1,2]. An important class of multipartite entangled states are graph states. By using vertices in a graph to represent qubits, and edges to represent an Ising type interaction that has taken place between two qubits, the graph formalism gives an effective characterization of entanglement by the presence of edges [3]. Special instances of graph states are the resource used in multi-party communication protocols, in quantum error correcting codes [4] and in one-way quantum computing [5].Initial proposals for the generation of graph states in physical systems focussed on qubit lattices of fixed geometry, where each qubit interacts only with its nearestneighbors [3]. Such a scheme has been experimentally implemented in 1D with optical lattices of neutral atoms via controlled collisions [1]. The graph states generated with this method follow the geometry of the lattice, and for 2D/3D square lattices they constitute, together with single qubit measurements, a universal resource for quantum computation [5]. However, the generation of more complex graphs, where the set of edges does not translate into a regular arrangement of qubits, e.g. the quantum Fourier transform graph state, requires the ability to pre-engineer a complicated geometry of the qubit interactions. A simple scheme in which any graph state can be created in a set of qubits with a regular fixed geometry is therefore highly desirable, and some progress has been made towards this with non-deterministic linear optical protocols [6].In this paper we propose a scheme for efficiently generating arbitrary graph states within a linear quantum register via an auxiliary entangling bus (EB). The EB is a fixed 'always on' system, equivalent, in a specific limit, to a non-interacting fermionic system where qubits trans-FIG. 1: (a) Consider a quantum register R which has 3 graph qubits in a state | + . (b) Two of them are transferred to the EB E where their state is mapped into local fermionic modes. (c) E evolves via H f for time τ , which results in the mirror-inversion of the two qub...

Quantum entanglement, after playing a significant role in the development of the foundations of quantum mechanics [1][2][3], has been recently rediscovered as a new physical resource with potential commercial applications such as, for example, quantum cryptography [4], better frequency standards [5] or quantum-enhanced positioning and clock synchronization [6]. On the mathematical side the studies of entanglement have revealed very interesting connections with the theory of positive maps [7,8]. The capacity to generate entangled states is one of the basic requirements for building quantum computers. Hence, efficient experimental methods for detection, verification and estimation of quantum entanglement are of great practical importance. Here, we propose an experimentally viable, direct detection of quantum entanglement which is efficient and does not require any a priori knowledge about the quantum state. In a particular case of two entangled qubits it provides an estimation of the amount of entanglement. We view this method as a new form of quantum computation, namely, as a decision problem with quantum data structure.Suppose we are given n pairs of particles, all in the same quantum state described by some density operator ̺, which is unknown. We need to decide whether the particles in each pair are entangled or not. From a mathematical point of view we need to assert whether ̺ can be written as a convex sum of product states [9],with α i and β i pertaining to different particles in the pair, and i p i = 1. It is assumed that the Hilbert spaces associated with each particle are of finite dimensions d (taken to be the same for the two particles), so that one can always find k ≤ d 2 . If ̺ were known then we could try either to find the decomposition (1) directly or to use one of the mathematical separability criteria [8]. For sufficiently large n we may indeed start with the quantum state estimation, however, this involves estimating d 4 − 1 real parameters of ̺, most of which are irrelevant in the context of the entanglement detection. In the following we describe a direct method of detecting quantum entanglement without invoking the state estimation.We construct a measurement which can be performed on all copies of ̺ and which is as powerful in detecting quantum entanglement as the best mathematical test based on positive maps [7]. The measurement can be viewed as two consecutive physical operations: firstly, we construct a transformation which maps ̺ into an appropriate state ̺ ′ and, secondly, we measure the lowest eigenvalue of ̺ ′ . This eigenvalue alone serves as a separability indicator.A convenient starting point for our construction is the most powerful, albeit purely mathematical and not directly implementable, separability criterion proposed to date. It is based on mathematical properties of linear positive maps acting on matrices [7]. Let M d be a space of matrices of dimension d; recall that Λ :

We show how to efficiently exploit decoherence free subspaces (DFSs), which are immune to collective noise, for realizing quantum repeaters with long lived quantum memories. Our setup consists of an assembly of simple modules and we show how to implement them in systems of cold, neutral atoms in arrays of dipole traps. We develop methods for realizing robust gate operations on qubits encoded in a DFS using collisional interactions between the atoms. We also give a detailed analysis of the performance and stability of all required gate operations and emphasize that all modules can be realized with current or near future experimental technology.

Non-linear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number parameters that specify the state. Here we extract a non-local and a non-linear quantity, namely the Renyi entropy, from local measurements on two pairs of polarization entangled photons. We also introduce a "phase marking" technique which allows to select uncorrupted outcomes even with non-deterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of a non-linear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-CHSH inequalities. PACS numbers: Many interesting properties of composite quantum systems , such as entanglement or entropy, are not measured directly but are inferred, usually from a full specification of a quantum state represented by a density operator. However, it is interesting to note that some of these properties can be measured in the same way we measure and estimate average values of observables. Here we illustrate this by extracting a non-local quantity, the Renyi entropy of the composite system, from local measurements on two pairs of polarization entangled photons. This quantity is a non-linear function of the density operator. We then use our experimental data to demonstrate the violation of entropic inequalities, which can be also interpreted as the experimental demonstration of a non-linear entangle-ment witness. Consider a source which generates pairs of photons. The photons in each pair fly apart from each other to two distant locations A and B. Let us assume that the polarization of each pair is described by some density operator ̺, which is unknown to us. Following Schrödinger's remarks on relations between the information content of the total system and its subsystems [1], it has been proven that for separable states global von Neumann en-tropy is always not less then local ones [2]. Subsequently a number of entropic inequalities have been derived, satisfied by all separable states [3, 4, 5, 6]. The simplest one is based on the Renyi entropy, or the purity measure , Tr (̺ 2) and can be rewritten as Tr (̺ 2 A) ≥ Tr (̺ 2), Tr (̺ 2 B) ≥ Tr (̺ 2), (1) where ̺ A and ̺ B are the reduced density operators pertaining to individual photons. The inequalities (1) involve non-linear functions of density operators and are known to be stronger than all Bell-CHSH inequalities [3, 7]. There are entangled states which are not S 2 S 1 A B 1 2 3 4 FIG. 1: An outline of our experimental setup. Sources S1 and S2 emit pairs of polarization-entangled photons. The entangled pairs are emitted into spatial modes 1 and 3, and 2 and 4. One photon from each pair is directed into location A and the other into location B. At the two locations photons impinge on beam-splitters and ar...

We propose a simple quantum network to detect multipartite entangled states of bosons and show how to implement this network for neutral atoms stored in an optical lattice. We investigate the special properties of cluster states, multipartite entangled states, and superpositions of distinct macroscopic quantum states that can be identified by the network.

We propose a method for the experimental generation of two different families of bound entangled states of three qubits. Our method is based on the explicit construction of a quantum network that produces a purification of the desired state. We also suggest a route for the experimental detection of bound entanglement, by employing a witness operator plus a test of the positivity of the partial transposes.