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We investigate quantum measurement strategies capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non- probabilistic state discrimination. We apply a postselection strategy to the measurement data of a homodyne detector as well as a photon number resolving detector in order to lower the error probability. We compare the two different receivers with an optimal intermediate measurement scheme where the error rate is minimized for a fixed rate of inconclusive results. The photon number resolving (PNR) receiver is experimentally demonstrated and compared to an experimental realization of a homodyne receiver with postselection. In the comparison it becomes clear, that the perfromance of the new PNR receiver surpasses the performance of the homodyne receiver, which we proof to be optimal within any Gaussian operations and conditional dynamics., Comment: 10 pages, 6 figures

This paper discusses energy-time entanglement experiments and their relation to Einstein-Podolsky-Rosen (EPR) elements of reality. The interferometric experiment proposed by J. D. Franson in 1989 provides the background, and the main issue here is a detailed discussion on whether a Local Realist model can give the Quantum-Mechanical predictions for this setup. The Franson interferometer gives the same interference pattern as the usual Bell experiment (modulo postselection). Even so, depending on the precise requirements made on the Local Realist model, this can imply a) no violation, b) smaller violation than usual, or c) full violation of the appropriate statistical bound. This paper discusses what requirements are necessary on the model to reach a violation, and the motivation for making these requirements. The alternatives include using a) only the measurement outcomes as EPR elements of reality, b) the emission time as EPR element of reality, and c) path realism. The subtleties of this discussion needs to be taken into account when designing and setting up future experiments of this kind, intended to test Local Realism.

We demonstrate and characterize interference between discrete photons emitted by two separate semiconductor quantum dot states in different samples excited by a pulsed laser. Their energies are tuned into resonance using strain. The photons have a total coalescence probability of 18.1% and the coincidence rate is below the classical limit. Post-selection of coincidences within a narrow time window increases the coalescence probability to 47%. The probabilities are reduced from unity because of dephasing and the postselection value is also reduced by the detector time response., Comment: 4 pages, 3 figures

We show that non-local Popescu-Rohrlich correlations can be observed in the post-selected results of binned position measurements on a two-party gaussian state. Our experiment is based on the spatial correlations of entangled photons and lens systems. We obtain a maximum violation of the CHSH inequality of 3.42, which corresponds to the implementation of a non-local AND gate with success probability of 0.93. These results do not conflict with quantum mechanics due to the post-selection required, and open up the possibility of experimental investigation of fundamental aspects of Popescu-Rohrlich non-locality with a reliable and simple experimental setup., 4 pages, 3 figures

Ti:LiNbO 3 waveguide devices consisting of cascaded two sections for generation of postselection-free polarization-entangled twin photons are proposed. Generation of the entangled photons in the telecom band is demonstrated by quantum interference experiments.

The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non-probabilistic state discrimination. We find that appropriate postselection of the measurement data of a photon number resolving detector can be used to discriminate two coherent states with small error probability. We compare our new receiver to an optimal intermediate measurement between minimum error discrimination and unambiguous state discrimination., 5 pages, 4 figures

We estimate the quantum state of a system between two measurements via a maximum likelihood strategy. This incorporates all the information provided by preselection and postselection in a legitimate quantum state. Moreover, it allows to include any other constraint derived from practical considerations.

We report on an experimental violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality using energy-time entangled photons. The experiment is not free of the locality and detection loopholes, but is the first violation of the Bell-CHSH inequality using energy-time entangled photons which is free of the postselection loophole described by Aerts et al. [Phys. Rev. Lett. 83, 2872 (1999)]., Comment: 4 pages, 3 figures, v2 minor corrections

We consider the distinguishability of Gaussian states from the view point of continuous-variable quantum cryptography using post-selection. Specifically, we use the probability of error to distinguish between two pure coherent (squeezed) states and two particular mixed symmetric coherent (squeezed) states where each mixed state is an incoherent mixture of two pure coherent (squeezed) states with equal and opposite displacements in the conjugate quadrature. We show that the two mixed symmetric Gaussian states (where the various components have the same real part) never give an eavesdropper more information than the two pure Gaussian states. Furthermore, when considering the distinguishability of squeezed states, we show that varying the amount of squeezing leads to a "squeezing" and "anti-squeezing" of the net information rates., Comment: 10 pages, 9 figures

We report the experimental realization of entanglement localization which restores polarization entanglement completely redirected after a linear coupling with incoherent and noisy surrounding photon. The method, based only on measurements of the surrounding photon after the coupling and on post-selection, can localize the entanglement back to original systems for any linear coupling., 4 pages, 4 figures

We present a detailed description of an architecture for fault-tolerant quantum computation, which is based on the cluster model of encoded qubits. In this cluster-based architecture, concatenated computation is implemented in a quite different way from the usual circuit-based architecture where physical gates are recursively replaced by logical gates with error-correction gadgets. Instead, some relevant cluster states, say fundamental clusters, are recursively constructed through verification and postselection in advance for the higher-level one-way computation, which namely provides error-precorrection of gate operations. A suitable code such as the Steane seven-qubit code is adopted for transversal operations. This concatenated construction of verified fundamental clusters has a simple transversal structure of logical errors, and achieves a high noise threshold ~ 3 % for computation by using appropriate verification procedures. Since the postselection is localized within each fundamental cluster with the help of deterministic bare controlled-Z gates without verification, divergence of resources is restrained, which reconciles postselection with scalability., Comment: 16 pages, 34 figures

We rigorously analyze Knill's Fibonacci scheme for fault-tolerant quantum computation, which is based on the recursive preparation of Bell states protected by a concatenated error-detecting code. We prove lower bounds on the threshold fault rate of .67\times 10^{-3} for adversarial local stochastic noise, and 1.25\times 10^{-3} for independent depolarizing noise. In contrast to other schemes with comparable proved accuracy thresholds, the Fibonacci scheme has a significantly reduced overhead cost because it uses postselection far more sparingly., 24 pages, 10 figures; supersedes arXiv:0709.3603. (v2): Additional discussion about the overhead cost

A novel description of quantum systems is employed for constructing a “time machine” capable of shifting in time the wave function of a quantum system. This device uses gravitational time dilations and a peculiar quantum interference effect due to preselection and postselection. In most trials this time machine fails to operate but when it does succeed it accomplishes tasks which no other machine can.

We demonstrate a linear optical device which performs optimal quantum measurement or minimum disturbance measurement on a single-photon polarization qubit with the help of an ancillary path qubit introduced to the same photon. We show theoretically and experimentally that this device satisfies the minimum disturbance measurement condition by investigating the relation between the information gain (estimation fidelity) and the state disturbance due to measurement (operation fidelity). Our implementation of minimal disturbance measurement is postselection-free in the sense that all detection events are counted toward evaluation of the estimation fidelity and the operation fidelity, i.e., there is no need for coincidence postselection of the detection events.

Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent pre- and post-selected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of post-selection and the choice of final state. The generalized law is illustrated for two interesting choices of post-selection., 7 pages, research paper, revised to incorporate some introductory background on the subject

The deep-rooted concept of ``realism''\char22{}a viewpoint according to which an external reality exists independent of observation, may have been shaken to some extent by a recent surprising advance in experimental test of a broad class of nonlocal hidden-variable (NLHV) theories [S. Gr\"oblacher, T. Paterek, R. Kaltenbaek, \ifmmode \check{C}\else \v{C}\fi{}. Brukner, M. \ifmmode \dot{Z}\else \.{Z}\fi{}ukowski, M. Aspelmeyer, and A. Zeilinger, Nature (London) 446, 871 (2007)], though there exists a detection loophole. In this paper a feasible propose for a loophole-free test of non-local realism is discussed based on the independent readout of two electron spins of donors $^{31}\text{P}$ in semiconductors in different cavities entangled through a 4.4 dB bright squeezed coherent light and a postselection based on homodyne measurement. The electron spins are read out by using optically induced spin to charge transduction detected by radio-frequency single electron transistor.

We report on the experimental demonstration of an all-optical pi cross-phase modulation jump. By performing a preselection, an optically induced unitary transformation, and then a postselection on the polarization degree of freedom, the phase of the output beam acquires either a zero or pi phase shift (with no other possible values). The postselection results in optical loss in the output beam. An input state may be chosen near the resulting phase singularity, yielding a pi phase shift even for weak interaction strengths. The scheme is experimentally demonstrated using a coherently prepared dark state in a warm atomic cesium vapor.

We report on the implementation of a new interferometric scheme that allows the generation of photon pairs entangled in the time-energy degree of freedom. This scheme does not require any kind of temporal post-selection on the generated pairs and can be used even with lasers with short coherence time., RevTex, 6 pages, 8 figures

We propose a scheme to generate four-photon polarization-entangled states, which enables the encoding of an arbitrary qubit into a four-qubit decoherence-free subspace robust against collective decoherence. The scheme is based on linear optical elements and postselection strategy, which is feasible with existing experimental technology.

We propose and demonstrate a linear optical device which deterministically performs optimal quantum measurement or minimum disturbance measurement on a single-photon polarization qubit with the help of an ancillary path qubit introduced to the same photon. We show theoretically and experimentally that this device satisfies the minimum disturbance measurement condition by investigating the relation between the information gain (estimation fidelity) and the state disturbance due to measurement (operation fidelity). Our implementation of minimum disturbance measurement is postselection-free in the sense that all detection events are counted toward evaluation of the estimation fidelity and the operation fidelity, i.e., there is no need for coincidence postselection of the detection events., 4 pages, 3 figures, 1 table

We propose a method for extracting an errorless secret key in a continuous-variable quantum key distribution protocol, which is based on Gaussian modulation of coherent states and homodyne detection. The crucial feature is an eight-dimensional reconciliation method, based on the algebraic properties of octonions. Since the protocol does not use any postselection, it can be proven secure against arbitrary collective attacks, by using well-established theorems on the optimality of Gaussian attacks. By using this new coding scheme with an appropriate signal to noise ratio, the distance for secure continuous-variable quantum key distribution can be significantly extended., 8 pages, 3 figures

We introduce an elementary optical gate for expanding polarization entangled $W$ states in which every pair of photons is entangled alike. The gate is composed of a pair of 50:50 beamsplitters and ancillary photons in the two-photon Fock state. By seeding one of the photons in an $n$-photon $W$ state into this gate, we obtain an $(n+2)$-photon $W$ state after postselection. This gate gives a better efficiency and a simpler implementation than previous proposals for $W$-state preparation.

We describe a protocol capable of preparing an arbitrary state of two photons in several spatial modes using pairs of photons generated by spontaneous parametric down-conversion, linear optical elements and single-photon detectors or post-selection. The protocol involves unitary and non-unitary transformations realizable by beam splitters and phase shifters. Non-unitary transformations are implemented by attenuation filters. The protocol contains several optimization capabilities with the goal of improving overall probability of its success. We also show how entangled two-photon states required for quantum computing with linear optics can be prepared using a very simple and feasible scheme., Comment: 9 pages, 9 figures, REVTeX4

We propose a scheme for long-distance distribution of quantum entanglement in which the entanglement between qubits at intermediate stations of the channel is established by using bright light pulses in squeezed states coupled to the qubits in cavities with a weak dispersive interaction. The fidelity of the entanglement between qubits at the neighbor stations (10 km apart from each other) obtained by postselection through the balanced homodyne detection of 7 dB squeezed pulses can reach F=0.99 without using entanglement purification, at same time, the probability of successful generation of entanglement is 0.34., Comment: 4 pages, 2 figures

The human eye can detect optical signals containing only a few photons. We investigate the possibility to demonstrate entanglement with such biological detectors. While one person could not detect entanglement by simply observing photons, we discuss the possibility for several observers to demonstrate entanglement in a Bell-type experiment, in which standard detectors are replaced by human eyes. Using a toy model for biological detectors that captures their main characteristic, namely, a detection threshold, we show that Bell inequalities can be violated, thus demonstrating entanglement. Remarkably, when the response function of the detector is close to a step function, quantum nonlocality can be demonstrated without any further assumptions. For smoother response functions, as for the human eye, postselection is required.

By performing a pre-selection, an optically-induced unitary transformation, and then a postselection on the polarization degree of freedom, the phase of the output beam acquires either a zero or π phase shift. The scheme is experimentally demonstrated using a coherently prepared dark-state in a warm atomic cesium vapor.

In this report, the security condition as well as the security key rate of the main three methods of reconciliation - direct reconciliation (DR), reverse reconciliation (RR) and postselection (PS) are discussed in a lossy and noisy channel, whose parameters are affected by individual attacks, using the channel model. Also disadvantage and advantage of each reconciliation protocol are researched.

We discuss conditions under which joint outcomes of simultaneous measurements of non-commuting canonical observables can be inferred with arbitrary precision. The feat is possible for certain pre- and postselections involving entanglement with ancillary systems.

We study the effects of realistic dephasing environments on a pair of solid-state single-photon sources in the context of the Hong-Ou-Mandel dip. By means of solutions for the Markovian or exact non-Markovian dephasing dynamics of the sources, we show that the resulting loss of visibility depends crucially on the timing of photon detection events. Our results demonstrate that the effective visibility can be improved via temporal post-selection, and also that time-resolved interference can be a useful probe of the interaction between the emitter and its host environment., Comment: 5 pages, 2 figures, published version, title changed, references updated

An optical procedure for measuring the recently introduced weak value of a photon polarization variable is suggested and some of its experimental aspects are discussed. The deflection of a beam passing through a birefringent prism is considered. It is shown that if the beam also passes through preselection and postselection polarization filters, it may have a deflection which is greater than the deflection of the beam without the filters. The magnitude of the deflection is give by weak measurement theory.

Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: Path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect entanglement into an extended graph state formalism. The subsequent growth of the improper graph state can be guided, through a series of strategic decisions, in such a way as to bound the growth of the error and eventually yield a high-fidelity graph state. As an implementation of these techniques, we develop an analytic model for atom (or atom-like) qubits in mismatched cavities, under the double-heralding entanglement procedure of Barrett and Kok [Phys. Rev. A 71, 060310 (2005)]. Compared to straightforward postselection techniques our protocol offers a dramatic improvement in growing complex high-fidelity graph states., 15 pages, 10 figures (which print to better quality than when viewed as an on screen pdf)

We describe a simple measure of fidelity for mixed state postselecting devices. The measure is most appropriate for postselection where the task performed by the output is only effected by a specific state., Comment: 8 Pages, 8 Figures

Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the procedure of weak measurement and postselection, and the interpretation of the associated weak value, using a theory of classical mechanics supplemented by an epistemic restriction that is known to be operationally equivalent to a subtheory of quantum mechanics. Both the real and imaginary components of the weak value appear as phase space displacements in the postselected expectation values of the measurement device's position and momentum distributions, and we recover the same displacements as in the quantum case by studying the corresponding evolution in the classical theory. By using this analogous classical theory, we gain insight into the appearance of the weak value as a result of the statistical effects of post selection, and this provides us with an operational interpretation of the weak value, both its real and imaginary parts. We find that the imaginary part of the weak value is a measure of how much postselection biases the mean phase space distribution for a given amount of measurement disturbance. All such biases proportional to the imaginary part of the weak value vanish in the limit where disturbance due to measurement goes to zero. Our analysis also offers intuitive insight into how measurement disturbance can be minimised and the limits of weak measurement., Comment: 9 pages, 2 figures, comments welcome; v2 added some references; v3 published version

We present a scheme for achieving amplification of the displacement of the mirror in optomechanical cavity using single-photon postselection where the mirror is initially prepared in squeezed coherent state. The amplification depends on the enhanced fluctuations of the squeezed coherent state, and it is is caused by the noncommutativity of quantum mechanics relying on the squeezed coherent state, which can not be explained by the standard weak measurement [1,25]., arXiv admin note: substantial text overlap with arXiv:1509.00621

We report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon–photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to an m-tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of (1/4)m−1.

We present an efficient scheme for preparing and purifying of four-photon Greenberger-Horne-Zeilinger (GHZ) state based on linear optics and postselection. First, we describe how to create a four-photon GHZ state in both polarization and spatial degrees of freedom from two pairs. Moreover, in the presence of depolarization noise our scheme is capable of purifying the desired state. In the regime of weak nonlinearity we design an indirect photon number-resolving detection to distinguish two states of the two pairs. At last, a fourfold coincidence detector click indicates creating of a polarization-entangled four-photon GHZ state., 13pages, 2 figures

We introduce schemes for linear-optical quantum state generation. A quantum state generator is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and postselection using photon counters. We show that this device can be concisely described in terms of polynomial equations and unitary constraints. We illustrate the power of this language by applying the Grobner-basis technique along with the notion of vacuum extensions to solve the problem of how to construct a quantum state generator analytically for any desired state, and use methods of convex optimization to identify bounds to success probabilities. In particular, we disprove a conjecture concerning the preparation of the maximally path-entangled |n,0)+|0,n) (NOON) state by providing a counterexample using these methods, and we derive a new upper bound on the resources required for NOON-state generation., 5 pages, 2 figures

We introduce a protocol for steady-state entanglement generation and protection based on detuning modulation in the dissipative interaction between a two-qubit system and a bosonic mode. The protocol is a global-addressing scheme which only requires control over the system as a whole. We describe a postselection procedure to project the register state onto a subspace of maximally entangled states. We also outline how our proposal can be implemented in a circuit-quantum electrodynamics setup., Comment: 9 pages, 8 figures, RevTeX4

We determine the computational power of preparing projected entangled pair states (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor networks. While creating PEPS allows us to solve $PP$ problems, the latter two tasks are both proven to be $#P$-complete. We further show how PEPS can be used to approximate ground states of gapped Hamiltonians and that creating them is easier than creating arbitrary PEPS. The main tool for our proofs is a duality between PEPS and postselection which allows us to use existing results from quantum complexity.

Introducing classical fields, we can transfer entanglement completely from discrete qubits into entangled coherent state. The entanglement also can be retrieved from the continuous-variable state of the cavities to the atomic qubits. Via postselection measure, atomic entangled state and entangled coherent state can be mutual transformed fully., 5 pages, 3 fighres. accepted by J Phys B

We report an experimental demonstration of effective entanglement in a prepare-and-measure type of quantum key distribution protocol. Coherent polarization states and heterodyne measurement to characterize the transmitted quantum states are used, thus enabling us to reconstruct directly their $Q$ function. By evaluating the excess noise of the states, we experimentally demonstrate that they fulfill a nonseparability criterion previously presented by Rigas et al. [J. Rigas, O. G\"uhne, and N. L\"utkenhaus, Phys. Rev. A 73, 012341 (2006)]. For a restricted eavesdropping scenario, we predict key rates using postselection of the heterodyne measurement results.

We propose efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection. By these phase encodings, the probability of basis mismatch is reduced and total efficiency is increased. We also propose mixed-state protocols by omitting a part of classical communication steps in the efficient-phase-encoding protocols. The omission implies a reduction of information to an eavesdropper and possibly enhances the security of the protocols. We investigate the security of the protocols against individual beam splitting attack., RevTeX4, 8 pages, 9 figures

We present a method of generating collective multi-qubit entanglement via global addressing of an ion chain following the guidelines of the Tavis-Cummings model, where several qubits are coupled to a collective motional mode. We show that a wide family of Dicke states and irradiant states can be generated by single global laser pulses, unitarily or helped with suitable postselection techniques., 6 pages, 3 figures. Accepted for publication in Physical Review A

We show how to generate maximally entangled mixed states of two photons from the singlet state by using local linear-optical channels and postselection. Both theoretical predictions and experimental findings are presented.

The evolution of entanglement for two identical two-level atoms coupled to a resonant thermal field is studied for two different families of input states. Entanglement enhancement is predicted for a well defined region of the parameter space of one of these families. The most intriguing result is the possibility of probabilistic production of maximally entangled atomic states even if the input atomic state is factorized and the corresponding output state is separable., Comment: accepted for publication in J. Phys. B

The highest current estimates for the amount of noise a quantum computer can tolerate are based on fault-tolerance schemes relying heavily on postselecting on no detected errors. However, there has been no proof that these schemes give even a positive tolerable noise threshold. A technique to prove a positive threshold, for probabilistic noise models, is presented. The main idea is to maintain strong control over the distribution of errors in the quantum state at all times. This distribution has correlations which conceivably could grow out of control with postselection. But in fact, the error distribution can be written as a mixture of nearby distributions each satisfying strong independence properties, so there are no correlations for postselection to amplify., Comment: 13 pages, FOCS 2006; conference version

We use a photon-number resolving detector to monitor the photon number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical non-linearities. Following a scheme by Bentley and Boyd [S.J. Bentley and R.W. Boyd, Optics Express 12, 5735 (2004)] we explore this effect to demonstrate interference patterns a factor of five smaller than the Rayleigh limit., Comment: 4 pages, 5 figures

It is a well-known fact that all the statistical predictions of quantum mechanics on the state of any physical system represented by a two-dimensional Hilbert space can always be duplicated by a noncontextual hidden-variables model. In this paper, I show that, in some cases, when we consider an additional independent (unentangled) two-dimensional system, the quantum description of the resulting composite system cannot be reproduced using noncontextual hidden variables. In particular, a no-hidden-variables proof is presented for two individual spin-1/2 particles preselected in an uncorrelated state AB and postselected in another uncorrelated state aB, B being the same state for the second particle in both preselection and postselection.

We prove that continuous variable quantum information processing via Gaussian preserving operations, with Gaussian input states plus a (highly nonclassical) Fock number state, and subject to homodyne measurements and feedforward, can be efficiently simulated on a classical computer. This result reinforces the importance of the cubic phase state as an offline resource for universal continuous variable quantum information processing. We study the practical realization of this state by determining the Wigner function for an approximate cubic phase state prepared via two-mode squeezing with postselection on the signal field by displacing and counting photons in the idler field.

It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, post-selection or non-local boxes. For instance, in the case of projective measurements, it is possible to solve this problem with protocols using one bit of communication or making one use of a non-local box. We show that this problem reduces to a distributed sampling problem. We give a new method to obtain samples from a biased distribution, starting with shared random variables following a uniform distribution, and use it to build distributed sampling protocols. This approach allows us to derive, in a simpler and unified way, many existing protocols for projective measurements, and extend them to positive operator value measurements. Moreover, this approach naturally leads to a local hidden variable model for Werner states., 13 pages, 2 figures