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We consider two memory nodes of a quantum network connected by flying qubits. We are particularly interested in the case where a flying qubit produced by one node has to be transformed before it can interface efficiently with the next node. Such transformations can be utilized as a key part of the distribution of quantum states and hence entanglement between the nodes of a hybrid quantum network linking together different quantum technologies. We show how and why the probability of interfacing successfully is determined by the overlap of the spectral shape of the actual flying qubit and the ideal shape. This allows us to analytically and numerically analyze how the probability of success is impacted by realistic errors, and show the utility of our scheme (in consonance with known error correction methods) in connecting hybrid nodes of a quantum network. We focus here on a concrete implementation in which the memory nodes consist of three-level atoms in cavities and the flying qubits are photons., Comment: manuscript: 17 pages, 7 figures; references: 9 pages; supplemental material: 39 pages, 9 figures

The Partial Information Decomposition (PID) takes one step beyond Shannon's theory in decomposing the information two variables $A,B$ possess about a third variable $T$ into distinct parts: unique, shared (or redundant) and synergistic information. Here we show how these concepts can be defined in a quantum setting. We apply a quantum PID to scrambling in quantum many-body systems, for which a quantum-theoretic description has been proven productive. Unique information in particular provides a finer description of scrambling than does the so-called tri-information.

We apply input-output theory with quantum pulses [AH Kiilerich, K M\o lmer, Phys. Rev. Lett. {\bf 123}, 123604 (2019)] to a model of a new type of two-photon detector consisting of one molecule that can detect two photons arriving sequentially in time. The underlying process is distinct from the usual two-photon absorption process where two photons arriving simultaneously and with frequencies adding up to the resonance frequency are absorbed by a single molecule in one quantum jump. Our detector model includes a Hamiltonian description of the amplification process necessary to convert the microscopic change in the single molecule to a macroscopic signal., Comment: 14 pages, 9 figures, minor changes in response to referee comments. To appear in Phys. Rev. A

We consider the quantum theory of paraxial non-relativistic electron beams in non-uniform magnetic fields, such as the Glaser field. We find the wave function of an electron from such a beam and show that it is a joint eigenstate of two ($z$-dependent) commuting gauge-independent operators. This generalized Laguerre-Gaussian vortex beam has a phase that is shown to consist of two parts, each being proportional to the eigenvalue of one of the two conserved operators and each having different symmetries. We also describe the dynamics of the angular momentum and cross-sectional area of any mode and how a varying magnetic field can split a mode into a superposition of modes. By a suitable change in frame of reference all of our analysis also applies to an electron in a quantum Hall system with a time-dependent magnetic field., Comment: 8 pages, 1 figure. Comments welcome

We construct a class of Hamiltonians that describe the photodetection process from beginning to end. Our Hamiltonians describe the creation of a photon, how the photon travels to an absorber (such as a molecule), how the molecule absorbs the photon, and how the molecule after irreversibly changing its configuration triggers an amplification process---at a wavelength that may be very different from the photon's wavelength---thus producing a macroscopic signal. We use a simple prototype Hamiltonian to describe the single-photon detection process analytically in the Heisenberg picture, which neatly separates desirable from undesirable effects. Extensions to more complicated Hamiltonians are pointed out., Comment: 9 pages, 4 figures, to appear in Phys. Rev. A

A recurring problem in quantum mechanics is to estimate either the state of a quantum system or the measurement operator applied to it. If we wish to estimate both, then the difficulty is that the state and the measurement always appear together: to estimate the state, we must use a measurement; to estimate the measurement operator, we must use a state. The data of such quantum estimation experiments come in the form of measurement frequencies. Ideally, the measured average frequencies can be attributed to an average state and an average measurement operator. If this is not the case, we have correlated state-preparation-and-measurement (SPAM) errors. We extend some tests developed to detect such correlated errors to apply to a cryptographic scenario in which two parties trust their individual states but not the measurement performed on the joint state., Comment: to be published in special issue on quantum tomography, Int, J,. Quant. Inf

Suppose a classical electron is confined to move in the $xy$ plane under the influence of a constant magnetic field in the positive $z$ direction. It then traverses a circular orbit with a fixed positive angular momentum $L_z$ with respect to the center of its orbit. It is an underappreciated fact that the quantum wave functions of electrons in the ground state (the so-called lowest Landau level) have an azimuthal dependence $\propto \exp(-im\phi) $ with $m\geq 0$, seemingly in contradiction with the classical electron having positive angular momentum. We show here that the gauge-independent meaning of that quantum number $m$ is not angular momentum, but that it quantizes the distance of the center of the electron's orbit from the origin, and that the physical angular momentum of the electron is positive and independent of $m$ in the lowest Landau levels. We note that some textbooks and some of the original literature on the fractional quantum Hall effect do find wave functions that have the seemingly correct azimuthal form $\propto\exp(+im\phi)$ but only on account of changing a sign (e.g., by confusing different conventions) somewhere on the way to that result., Comment: Accepted for publication in the American Journal of Physics

Single photon detection generally consists of several stages: the photon has to interact with one or more charged particles, its excitation energy will be converted into other forms of energy, and amplification to a macroscopic signal must occur, thus leading to a "click." We focus here on the part of the detection process before amplification (which we have studied in a separate publication). We discuss how networks consisting of coupled discrete quantum states and structured continua (e.g. band gaps) provide generic models for that first part of the detection process. The input to the network is a continuum (the continuum of single-photon states), the output is again a continuum describing the next irreversible step. The process of a single photon entering the network, its energy propagating through that network and finally exiting into another output continuum of modes can be described by a single dimensionless complex transmission amplitude, $T(\omega)$. We discuss how to obtain from $T(\omega)$ the photo detection efficiency, how to find sets of parameters that maximize this efficiency, as well as expressions for other input-independent quantities such as the frequency-dependent group delay and spectral bandwidth. We then study a variety of networks and discuss how to engineer different transmission functions $T(\omega)$ amenable to photo detection., Comment: 21 pages 22 figures

How do indistinguishable identical bosons manage to obey Bose-Einstein statistics---and hence be correlated---even when they do not interact with each other? Part of the answer is that the bosons have to interact indirectly with each other by interacting with the same environment. A joint measurement interaction provides a good example. Thermalization occurs whenever there are two competing processes, one diagonal in the energy basis (namely, reversible Hamiltonian evolution), the other irreversible and diagonal in a complementary basis (for example, a measurement in a spatially localized basis). Correlations arise only from initial states in which the bosons start in different (orthogonal) states., Comment: Part 1 of 2 similar papers on identical particles

The phase factor $(-1)^{2s}$ that features in the exchange symmetry for identical spin-$s$ fermions or bosons is not simply and automatically equal to the phase factor one can observe in an interference experiment that involves physically exchanging two such particles. The observable phase contains, in general, single-particle geometric and dynamical phases as well, induced by both spin and spatial exchange transformations. By extending the analysis to (non-abelian) anyons it is argued that, similarly, there are single-anyon geometric and dynamical contributions in addition to purely topological unitary transformations that accompany physical exchanges of anyons. Work remains to be done in order to demonstrate---if it is still true---that those additional contributions to the gates in anyonic topological quantum computers do not destroy the inherent robustness of the ideal gates. This negative result is described most clearly in terms of the Berry matrix., Comment: New title, same concerns, 7 pages

We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for \emph{nonlinear} photon-number amplification schemes with optimistic implications for single-photon detection. Four commutator-preserving transformations are presented: one idealized (which is optimal) and three more realistic (less than optimal). Our description makes clear that nonlinear amplification takes place, in general, at a different frequency $\omega'$ than the frequency $\omega$ of the input photons. This can be exploited to suppress thermal noise even further up to a fundamental limit imposed by amplification into a single bosonic mode. A practical example that fits our description very well is electron-shelving.

We experimentally demonstrate that loop state-preparation-and-measurement (SPAM) tomography is capable of detecting correlated errors in a two-qubit system. We prepare photon pairs in a state that approximates a Werner state, which may or may not be entangled. By performing measurements with multiple different detector settings we are able to detect correlated errors between two single-qubit measurements performed in different locations. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positive-operator-valued measures describing the detectors are known. The only other needed information is experimentally measured expectation values, which are analyzed for self-consistency. This demonstrates that loop SPAM tomography is a useful technique for detecting errors that would degrade the performance of multiple-qubit quantum information processors., Comment: 6 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1802.02526

It is possible for two parties, Alice and Bob, to establish a secure communication link by sharing an ensemble of entangled particles, and then using these particles to generate a secret key. One way to establish that the particles are indeed entangled is to verify that they violate a Bell inequality. However, it might be the case that Bob is not trustworthy and wishes Alice to believe that their communications are secure, when in fact they are not. He can do this by managing to have prior knowledge of Alice's measurement device settings and then modifying his own settings based upon this information. In this case it is possible for shared particle states that must satisfy a Bell inequality to appear to violate this inequality, which would also make the system appear secure. When Bob modifies his measurement settings, however, he produces false correlations. Here we demonstrate experimentally that Alice can detect these false correlations, and uncover Bob's trickery, by using loop-state-preparation-and-measurement (SPAM) tomography. More generally, we demonstrate that loop SPAM tomography can detect false correlations (correlated errors) in a two-qubit system without needing to know anything about the prepared states or the measurements, other than the dimensions of the operators that describe them., Comment: 3 Figures

A photodetector may be characterized by various figures of merit such as response time, bandwidth, dark count rate, efficiency, wavelength resolution, and photon-number resolution. On the other hand, quantum theory says that any measurement device is fully described by its POVM, which stands for Positive-Operator-Valued Measure, and which generalizes the textbook notion of the eigenstates of the appropriate hermitian operator (the "observable") as measurement outcomes. Here we show how to define a multitude of photodetector figures of merit in terms of a given POVM. We distinguish classical and quantum figures of merit and issue a conjecture regarding trade-off relations between them. We discuss the relationship between POVM elements and photodetector clicks, and how models of photodetectors may be tested by measuring either POVM elements or figures of merit. Finally, the POVM is advertised as a platform-independent way of comparing different types of photodetectors, since any such POVM refers to the Hilbert space of the incoming light, and not to any Hilbert space internal to the detector., Comment: 8 pages, to appear in Journal of Physics Communications

Suppose we measure the time-dependent spectrum of a single photon. That is, we first send the photon through a set of frequency filters (which we assume to have different filter frequencies but the same finite bandwidth $\Gamma$), and then record at what time (with some finite precision $\Delta t$, and with some finite efficiency $\eta$) and after passing what filter the photon is detected. What is the POVM (Positive-Operator Valued Measure, the most general description of a quantum measurement) corresponding to such a measurement? We show how to construct the POVM in various cases, with special interest in the case $\Gamma\Delta t\ll 1$ (time-frequency uncertainty still holds, even in that limit). One application of the formalism is to heralding single photons. We also find a Hong-Ou-Mandel type of interference effect with two photons entering a frequency filter., Comment: expanded version, 8 pages

We have performed an experiment demonstrating that loop state-preparation-and-measurement (SPAM) tomography [C. Jackson and S. J. van Enk, Phys. Rev. A 92, 042312 (2015)] is capable of detecting correlated errors between the preparation and the measurement of a quantum system. Specifically, we have prepared pure and mixed states of single qubits encoded in the polarization of heralded individual photons. By performing measurements using multiple state preparations and multiple measurement device settings we are able to detect if there are any correlated errors between them, and are also able to determine which state preparations are correlated with which measurements. This is accomplished by going around a 'loop' in parameter space, which allows us to check for self-consistency. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positive-operator-valued measures (POVM) describing the detector are known. In cases where no correlations are found we are able to perform quantum state tomography of the polarization qubits by using knowledge of the detector POVMs, or quantum detector tomography by using knowledge of the state preparations., Comment: 23 pages, 4 figures

Two-photon interference effects, such as the Hong-Ou-Mandel (HOM) effect, can be used to characterize to what extent two photons are identical. Furthermore, these interference effects underly linear optics quantum computation. We show here how nonlinear optical effects, such as those mediated by atoms or quantum dots in a cavity, degrade the interference. This implies that, on the one hand, nonlinearities are to be avoided if one wishes to utilize the interference, but on the other hand, one may be able to measure or detect nonlinearities by observing the disappearance of the interference., Comment: 8 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1406.1232

Whereas in standard quantum state tomography one estimates an unknown state by performing various measurements with known devices, and whereas in detector tomography one estimates the POVM elements of a measurement device by subjecting to it various known states, we consider here the case of SPAM (state preparation and measurement) tomography where neither the states nor the measurement device are assumed known. For $d$-dimensional systems measured by $d$-outcome detectors, we find there are at most $d^2(d^2-1)$ "gauge" parameters that can never be determined by any such experiment, irrespective of the number of unknown states and unknown devices. For the case $d=2$ we find new gauge-invariant quantities that can be accessed directly experimentally and that can be used to detect and describe SPAM errors. In particular, we identify conditions whose violations detect the presence of correlations between SPAM errors. From the perspective of SPAM tomography, standard quantum state tomography and detector tomography are protocols that fix the gauge parameters through the assumption that some set of fiducial measurements is known or that some set of fiducial states is known, respectively.

I explore the possibility that a quantum system S may be described completely by the combination of its standard quantum state $|\psi\rangle$ and a (hidden) quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that the outcome of any standard projective measurement on the system S is determined once the two quantum states are specified. I construct an algorithm that retrieves the standard quantum-mechanical probabilities, which depend only on $|\psi\rangle$, by assuming that the (hidden) quantum state $|\phi\rangle$ is drawn at random from some fixed probability distribution Pr(.) and by averaging over Pr(.). Contextuality and Bell nonlocality turn out to emerge automatically from this algorithm as soon as the dimension of the Hilbert space of S is larger than 2. If $|\phi\rangle$ is not completely random, subtle testable deviations from standard quantum mechanics may arise in sequential measurements on single systems., Comment: As Michael Hall pointed out to me, the main idea (to use a 2nd quantum state as hidden variable) was discussed by Bohm and Bub in 1966. I found then that two more ideas were anticipated by Mattuck and by Papalilios. I have indicated these anticipations in blue. I leave the manuscript here as it does seem to give more "applications" of the Bohm-Bub model, and it might still lead to other ideas

Jaynes invented the Brandeis Dice Problem as a simple illustration of the MaxEnt (Maximum Entropy) procedure that he had demonstrated to work so well in Statistical Mechanics. I construct here two alternative solutions to his toy problem. One, like Jaynes' solution, uses MaxEnt and yields an analogue of the canonical ensemble, but at a different level of description. The other uses Bayesian updating and yields an analogue of the micro-canonical ensemble. Both, unlike Jaynes' solution, yield error bars, whose operational merits I discuss. These two alternative solutions are not equivalent for the original Brandeis Dice Problem, but become so in what must, therefore, count as the analogue of the thermodynamic limit, $M$-sided dice with $M\rightarrow\infty$. Whereas the mathematical analogies between the dice problem and Stat Mech are quite close, there are physical properties that the former lacks but that are crucial to the workings of the latter. Stat Mech is more than just MaxEnt., Comment: to appear in Studies in the History and Philosophy of Modern Physics

Two-photon interference effects, such as the Hong-Ou-Mandel (HOM) effect, can be used to characterize to what extent two photons are identical. Identical photons are necessary for both linear optics quantum computing and single-photon quantum cryptography. We study here how storage and delay of photons in coupled cavity arrays, which inevitably will lead to changes in the photons' spectral and temporal profiles, affects their HOM interference. In addition we consider various types of entanglement that occur naturally in such a context.

We consider how a single photon can probe the quantum nature of a moving mirror in the context of quantum optomechanics. In particular, we demonstrate how the single-photon spectrum reveals resonances that depend on how many phonons are created as well as on the strength of the mirror-photon interaction. A dressed-state picture is used to explain positions and relative strengths of those resonances. The time-dependent spectrum shows how the resonances are built up over time by the photon interacting with the moving mirror.

We consider the concept of "the permutationally invariant (PI) part of a density matrix," which has proven very useful for both efficient quantum state estimation and entanglement characterization of $N$-qubit systems. We show here that the concept is, in fact, basis-dependent, but that this basis dependence makes it an even more powerful concept than has been appreciated so far. By considering the PI part $\rho^{{\rm PI}}$ of a general (mixed) $N$-qubit state $\rho$, we obtain: (i) strong bounds on quantitative nonseparability measures, (ii) a whole hierarchy of multi-partite separability criteria (one of which entails a sufficient criterion for genuine $N$-partite entanglement) that can be experimentally determined by just $2N+1$ measurement settings, (iii) a definition of an efficiently measurable degree of separability, which can be used for quantifying a novel aspect of decoherence of $N$ qubits, and (iv) an explicit example that shows there are, for increasing $N$, genuinely $N$-partite entangled states lying closer and closer to the maximally mixed state. Moreover, we show that if the PI part of a state is $k$-nonseparable, then so is the actual state. We further argue to add as requirement on any multi-partite entanglement measure $E$ that it satisfy $E(\rho)\geq E(\rho^{{\rm PI}})$, even though the operation that maps $\rho\rightarrow\rho^{{\rm PI}}$ is not local.

We show how the input-output formalism for cascaded quantum systems combined with the quantum trajectory approach yields a compact and physically intuitive description of single photons propagating through a coupled cavity array. As a new application we obtain the time-dependent spectrum of such a single photon, which directly reflects the fact that only certain frequency components of single-photon wavepackets are trapped inside the cavities and hence are delayed in time. We include in our description the actual generation of the single photon, by assuming we have a single emitter in one of the resonators.

In continuous-variable quantum information processing detectors are necessarily coarse grained and of finite range. We discuss how especially the latter feature is a bug and may easily lead to overoptimistic estimates of entanglement and of security, when missed data outside the detector range are ignored. We show that entropic separability or security criteria are much superior to variance-based criteria for mitigating the negative effects of this bug.

The concept of electric and magnetic field lines is intrinsically non-relativistic. Nonetheless, for certain types of fields satisfying certain geometric properties, field lines can be defined covariantly. More precisely, two Lorentz-invariant 2D surfaces in spacetime can be defined such that magnetic and electric field lines are determined, for any observer, by the intersection of those surfaces with spacelike hyperplanes. An instance of this type of field is constituted by the so-called Hopf-Ranada solutions of the source-free Maxwell equations, which have been studied because of their interesting topological properties, namely, linkage of their field lines. In order to describe both geometric and topological properties in a succinct manner, we employ the tools of Geometric Algebra (aka Clifford Algebra) and use the Clebsch representation for the vector potential as well as the Euler representation for both magnetic and electric fields. This description is easily made covariant, thus allowing us to define electric and magnetic field lines covariantly in a compact geometric language. The definitions of field lines can be phrased in terms of 2D surfaces in space. We display those surfaces in different reference frames, showing how those surfaces change under Lorentz transformations while keeping their topological properties. As a byproduct we also obtain relations between optical helicity, optical chirality and generalizations thereof, and their conservation laws., Comment: Amended version, incorporating referees' comments

The principle behind quantum tomography is that a large set of observations -- many samples from a "quorum" of distinct observables -- can all be explained satisfactorily as measurements on a single underlying quantum state or process. Unfortunately, this principle may not hold. When it fails, any standard tomographic estimate should be viewed skeptically. Here we propose a simple way to test for this kind of failure using Akaike's Information Criterion (AIC). We point out that the application of this criterion in a quantum context, while still powerful, is not as straightforward as it is in classical physics. This is especially the case when future observables differ from those constituting the quorum., Comment: To appear in New Journal of Physics, Focus on Quantum Tomography. Two more references added

While it is known that Tr(\rho^n) can be measured directly (i.e., without first reconstructing the density matrix) by performing joint measurements on n copies of the same state rho, it is shown here that random measurements on single copies suffice, too. Averaging over the random measurements directly yields estimates of Tr(\rho^n), even when it is not known what measurements were actually performed (so that one cannot reconstruct \rho).

We point out that the Sagnac effect can be measured by means of the Hong-Ou-Mandel effect. The latter is not sensitive to phase shifts, and thus the Hong-Ou-Mandel Sagnac effect hinges on the fact that the Sagnac effect is, fundamentally, a time delay, not a phase shift., Comment: 3 pages, 1 figure

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively introducing certain simplifying assumptions on the form of the quantum state, and subsequently using the data to rigorously verify these assumptions. The simplifying assumptions considered so far were (i) the state can be well approximated to be of low rank, or (ii) the state can be well approximated as a matrix product state. We add one more method in that same spirit: we allow in principle any model for the state, using any (small) number of parameters (which can, e.g., be chosen to have a clear physical meaning), and the data are used to verify the model. The proof that this method is valid cannot be as strict as in above-mentioned cases, but is based on well-established statistical methods that go under the name of "information criteria." We exploit here, in particular, the Akaike Information Criterion (AIC). We illustrate the method by simulating experiments on (noisy) Dicke states.

We propose and analyze a method to detect and characterize the drift of a nonstationary quantum source. It generalizes a standard measurement for detecting phase diffusion of laser fields to quantum systems of arbitrary Hilbert space dimension, qubits in particular. We distinguish diffusive and systematic drifts, and examine how quickly one can determine that a source is drifting. We show that for single-photon wavepackets our measurement is implemented by the Hong-Ou-Mandel effect., Comment: 5 pages, 2 figures

Quantum networks are composed of quantum nodes that interact coherently by way of quantum channels and open a broad frontier of scientific opportunities. For example, a quantum network can serve as a `web' for connecting quantum processors for computation and communication, as well as a `simulator' for enabling investigations of quantum critical phenomena arising from interactions among the nodes mediated by the channels. The physical realization of quantum networks generically requires dynamical systems capable of generating and storing entangled states among multiple quantum memories, and of efficiently transferring stored entanglement into quantum channels for distribution across the network. While such capabilities have been demonstrated for diverse bipartite systems (i.e., N=2 quantum systems), entangled states with N > 2 have heretofore not been achieved for quantum interconnects that coherently `clock' multipartite entanglement stored in quantum memories to quantum channels. Here, we demonstrate high-fidelity measurement-induced entanglement stored in four atomic memories; user-controlled, coherent transfer of atomic entanglement to four photonic quantum channels; and the characterization of the full quadripartite entanglement by way of quantum uncertainty relations. Our work thereby provides an important tool for the distribution of multipartite entanglement across quantum networks., Comment: 4 figures

Suppose an experimentalist wishes to verify that his apparatus produces entangled quantum states. A finite amount of data cannot conclusively demonstrate entanglement, so drawing conclusions from real-world data requires statistical reasoning. We propose a reliable method to quantify the weight of evidence for (or against) entanglement, based on a likelihood ratio test. Our method is universal in that it can be applied to any sort of measurements. We demonstrate the method by applying it to two simulated experiments on two qubits. The first measures a single entanglement witness, while the second performs a tomographically complete measurement., Comment: 4 pages, 3 pretty pictures

We consider the interference of two photons with different colors in the context of a Hong-Ou-Mandel experiment, in which single photons enter each of the input ports of a beam splitter, and exit in the same, albeit undetermined, output port. Such interference is possible if one uses an active (energy-non-conserving) beam splitter. We find scenarios in which one "red" and one "blue" photon enter the beam splitter, and either two red or two blue photons exit, but never one of each color. We show how the precise form of the active beam-splitter transformation determines in what way the spectral degrees of freedom of the input photons should be related to each other for perfect destructive interference of the different-color components in the output. We discuss two examples of active beam splitters: one is a gedanken experiment involving a moving mirror and the other is a more realistic example involving four-wave mixing in an optical fiber., Comment: Published in a special issue of Optics Communications, dedicated to Krzysztof Wodkiewicz

We discuss how to characterize entanglement sources with finite sets of measurements. The measurements do not have to be tomographically complete, and may consist of POVMs rather than von Neumann measurements. Our method yields a probability that the source generates an entangled state as well as estimates of any desired calculable entanglement measures, including their error bars. We apply two criteria, namely Akaike's information criterion and the Bayesian information criterion, to compare and assess different models (with different numbers of parameters) describing entanglement-generating devices. We discuss differences between standard entanglement-verificaton methods and our present method of characterizing an entanglement source., Comment: This submission, together with the next one, supersedes arXiv:0806.4165

Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum descriptions of one's measurements. With the help of these assumptions it is possible to derive a strengthened Bell inequality whose violation implies entanglement. We generalize known examples of such inequalities by relating the expectation value of the Bell operator to a particular quantitative measure of entanglement, namely the negativity. Moreover, we obtain statistics illustrating the fact that violating a given (strengthened or not) Bell inequality is a much more rare feat for a quantum state of two qubits than it is to be entangled., Comment: This submission, together with the previous one, supersedes arXiv:0806.4165

We show that when an electron or photon propagates in a cylindrically symmetric waveguide, its spin angular momentum (SAM) and its orbital angular momentum (OAM) interact. Remarkably, we find that the dynamics resulting from this spin-orbit interaction are quantitatively described by a single expression applying to both electrons and photons. This leads to the prediction of several novel rotational effects: the spatial or time evolution of either particle's spin/polarization vector is controlled by the sign of its OAM quantum number, or conversely, its spatial wavefunction is controlled by its SAM. We show that the common origin of these effects in electrons and photons is a universal geometric phase. We demonstrate how these phenomena can be used to reversibly transfer entanglement between the SAM and OAM degrees of freedom of two-particle states., Comment: 4 pages, 2 figures, final version

We construct a method for verifying mode entanglement of N-mode W states. The ideal W state contains exactly one excitation symmetrically shared between N modes, but our method takes the existence of higher numbers of excitations into account, as well as the vacuum state and other deviations from the ideal state. Moreover, our method distinguishes between full N-party entanglement and states with M-party entanglement with M

So-called direct measurements of entanglement are collective measurements on multiple copies of a (bipartite or multipartite) quantum system that directly provide one a value for some entanglement measure, such as the concurrence for bipartite states. Multiple copies are needed since the entanglement of a mixed state is not a linear function of the density matrix. Unfortunately, so far all experimental implementations of direct measurements made unverified assumptions about the form of the states, and, therefore, do not qualify as entanglement verification tests. I discuss how a direct measurement can be turned into a quantitative entanglement verification test by exploiting a recent theorem by Renner (R. Renner, Nature Physics 3, 645 (2007))., Comment: 4 pages, 3 figures

There is a constraining relation between the reliability of a quantum measurement and the extent to which the measurement process is, in principle, reversible. The greater the information that is gained, the less reversible the measurement dynamics become. To illustrate this relation, we develop a simple physical model for quantum measurement, as well as a hypothetical scheme by which the experimenters can determine the reliability and reversibility. We derive an "uncertainty" (constraining) relation between reliability and reversibility, which holds even when there is no interaction with any external environment other than the fundamental information recording device., Comment: 18 pages, 5 figures, submitted to Am. J. Phys

I consider two identical quantum particles in two boxes. We can split each box, and thereby the wavefunction of each particle, into two parts. When two half boxes are interchanged and combined with the other halves, where do the two particles end up? I solve this problem for two identical bosons and for two identical fermions. The solution can be used to define a measurement that yields some information about the relative phase between the two parts of a split wavefunction., Comment: The following article has been submitted to the American Journal of Physics. After it is published, it will be found at http://scitation.aip.org/ajp

We show how a straightforward Bayesian updating procedure allows one to detect and quantify entanglement from any finite set of measurement results. The measurements do not have to be tomographically complete, and may consist of POVMs rather than von Neumann measurements. One obtains a probability that one's state is entangled and an estimate of any desired entanglement measure, including their error bars. As an example we consider (tomographically incomplete) spin correlation measurements on both 2-qubit and 3-qubit states. As byproducts we obtain estimates of the volume of entangled states vs. states that violate a given Bell inequality for both pure and mixed states, and an inequality that relates the expectation value of the Bell operator to the negativity., Comment: superseded by 0908.0265 and 0908.0267

Whereas single- and two-photon wave packets are usually treated as pure states, in practice they will be mixed. We study how entanglement created with mixed photon wave packets is degraded. We find in particular that the entanglement of a delocalized single-photon state of the electro-magnetic field is determined simply by its purity. We also discuss entanglement for two-photon mixed states, as well as the influence of a vacuum component., Comment: 11 pages, 10 figures, 1 debuting author

We propose a quantum theory of rotating light beams and study some of its properties. Such beams are polychromatic and have either a slowly rotating polarization or a slowly rotating transverse mode pattern. We show there are, for both cases, three different natural types of modes that qualify as rotating, one of which is a new type not previously considered. We discuss differences between these three types of rotating modes on the one hand and non-rotating modes as viewed from a rotating frame of reference on the other. We present various examples illustrating the possible use of rotating photons, mostly for quantum information processing purposes. We introduce in this context a rotating version of the two-photon singlet state., Comment: enormously expanded: 12 pages, 3 figures; a new, more informative, but less elegant title, especially designed for Phys. Rev. A

The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the Bell-CHSH inequality violations., Comment: in which the author breaks his vow to never use the words "ontic" and "epistemic" in public

We propose a scheme of generating and verifying mesoscopic-level entanglement between two atomic ensembles using non-resonant stimulated Raman scattering. Entanglement can be generated by direct detection or balanced homodyne detection of the Stokes fields from the two cells, after they interfere on a beam splitter. The entanglement of the collective atomic fields can be transferred to the anti-Stokes fields in a readout process. By measuring the operator moments of the anti-Stokes fields, we can verify the presence of entanglement. We model the effects of practical factors such as Stokes field detector quantum efficiency and additive thermal noise in the entanglement generating process, and anti-Stokes field losses in the entanglement verification process, and find achievable regimes in which entanglement can be verified at the levels of tens to hundreds of atomic excitations in the ensembles., Comment: 35 papges, 6 figures and 1 table, accepted by Phys. Rev. A

We give an overview of different types of entanglement that can be generated in experiments, as well as of various protocols that can be used to verify or quantify entanglement. We propose several criteria that, we argue, should be applied to experimental entanglement verification procedures. Explicit examples demonstrate that not following these criteria will tend to result in overestimating the amount of entanglement generated in an experiment or in infering entanglement when there is none. We distinguish protocols meant to refute or eliminate hidden-variable models from those meant to verify entanglement., Comment: 15 pages

I raise some doubts concerning a protocol recently applied in an experiment (Walborn et al, Nature) to measure entanglement. The protocol is much simpler than other known entanglement-verification methods, but, I argue, needs assumptions (namely that the state generated is known and pure) that are too strong to be allowed and that are not justified in most experiments. An extension of the protocol suggested in quant-ph/0605250 is much harder to implement and still relies on assumptions not justified in entanglement-verification protocols, as demonstrated by an explicit example., Comment: No

We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communication model., Comment: pretty pointless, published nonetheless