Synthesizing arbitrary two-photon polarization mixed states
Tzu-Chieh Wei, Joseph B. Altepeter, David Branning, Paul M. Goldbart, D. F. V. James, Evan Jeffrey, Paul G. Kwiat, Swagatam Mukhopadhyay, Nicholas A. Peters
Two methods for creating arbitrary two-photon polarization pure states are introduced. Based on these, four schemes for creating two-photon polarization mixed states are proposed and analyzed. The first two schemes can synthesize completely arbitrary two-qubit mixed states, i.e., control all 15 free parameters: Scheme I requires several sets of crystals, while Scheme II requires only a single set, but relies on decohering the pump beam. Additionally, we describe two further schemes which are much easier to implement. Although the total capability of these is still being studied, we show that they can synthesize all two-qubit Werner states, maximally entangled mixed states, Collins-Gisin states, and arbitrary Bell-diagonal states.
We propose a scheme for preparing arbitrary two photons polarization entangled mixed states via controlled location decoherence. The scheme uses only linear optical devices and single-mode optical fibers, and may be feasible in experiment within current optical technology.
We introduce a quantum channel describing photon losses depending on the degree of polarization mixedness. This can be regarded as a model of quantum channel with correlated errors between discrete and continuous degrees of freedom. We consider classical information over a continuous alphabet encoded on weak coherent states as well as classical information over a discrete alphabet encoded on single photons using dual rail representation. In both cases we study the one-shot capacity of the channel and its behaviour in terms of correlation between losses and polarization mixedness.
Features of biphoton polarization-frequency ququarts are considered. Their wave functions are defined as functions of both polarization and frequency variables of photons with the symmetry obligatory for two-boson states taken into account. In experiments, biphoton ququarts can display different features in dependence on whether experiments involve purely polarization or (alternatively) polarization-frequency measurements. If in experiments one uses only polarization measurements, the originally pure states of ququarts can be seen as mixed biphoton polarization states. Features of such states …
Non-classical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization qubit. In the process we highlight some of subtleties involved in common methods for generating decoherence in quantum optics.
We calculate the effect of polarization-dependent scattering by disorder on the degree of polarization-entanglement of two beams of radiation. Multi-mode detection converts an initially pure state into a mixed state with respect to the polarization degrees of freedom. The degree of entanglement decays exponentially with the number of detected modes if the scattering mixes the polarization directions and algebraically if it does not.
We have investigated the excitation-power dependence of polarization-entangled photon-pairs generated from a CuCl single crystal using biexciton resonant hyper-parametric scattering. The measured two-photon polarization density matrix which corresponds to the two-photon polarization state changes with increasing the excitation power. The evaluation of the tangle and the linear entropy obtained from the measured density matrix indicates that the two-photon polarization density matrix can be expressed as the mixed state of an ideal state and a totally mixed state, and the mixture ratio of the to…
We present two efficient schemes which can simultaneously accomplish hyperentanglement concentration and purification for two-photon four-qubit systems in an unknown partially hyperentangled mixed states. The first can correct errors in the polarization entanglement and extract maximal hyperentanglement in polarization and spatial mode with additional partial frequency entanglement. The second uses additional maximal frequency entanglement to purify and concentrate hyperentanglement in polarization and spatial mode deterministically. Both of the two schemes are only based on existing optical d…
In this article we make a comparison between the behavior of entanglement and quantum degree of polarization for a special class of states of the radiation field, namely the Bell-type diagonal mixed states. For the three-photon mixed states we have plotted the concurrence and the Chernoff quantum degree of polarization in terms of the parameter, which defines the state. We find the the entanglement and the quantum degree of polarization are incomparable measures.
We analyze features of mixed biphoton polarization states which arise from pure states of polarization-frequency biphoton ququarts after averaging over frequencies of photons. For mixed states we find their concurrence C, Schmidt parameter K and degree of polarization P, as well as the von Neumann mutual information I. In some simple cases we find also the relative entropy S_{rel} and the degree of classical correlations C_{cl}. We show that in mixed states the Schmidt parameter does not characterize anymore the degree of entanglement, as it does in pure states. Nevertheless, the Schmidt param…
We report experimental results on mixed-state generation by multiple scattering of polarization-entangled photon pairs created from parametric down-conversion. By using a large variety of scattering optical systems we have experimentally obtained entangled mixed states that lie upon and below the Werner curve in the linear entropy-tangle plane. We have also introduced a simple phenomenological model built on the analogy between classical polarization optics and quantum maps. Theoretical predictions from such model are in full agreement with our experimental findings.
We present a concentration and purification scheme for nonmaximally entangled pure and mixed porization entangled state. We firstly show that two distant parties Alice and Bob first start with two shared but less entangled photon pure states to produce a four photon GHZ state, and then perform a 45 polarization measurement onto one of the two photons at each location such that the remaining two photon are projected onto a maximally entangled state. We further show the scheme also can be used to purify a class of mixed polarization-entangled state.
We present an experimental implementation of optimum measurements for quantum state discrimination. Optimum maximum-confidence discrimination and optimum unambiguous discrimination of two mixed single-photon polarization states were performed. For the latter the states of rank two in a four-dimensional Hilbert space are prepared using both path and polarization encoding. Linear optics and single photons from a true single-photon source based on a semiconductor quantum dot are utilized.
We propose a deterministic remote state preparation scheme for photon polarization qubit states, where entanglement, local operations and classical communication are used. By consuming one maximally entangled state and two classical bits, an arbitrary (either pure or mixed) qubit state can be prepared deterministically at a remote location. We experimentally demonstrate the scheme by remotely preparing 12 pure states and 6 mixed states. The fidelities between the desired and achieved states are all higher than 0.99 and have an average of 0.9947.
The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin 1/2 states and study its squeezing behaviour as a function of the individual polarizations of the two spinors.
Contrary to the usual assumption that the experimental preparation of pure entangled states can be described by mixed states due to white noise, a more realistic description for polarization-entangled states produced by parametric down-conversion is that they are mixed states due to decoherence in a preferred polarization basis. This distinction between white and colored noise is crucial when we look for maximal violations of Bell's inequalities for two-qubit and two-qutrit entangled states. We find that violations of Bell's inequalities with realistic noise for polarization-entangled photons …
In this work, we construct a polarization-mediated magic-intensity (MI) optical dipole trap (ODT) array, in which the detrimental effects of light shifts on the mixed-species qubits are efficiently mitigated so that the coherence times of the mixed-species qubits are both substantially enhanced and balanced for the first time. This mixed-species magic trapping technique relies on the tunability of the coefficient of the third-order cross term and ground state hyperpolarizability, which are inherently dependent on the degree of circular polarization of the trap laser. Experimentally, polarizati…
We present a general theoretical method to generate maximally entangled mixed states of a pair of photons initially prepared in the singlet polarization state. This method requires only local operations upon a single photon of the pair and exploits spatial degrees of freedom to induce decoherence. We report also experimental confirmation of these theoretical results.
We report a controllable method for producing mixed two-photon states via Spontaneous Parametric Down-Conversion with a two-type-I crystal geometry. By using variable polarization rotators (VPRs), one obtains mixed states of various purities and degrees of entanglement depending on the parameters of the VPRs. The generated states are characterized by quantum state tomography. The experimental results are found to be in good agreement with the theory. The method can be easily implemented for various experiments which require the generation of states with controllable degrees of entanglement or …
Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for {\it mixed} input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.
We report a novel Bell-state synthesizer in which an interferometric entanglement concentration scheme is used. An initially mixed polarization state from type-II spontaneous parametric down-conversion becomes entangled after the interferometric entanglement concentrator. This Bell-state synthesizer is universal in the sense that the output polarization state is not affected by spectral filtering, crystal thickness, and, most importantly, the choice of pump source. It is also robust against environmental disturbance and a more general state, partially mixed$-$partially entangled state, can be …
In our investigation into the effects of the degree of polarization in modulation of partially polarized light we assume general settings of the interferometry of partially polarized lightwaves and perform theoretical analysis of the Uhlmann and the interferometric phases. We introduce the relative Uhlmann phase determined by the Uhlmann holonomies of interfering beams and show that the interferometric phase generalized to the case of nonunitary evolution can, similar to the Uhlmann phase, be cast into the holonomy defined form. By using the technique based on a two-arm Mach-Zehnder interferom…
We study optical excitations of an ultracold gas in an optical lattice in the Mott insulator case and with anisotropic properties. The anisotropy is induced by an oriented transition dipole generated by optical pumping and external static fields, and is of the type of uniaxial crystals. Within a cavity, the electronic excitations and the cavity photons of both TE and TM polarizations are coherently mixed to form two polariton branches. Also a photonic branch appears which decouples from the electronic transitions. The photon polarization mixing can be observed by linear optical spectra. For ex…
We propose a feasible scheme to create $n$-party ($n\geq 2$) polarization-entangled photon states in a controllable way. The scheme requires only single-photon sources, single-photon quantum non-demolition measurement (SP-QNDM) and simple linear optical elements, usually with high perfections. The SP-QNDM acts as a non-destructive projection measurement onto the wanted entangled states and filters out the unwanted terms. Our scheme in fact realizes entanglement of non-interacting photons; the interaction occurs only implicitly in the optical elements and SP-QNDM. We also briefly consider purif…
We report on experimental implementation of the optimal universal asymmetric 1->2 quantum cloning machine for qubits encoded into polarization states of single photons. Our linear optical machine performs asymmetric cloning by partially symmetrizing the input polarization state of signal photon and a blank copy idler photon prepared in a maximally mixed state. We show that the employed method of measurement of mean clone fidelities exhibits strong resilience to imperfect calibration of the relative efficiencies of single-photon detectors used in the experiment. Reliable characterization of the…
In a recent paper [Bardyn et al. Phys. Rev. X 8, 011035 (2018)], it was shown that the generalization of the many-body polarization to mixed states can be used to construct a topological invariant which is also applicable to finite-temperature and non-equilibrium Gaussian states of lattice fermions. The many-body polarization defines an ensemble geometric phase (EGP) which is identical to the Zak phase of a fictitious Hamiltonian, whose symmetries determine the topological classification. Here we show that in the case of Gaussian states of bosons the corresponding topological invariant is alwa…
A formalism for two-photon Stokes parameters is introduced to describe the polarization entanglement of photon pairs. This leads to the definition of a degree of two-photon polarization, which describes the extent to which the two photons act as a pair and not as two independent photons. This pair-wise polarization is complementary to the degree of polarization of the individual photons. The approach provided here has a number of advantages over the density matrix formalism: it allows the one- and two-photon features of the state to be separated and offers a visualization of the mixedness of t…
We analyze the polarization of a quantum radiation field under a de-Gaussification process. Specifically, we consider the addition of photons to a two-mode thermal state to get mixed non-Gaussian and nonclassical states which are still diagonal in the Fock basis. Stokes-operator-based degrees of polarization and two distance-type measures defined with Hilbert-Schmidt and Bures metrics are investigated. For a better insight we here introduce a polarization degree based on the relative entropy. Polarization of the thermal states is fully investigated and simple closed expressions are found for a…
Photons carrying a well-defined orbital angular momentum have been proven to modify spectroscopic selection rules in atomic matter. Excitation profiles of electric quadrupole transitions have been measured with single trapped $^{40}$Ca$^+$ ions for varying polarizations. We further develop the photo-absorption formalism to study the case of arbitrary alignment of the beam's optical axis with respect to the ion's quantization axis and mixed multipolarity. Thus, predictions for M1-dominated $^{40}Ar^{13+}$, E3-driven $^{171}Yb^+$ and $^{172}Yb^+$, and B-like $^{20}Ne^{5+}$ are presented. The lat…
Hyperentanglement has attracted much attention for its fascinating applications in quantum communication. However, it is impossible to purify a pair of photon systems in a mixed hyperentangled state with errors in two degrees of freedom using linear optical elements only, far different from all the existing entanglement purification protocols in a degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of purifying a spatial-polarization mixed hyperentangled Bell state with the errors in both the spatial mode and polarization DOFs, resorting to the nonlinear optics of…
We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-\emph{vs}-quantum formalism, we show how two-qubit maximally entangled mixed states (MEMS), can be generated by us…
Due to electron-nucleus weak interaction, atomic bound states with different parities turn out to be mixed. We discuss a prospect for measuring the mixing parameter between the nearly degenerate metastable states 1s_{1/2} 2s_{1/2} : J = 0 and 1s_{1/2} 2p_{1/2} : J = 0 in heliumlike Uranium. Our analysis is based on the polarization properties of the photons emitted in the two-photon decays of such states.
Polarization of light is harnessed in an abundance of classical and quantum applications. Characterizing polarization in a classical sense is done resoundingly successfully using the Stokes parameters, and numerous proposals offer new quantum counterparts of this characterization. The latter often rely on distance measures from completely polarized or unpolarized light. We here show that the accepted class of perfectly polarized quantum states of light is severely lacking in terms of both pure states and mixed states. By appealing to symmetry and geometry arguments we determine all of the stat…
