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We investigate the security of continuous-variable (CV) quantum key distribution (QKD) using coherent states in the presence of quadrature excess noise. We consider an eavesdropping attack which uses a linear amplifier and beam splitter. This attack makes a link between beam-splitting attack and intercept-resend attack (classical teleportation attack). We also show how postselection loses its efficiency in a realistic channel., Revtex4, 4 pages, 2 figures

We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave theory, due to the two-photon entanglement. We observe the variation in the size of the weak value with measurement strength, obtaining an average measurement of the S1 Stokes parameter more than an order of magnitude outside of the operator's spectrum for the smallest measurement strengths.

Photonic quantum information processing schemes, such as linear optics quantum computing, and other experiments relying on single-photon interference, inherently require complete photon indistinguishability to enable the desired photonic interactions to take place. Mode-mismatch is the dominant cause of photon distinguishability in optical circuits. Here we study the effects of photon wave-packet shape on tolerance against the effects of mode-mismatch in linear optical circuits, and show that Gaussian distributed photons with large bandwidth are optimal. The result is general and holds for arbitrary linear optical circuits, including ones which allow for post-selection and classical feed-forward., 6 pages, 4 figures

Multiphoton path entanglement is created without applying post-selection, by manipulating the state of stimulated parametric down-conversion. A specific measurement on one of the two output spatial modes leads to the non-local bunching of the photons of the other mode, forming the desired multiphoton path entangled state. We present experimental results for the case of a heralded two-photon path entangled state and show how to extend this scheme to higher photon numbers., 4 pages, 5 figures, published version

Efficient application of optical qubits for quantum information processing is impossible without a robust technology of their characterization. To date, characterization of optical logical ensembles has been based on studying relative photon number statistics in each mode and in their various linear superpositions as well as (in the case of multiple qubits) photon number correlations between modes. This approach is based on postselection and does not provide a correct performance estimate of an experimental scheme under investigation, in particular, it does not allow one to evaluate its scalability.

We investigate the performance of continuous variable quantum key distribution scheme in a practical setting. More specifically, we take non-ideal error reconciliation procedure into account. The quantum channel connecting the two honest parties is assumed to be lossy but noiseless. Secret key rates are given for the case that the measurement outcomes are postselected or a reverse reconciliation scheme is applied. The reverse reconciliation scheme loses its initial advantage in the practical setting. If one combines postselection with reverse reconciliation however, much of this advantage can be recovered., Comment: 7 pages, 2 figures

We previously suggested that photon exchange interactions could be used to produce nonlinear effects at the two-photon level, and similar effects have been experimentally observed by Resch et al. (e-print quant-ph/0306198). Here we note that photon exchange interactions are not useful for quantum information processing because they require the presence of substantial photon loss. This dependence on loss is somewhat analogous to the postselection required in the linear optics approach to quantum computing suggested by Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)].

We propose a distribution scheme of polarization states of a single photon over collective-noise channel. By adding one extra photon with a fixed polarization, we can protect the state against collective noise via a parity-check measurement and post-selection. While the scheme succeeds only probabilistically, it is simpler and more flexible than the schemes utilizing decoherence-free subspace. An application to BB84 protocol through collective noise channel, which is robust to the Trojan horse attack, is also given., 4 pages, 3 figures; published version in Phys. Rev. Lett

We describe several different methods for generating the entangled ancilla states that are required for linear optics quantum computing. We show that post-selection can be used in combination with linear optical elements to generate the entangled ancilla, but with an exponentially-small efficiency. Alternatively, the ancilla can be efficiently generated using solid-state devices consisting of quantum wells coupled with tunnel junctions. Finally, we consider the possibility of using encoded ancilla in order to reduce the effects of decoherence and measurement errors., Comment: 23 pages, 10 figures

We experimentally demonstrate a simple classical-field optical heterodyne method which employs postselection to reproduce the polarization correlations of a four-particle entangled state. We give a heuristic argument relating this method to the measurement of multiple quantum fields by correlated homodyne detection. We suggest that using multiple classical fields and postselection, one can reproduce the polarization correlations obtained in quantum experiments which employ multiple single-photon sources and linear optics to prepare multiparticle entangled states. Our experimental scheme produces four spatially separated beams which are separately detected by mixing with four independent optical local oscillators (LO) of variable polarization. Analog multiplication of the four beat signals enables projection onto a four-particle polarization-state basis. Appropriate band pass filtering is used to produce a signal proportional to the projections of the maximally entangled four-field polarization state, $\ensuremath{\mid}{H}_{1})\ensuremath{\mid}{H}_{2})\ensuremath{\mid}{H}_{3})\ensuremath{\mid}{H}_{4})+\ensuremath{\mid}{V}_{1})\ensuremath{\mid}{V}_{2})\ensuremath{\mid}{V}_{3})\ensuremath{\mid}{V}_{4})$, onto the product of the four LO polarizations. Since the data from multiple observers is combined prior to postselection, this method does not constitute a test of nonlocality. However, we reproduce the polarization correlations of the 32 elements in the truth table from the quantum mechanical Greenberger-Horne-Zeilinger experiments on the violation of local realism. We also demonstrate a form of classical entanglement swapping in a four-particle basis.

The communication protocol of Home and Whitaker [Phys. Rev. A 67, 022306 (2003)] is examined in some detail, and found to work equally well using a separable state. The protocol is in fact completely classical, based on simple post-selection of suitable experimental runs. The quantum cryptography protocol proposed in the same publication is also examined, and is found to indeed need quantum properties for the system to be secure. However, the security test proposed in the mentioned paper is found to be insufficient, and a modification is proposed here that will ensure security., revtex4, 9 pages

In this letter, first, we investigate the security of a continuous-variable quantum cryptographic scheme with a postselection process against individual beam splitting attack. It is shown that the scheme can be secure in the presence of the transmission loss owing to the postselection. Second, we provide a loss limit for continuous-variable quantum cryptography using coherent states taking into account excess Gaussian noise on quadrature distribution. Since the excess noise is reduced by the loss mechanism, a realistic intercept-resend attack which makes a Gaussian mixture of coherent states gives a loss limit in the presence of any excess Gaussian noise., RevTeX4, 4 pages, 5 figures

We show that retrodictive quantum mechanics provides a simple method of calculating the probability that a postselecting device produces the required output state. A retrodictive equivalence between optical attenuators and amplifiers allows us to simplify the calculation.

We present an experimental quantum key distribution system with coherent light. Polarisation encoding ensures simple preparation and local oscillator free measurement. By postselection, a potential secret key can be established even in presence of losses >3 dB

We used quantum process tomography to investigate and identify the function of a nonideal two-qubit quantum-state filters subject to various degree of decoherence. We present a simple decoherence model that explains the experimental results and point out that a beamsplitter followed by a post-selection process is not, as commonly believed, a singlet-state filter. In the ideal case it is a triplet-state filter., Comment: 4 pages, 4 figures, RevTeX, to be published in Phys. Rev. Lett

Multiphoton entanglement is an important resource for linear optics quantum computing. Here we show that a wide range of highly entangled multiphoton states, including W-states, can be prepared by interfering single photons inside a Bell multiport beam splitter and using postselection. A successful state preparation is indicated by the collection of one photon per output port. An advantage of the Bell multiport beam splitter is that it redirects the photons without changing their inner degrees of freedom. The described setup can therefore be used to generate polarisation, time-bin and frequency multiphoton entanglement, even when using only a single photon source., Comment: 8 pages, 2 figures, carefully revised version, references added

Recently, entanglement concentrations have been experimentaly demonstrated by postselection [T. Yamamoto et al., Nature (London) 421, 343 (2003), and Z. Zhao et al., Phys. Rev. Lett. 90, 207901 (2003)], i.e., to each individual outcome state, one has to destroy it to know whether it has been purified. Here we give proposal for entanglement concentration without any postselection by using only practically existing linear optical devices. In particular, a sophisticated photon detector to distinguish one photon or two photons is not required.

By quantum mechanics principle, two remote parties that have never interacted each other can be entangled through entanglement swapping operation done by a third party. Currently existing entanglement swapping experiments are done probabilistically by post-selection, i.e., once a successful swapping is verified, the resultant entanglement is destructed. We propose a simple non-post-selection scheme to probabilistically make the high quality quantum entanglement swapping with the spontaneous parametric down conversion(SPDC) process. After the swapping, two spatially separated parties who have never interacted each other are entangled through a single photon entangled state. Our scheme only requires the normal photon detectors which can distinguish the vacuum and non-vacuum Fock states.

We show first reconstructions of the photon-number distribution obtained with a multi-channel fiber-loop detector. Apart from analyzing the statistics of light pulses this device can serve as a sophisticated postselection device for experiments in quantum optics and quantum information. We quantify its efficiency by means of the Fisher information and compare it to the efficiency of the ideal photodetector., Comment: 5 pages, 6 figures

We show that weak measurements with post-selection, proposed in the context of the quantum theory of measurement, naturally appear in the everyday physics of fiber optics telecom networks through polarization-mode dispersion (PMD) and polarization-dependent losses (PDL). Specifically, the PMD leads to a time-resolved discrimination of polarization; the post-selection is done in the most natural way: one post-selects those photons that have not been lost because of the PDL. The quantum formalism is shown to simplify the calculation of optical networks in the telecom limit of weak PMD., 4 pages, 1 figure

Hall's recent derivation of an exact uncertainty relation [Phys. Rev. A64, 052103 (2001)] is revisited. It is found that the Bayes estimator of an observable between pre- and postselection equals the real part of the weak value. The quadratic loss function equals the expectation of the squared imaginary part of the weak value., Comment: 5 pages, accepted in Phys. Lett. A

We report a novel Bell state preparation experiment. High-purity Bell states are prepared by using femtosecond pulse pumped \emph{nondegenerate} collinear spontaneous parametric down-conversion. The use of femtosecond pump pulse {\em does not} result in reduction of quantum interference visibility in our scheme in which post-selection of amplitudes and other traditional mechanisms, such as, using thin nonlinear crystals or narrow-band spectral filters are not used. Another distinct feature of this scheme is that the pump, the signal, and the idler wavelengths are all distinguishable, which is very useful for quantum communications., Comment: 4 pages, submitted to PRL

We theoretically demonstrate a method for producing the maximally path-entangled state (1/Sqrt[2]) (|N,0> + exp[iN phi] |0,N>) using intensity-symmetric multiport beamsplitters, single photon inputs, and either photon-counting postselection or conditional measurement. The use of postselection enables successful implementation with non-unit efficiency detectors. We also demonstrate how to make the same state more conveniently by replacing one of the single photon inputs by a coherent state., 4 pages, 1 figure. REVTeX4. Replaced with published version

A source of photon-number-squeezed light based on postse-lection from entangled photon pairs produced by parametric frequency down-conversion is suggested. Postselection device consists of 1 x N coupler and N detectors. All possible sources of noise are taken into account. The dependence of the Fano factor of generated light on various parameters is examined.

A single beam of light created via spontaneous parametric down-conversion has a random phase. We show it is possible to induce a well-defined absolute phase in one beam by overlapping the other with a weak coherent state and conditioning on detection of a photon. This post-selection fixes the phase of the down-conversion even though stimulated emission is negligibly small.

We describe an experiment in which a physical qubit represented by the polarization state of a single-photon was probabilistically encoded in the logical state of two photons. The experiment relied on linear optics, post-selection, and three-photon interference effects produced by a parametric down-conversion photon pair and a weak coherent state. An interesting consequence of the encoding operation was the ability to observe entangled three-photon Greenberger-Horne-Zeilinger states., Comment: 4 pages, 4 figures; submitted to Phys. Rev. A

The notion of the weak value of a quantum mechanical observable has recently been introduced by Aharonov et al. (Phys. Rev A 41,11 (1990)), hereafter referred to as AAV. We have performed an experiment similar to one proposed by Knight et al. (1990) and demonstrated that weak values can be observed and that they exhibit the properties described by AAV within the regime of validity. We suggest that preselection and postselection measurement techniques could be useful for study of physical phenomena that might be otherwise unobservable.

Recently it was realized that linear optics and photodetectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation is to design a simple postselected gate that implements a nonlinear phase shift on one mode. Here a computational strategy is given for finding postselected gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained. What is the maximum efficiency for such gates? This question is posed and it is shown that the probability of success cannot be 1.

Knill, Laflamme, and Milburn recently showed that non-deterministic quantum logic operations could be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors [Nature 409, 46 (2001)]. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT (CNOT) gate and a quantum parity check. These two devices can be combined with a pair of entangled photons to implement a conventional (non-destructive) CNOT that succeeds with a probability of 1/4., Comment: 4 pages, 5 figures; Minor changes

It is well known that spontaneous parametric down-conversion can be used to probabilistically prepare single-photon states. We have performed an experiment in which arbitrary superpositions of zero- and one-photon states can be prepared by appropriate postselection. The optical phase, which is meaningful only for superpositions of photon number, is related to the relative phase between the zero- and one-photon states. Whereas the light from spontaneous parametric down-conversion has an undefined phase, we show that this technique collapses one beam to a state of well-defined optical phase when a measurement succeeds on the other beam.

I propose a "quantum annealing" heuristic for the problem of combinatorial search among a frustrated set of states characterized by a cost function to be minimized. The algorithm is probabilistic, with postselection of the measurement result. A unique parameter playing the role of an effective temperature governs the computational load and the overall quality of the optimization. Any level of accuracy can be reached with a computational load independent of the dimension {\it N} of the search set by choosing the effective temperature correspondingly low. This is much better than classical search heuristics, which typically involve computation times growing as powers of log({\it N}), Revised, published version

A photon source based on postselection from entangled photon pairs produced by parametric frequency down-conversion is suggested and applied in quantum cryptography. Its ability to provide good approximations of single-photon states is examined. Use of this source for quantum key distribution is discussed. Advantages of this quantum-key-distribution system are clarified.

Typical address-oriented computer memories cannot recognize incomplete or noisy information. Associative (content-addressable) memories solve this problem but suffer from severe capacity shortages. I propose a model of a quantum memory that solves both problems. The storage capacity is exponential in the number of qbits and thus optimal. The retrieval mechanism for incomplete or noisy inputs is probabilistic, with postselection of the measurement result. The output is determined by a probability distribution on the memory which is peaked around the stored patterns closest in Hamming distance to the input., Comment: Revised version to appear in Phys. Rev. Lett

Experimental tests of Bell inequalities ought to take into account all detection events. If the latter are postselected, and only some of these events are included in the statistical analysis, a Bell inequality may be violated, even by purely classical correlations. The paradoxical properties of Werner states, recently pointed out by Popescu, can be explained as the result of a postselection of the detection events, or, equivalently, as due to the preparation of a new state by means of a nonlocal process.

We report a two-photon interference experiment that realizes a postselection-free test of Bell's inequality based on energy-time entanglement. In contrast with all previous experiments of this type, the employed entangled states are obtained without the use of a beam splitter or a short coincidence window to "throw away" unwanted amplitudes. A (95.0\ifmmode\pm\else\textpm\fi{}1.4)% interference fringe visibility is observed, implying a strong violation of the Bell inequality. The scheme is very compact and has demonstrated excellent stability, suggesting that it may be useful, for example, in practical quantum cryptography.

Recent neutron interference experiments, based on the post-selection of narrow momentum states behind the interferometer, have shown that coherent wave packets remain totally coupled in configuration space, even when they become separated in ordinary space. Such non-overlapping wave packets in real space (Schrodinger-cat-like states) show a characteristical spectral modulation and squeezing indicating its nonclassical features. This shows analogies to EPR- experiments, with consequences for the debate about the non-locality phenomena of quantum mechanics.

A two-step measurement protocol of a quantum system, known as weak value (WV), has been introduced more than two decades ago by Aharonov et al. [1], and has since been studied in various contexts. Here we discuss another two-step measurement protocol which we dub null weak value (NWV). The protocol consists of a partial-collapse measurement followed by quantum manipulation on the system and finally a strong measurement. The first step is a strong measurement which takes place with small probability. The second strong measurement is used as postselection on the outcome of the earlier step. Not being measured in the partial-collapse stage (null outcome) leads to a non-trivial correlation between the two measurements. The NVW protocol, first defined for a two-level system [2], is generalized to a multi-level system, and compared to the standard-WV protocol., Comment: 5 pages, 2 figures, conference proceeding

We present a scheme for remote preparing a general two-particle state by two entangled states serving as the quantum communication channel. In this scheme, it is possible for the receiver to perfectly reconstruct the initial state that the sender hopes to prepare with the method of introducing an auxiliary qubit and postselection measurements in the situation of non-maximal entangled quantum channel. Furthermore, we investigate the influence of the dissipation factors on the processing of the remote state preparation when the entangled resources are in the Markovian and non-Markovian noisy environments. It is shown that the fidelity of remote state preparation is decreasing exponentially over time in Markovian environments and attenuating oscillatorily in non-Markovian. However, when the non-Markovian and the detuning conditions are satisfied simultaneously, the fidelity can be preserved at comparative high levels, effectively.

We evaluate the after-pulse probability of a gated-mode single-photon detector operating at 1550 nm. The experimental results are applied to the simulation of quantum key distribution to estimate the obtainable key rate, which decreases at higher gate frequencies because of a large number of after-pulse-related errors. In this paper, we present a postselection method of discarding after-pulses to improve the key rate.

The transverse structure of the nucleon as probed in hard exclusive processes plays critical role in the understanding of the structure of the underlying event in hard collisions at the LHC, and multiparton interactions. We summarize results of our recent studies of manifestation of transverse nucleon structure in the hard collisions at the LHC, new generalized parton distributions involved in multiparton interactions, presence of parton fluctuations. The kinematic range where interaction of fast partons of the projectile with the target reach black disk regime (BDR) strength is estimated. We demonstrate that in the BDR postselection effect leads to effective fractional energy losses. This effect explains regularities of the single and double forward pion production in $ dAu$ collisions at RHIC and impacts on the forward physics in $pp$ collisions at the LHC.

Weak values, resulting from the action of an operator on a preselected state when measured after postselection by a different state, can lie outside the spectrum of eigenvalues of the operator: they can be 'superweak'. This phenomenon can be quantified by averaging over an ensemble of the two states, and calculating the probability distribution of the weak values. If there are many eigenvalues, distributed within a finite range, this distribution takes a simple universal generalized lorentzian form, and the 'superweak probablility', of weak values outside the spectrum, can be as large as 1–1/ = 0.293.... By contrast, the familiar expectation values always lie within the spectral range, and their distribution, although approximately gaussian for many eigenvalues, is not universal.

We propose a novel linear optical scheme to generate a three-photon W state, which is based on postselection of final outcome events. The success probability of our proposal has been improved to be 21/32, higher than that of the previous methods using the linear optical system. We also discuss the effects of realistic photon resources on its experimental realization and compare our scheme with the nonlinear optical approach to the three-photon W state generation. The idea of our proposal suggests a new way to improve the generation efficiency of some other entangled states and may have a promising application.

The fidelity of postselecting devices based on direct photon number detection can be significantly improved by insertion of a phase-insensitive optical amplifier in front of the detector. The scheme is simple, and the cost to the probability of obtaining the appropriate detector outcome is low.

PHYSICS Quantum information processing requires techniques for the generation and transportation of quantum data. The use of photons as the carriers of that quantum information, with the data encoded as different polarization states of the light, is particularly appealing because photons are robust against decoherence effects and can be transported over long distances. The photons, however, need to be indistinguishable; i.e., identical and in a pure quantum state. Although techniques exist for the generation for single photons, determining whether they are in fact indistinguishable and pure has generally required a postselection or spectral filtering process that compromises their quantum utility. By careful design of the parametric downconversion process, in which a single photon is divided into two entangled photons, Mosley et al. show that restricting the optical modes into which the photon pairs emerge can provide a method for the generation of heralded (by measurement of one member of the pair) indistinguishable single photons of high purity. — ISO Phys. Rev. Lett. 100 , 133601 (2008).

In this investigation, a decision-making IIT approach for materials selection has been proposed. This approach consists of three phases which are the preselection, selection, and postselection and techno-economic phases. This approach differs from other approaches in taking into consideration the economic and business issues factors. Going from one phase to another, a number of the candidate materials are eliminated step by step until the optimum material is reached. This approach was also translated into a computer programme which consists of the complementary work of the modules that have screening properties. A case study was presented to test the proposed model and good results have been obtained.

We show how to convert between partially coherent superpositions of a single photon with the vacuum using linear optics and postselection based on homodyne measurements. We introduce a generalized quantum efficiency for such states and show that any conversion that decreases this quantity is possible. We also prove that our scheme is optimal by showing that no linear optical scheme with generalized conditional measurements, and with one single-rail qubit input can improve the generalized efficiency., 3 pages, 2 figures

We have found that the usual measuring procedure for preselected and postselected ensembles of quantum systems gives unusual results. Under some natural conditions of weakness of the measurement, its result consistently defines a new kind of value for a quantum variable, which we call the weak value. A description of the measurement of the weak value of a component of a spin for an ensemble of preselected and postselected spin-(1/2 particles is presented.

A Comment on the Letter by Yakir Aharonov, David Z. Albert, and Lev Vaidman, Phys. Rev. Lett. 60, 1351 (1988).