Search

We show that, in the relativistic limit, the quantum theory of neutrino oscillations can be described through the theory of weak measurements with pre and post-selection. The weak nature of neutrino detection allows simultaneous determination of flavor and energy without problems related to the collapse of the wavefunction. Together with post-selection, a non-trivial quantum interference emerges, allowing one to describe a flavor neutrino as one single particle, despite its superposition of masses. We write down the flavor equation of motion and calculate the flavor oscillation probability by showing precisely how a single neutrino interferes with itself., 21 pages, 5 figures, references added

Using Bochner's theorem, we derive a necessary and sufficient hierarchy of measurable conditions in terms of the characteristic function of quasi-moments of a weakly measured observable. A quantum ...

Entanglement verification and measurement is essential for experimental tests of quantum mechanics and also for quantum communication and information science. Standard methods of verifying entanglement in a bipartite mixed state require detection of both particles and involve coincidence measurement. We present a method that enables us to verify and measure entanglement in a two-photon mixed state without detecting one of the photons, i.e., without performing any coincidence measurement or postselection. We consider two identical sources, each of which can generate the same two-photon mixed state but they never emit simultaneously. We show that one can produce a set of single-photon interference patterns, which contain information about entanglement in the two-photon mixed state. We prove that it is possible to retrieve the information about entanglement from the visibility of the interference patterns. Our method reveals a distinct avenue for verifying and measuring entanglement in mixed states., 10 pages, 3 figures

Twin-field quantum key distribution (TF-QKD) can overcome the fundamental rate-loss limit without quantum repeaters, which has stimulated intense research interests both in theory and experiment. Recently, TF-QKD protocols with discrete-phase-randomized sources have been widely studied. However, all these protocols require the phase postselection step in the test mode. To bypass this step, we propose a discrete-phase-randomized TF-QKD protocol without phase postselection in the test mode, which reduces the amount of information transmitted in the classical post-processing stage and thus reduces the consumption of secret keys in the authentication of classical information. Moreover, the numerical simulation of our protocol can be easily solved by linear programming. Simulation results show that, with only a few number of discrete phases, our protocol can beat the rate-loss bound and approximate the case of continuous phases, which is very practical in some real-life implementations of TF-QKD.

Direct state measurement (DSM) is a tomography method that allows for retrieving quantum states' wave functions directly. However, a shortcoming of current studies on the DSM is that it does not provide access to noisy quantum systems. Here, we attempt to fill the gap by investigating the DSM measurement precision that undergoes the state-preparation-and-measurement (SPAM) errors. We manipulate a quantum controlled measurement framework with various configurations and compare the efficiency between them. Under such SPAM errors, the state to be measured lightly deviates from the true state, and the measurement error in the postselection process results in less accurate in the tomography. Our study could provide a reliable tool for SPAM errors tomography and contribute to understanding and resolving an urgent demand for current quantum technologies., Comment: 11 pages, 7 figures

Is it possible that a measurement of a spin component of a spin-1/2 particle yields the value 100? In 1988 Aharonov, Albert and Vaidman argued that upon pre- and postselection of particular spin states, weakening the coupling of a standard measurement procedure ensures this paradoxical result. This theoretical prediction, called weak value, was realized in numerous experiments, but its meaning remains very controversial, since its "anomalous" nature, i.e. the possibility to exceed the eigenvalues range, as well as its "quantumness" are debated. We address these questions by presenting the first experiment measuring anomalous weak values with just a single click, without any statistics. The measurement uncertainty is significantly smaller than the gap between the measured weak value and the nearest eigenvalue. Beyond clarifying the meaning of weak values, this result represents a breakthrough in understanding quantum measurement foundations, paving the way to further applications of weak values to quantum photonics., Revised version to appear in Light: Science & Applications

A quantum system subject to continuous measurement and post-selection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the rate of post-selection, this non-Hermitian Hamiltonian undergoes a spectral phase transition. On one side of this phase transition (for weak post-selection) an initially mixed density matrix remains mixed at all times, and an initially unentangled state develops volume-law entanglement; on the other side, an arbitrary initial state approaches a unique pure state with low entanglement. We identify this transition with an exceptional point in the spectrum of the non-Hermitian Hamiltonian, at which PT symmetry is spontaneously broken. We characterize the transition as well as the nontrivial steady state that emerges at late times in the mixed phase using exact diagonalization and an approximate, analytically tractable mean-field theory; these methods yield consistent conclusions., 8 pages, 6 figures

In a quantum-noise limited system, weak-value amplification using post-selection normally does not produce more sensitive measurements than standard methods for ideal detectors: the increased weak value is compensated by the reduced power due to the small post-selection probability. Here we experimentally demonstrate recycled weak-value measurements using a pulsed light source and optical switch to enable nearly deterministic weak-value amplification of a mirror tilt. Using photon counting detectors, we demonstrate a signal improvement by a factor of $4.4 \pm 0.2$ and a signal-to-noise ratio improvement of $2.10 \pm 0.06$, compared to a single-pass weak-value experiment, and also compared to a conventional direct measurement of the tilt. The signal-to-noise ratio improvement could reach around 6 for the parameters of this experiment, assuming lower loss elements., 6 pages, 3 figures

The deterministic quantum computation with one qubit (DQC1) model is a restricted model of quantum computing able to calculate efficiently the normalized trace of a unitary matrix. In this work, we analyze the quantum correlations called entanglement, Bell's nonlocality, quantum discord, and coherence generated by the DQC1 circuit considering only two qubits (auxiliary and control). For the standard DQC1 model, only quantum discord and coherence appear. By introducing a filter in the circuit we purify the auxiliary qubit, taking it out from the totally mixed state and consequently promoting other quantum correlations between the qubits, such as entanglement and Bell's nonlocality. Through the optimization of the purification process, we conclude that even a small purification is enough to generate entanglement and Bell's nonlocality. We obtain, that by applying the purification process repeatedly an average of 12 times, the auxiliary qubit becomes $99%$ pure. In this situation, almost maximally entangled states are achieved, which almost maximally violate Bell's inequality. This result suggests that with a simple modification, the DQC1 model can be promoted to a universal model of quantum computing.

Weak measurement as a nonperturbative theory has been shown to be powerful in the fundamentals of quantum mechanics and high-precision metrology, in which the pointer is of great importance to parameter estimation and experimental design. In this work, we find that under the conditions of weak coupling and Gaussian meter, the probability distribution after the postselection follows a bimodal function and the peak contrast ratio (PCR) can be applied as a special pointer, which is different from the shift of mean value. To obtain the PCR, only two values corresponding to the two peaks in the distribution function are required. We theoretically present the relation of the PCR and parameters to be estimated, and then demonstrate it in an experiment. Weak measurement with the PCR pointer has the advantages of reducing the requirements of the apparatus and suppressing noise, which also provides a heuristic approach for studying weak measurement when the weak value is very large.

Accurate quantum chemistry simulations remain challenging on classical computers for problems of industrially relevant sizes and there is reason for hope that quantum computing may help push the boundaries of what is technically feasible. While variational quantum eigensolver (VQE) algorithms may already turn noisy intermediate scale quantum (NISQ) devices into useful machines, one has to make all efforts to use the scarce quantum resources as efficiently as possible. We combine the so-called seniority-zero, or paired-electron, approximation of computational quantum chemistry with techniques for simulating molecular chemistry on gate-based quantum computers and obtain a very resource efficient quantum simulation algorithm. While some accuracy is lost through the paired-electron approximation, we show that using the freed-up quantum resources for increasing the basis set can lead to more accurate results and reductions in the necessary number of quantum computing runs by several orders of magnitude, already for a simple system like lithium hydride. We also discuss an error mitigation scheme based on post-selection which shows an attractive scaling when the given Hamiltonian format is considered, increasing the viability of its NISQ implementation., Comment: 12 pages, 4 figures

Free-space channels provide the possibility of establishing continuous-variable quantum key distribution in global communication networks. However, the fluctuating nature of transmissivity in these channels introduces an extra noise which reduces the achievable secret key rate. We consider two classical postprocessing strategies, postselection of high-transmissivity data and data clusterization, to reduce the fluctuation-induced noise of the channel. We undertake the investigation of such strategies utilizing a composable security proof in a realistic finite-size regime against both collective and individual attacks. We also present an efficient parameter estimation approach to estimate the effective Gaussian parameters over the postselected data or the clustered data. Although the composable finite-size effects become more significant with the postselection and clusterization both reducing the size of the data, our results show that these strategies are still able to enhance the finite-size key rate against both individual and collective attacks with a remarkable improvement against collective attacks, even moving the protocol from an insecure regime to a secure regime under certain conditions.

We introduce a new quantity, called pseudo-entropy, as a generalization of entanglement entropy via postselection. We expect this quantity to provide a new class of order parameters in quantum many-body systems. In the anti–de Sitter space (AdS)/conformal field theory (CFT) correspondence, this quantity is dual to areas of minimal area surfaces in time-dependent Euclidean spaces which are asymptotically AdS. We call this geometric computation of pseudo-entropy via the AdS/CFT the holographic pseudo-entropy. We study its basic properties and classifications in qubit systems. In specific examples, we provide a quantum information theoretic meaning of this new quantity as an averaged number of Bell pairs when the post-selection is performed. We also present properties of the pseudo-entropy for random states. We then calculate the pseudo-entropy in the presence of local operator excitations for both the two dimensional free massless scalar CFT and two dimensional holographic CFTs. We find a general property in CFTs that the pseudo-entropy is highly reduced when the local operators get closer to the boundary of the subsystem. We also compute the holographic pseudo-entropy for a Janus solution, dual to an exactly marginal perturbation of a two dimensional CFT and find its agreement with a perturbative calculation in the dual CFT. We show the linearity property holds for holographic states, where the holographic pseudo-entropy coincides with a weak value of the area operator. Finally, we propose a mixed state generalization of pseudo-entropy and give its gravity dual.

Wheeler's delayed-choice experiment was conceived to illustrate the paradoxical nature of wave-particle duality in quantum mechanics. In the experiment, quantum light can exhibit either wave-like interference patterns or particle-like anti-correlations, depending upon the (possibly delayed) choice of the experimenter. A variant known as the quantum eraser uses entangled light to recover the lost interference in a seemingly nonlocal and retrocausal manner. Although it is believed that this behavior is incompatible with classical physics, here we show that the observed quantum phenomena can be reproduced by adopting a simple deterministic detector model and supposing the existence of a random zero-point electromagnetic field., 12 pages, 12 figures

The distribution of entangled states across the nodes of a future quantum internet will unlock fundamentally new technologies. Here we report on the experimental realization of a three-node entanglement-based quantum network. We combine remote quantum nodes based on diamond communication qubits into a scalable phase-stabilized architecture, supplemented with a robust memory qubit and local quantum logic. In addition, we achieve real-time communication and feed-forward gate operations across the network. We capitalize on the novel capabilities of this network to realize two canonical protocols without post-selection: the distribution of genuine multipartite entangled states across the three nodes and entanglement swapping through an intermediary node. Our work establishes a key platform for exploring, testing and developing multi-node quantum network protocols and a quantum network control stack., Comment: 9 pages, 5 figures, supplementary materials

We propose a post-selection technique, based on quantum error detection, for quantum key distribution (QKD) systems that run over quantum repeaters with encoding. In such repeaters, quantum error correction techniques are used for entanglement distillation. By developing an analytical approach to study such quantum repeaters, we show that, in the context of QKD, it is often more efficient to use the error detection, rather than the error correction, capability of the underlying code to sift out cases where an error has been detected. We implement our technique for three-qubit repetition codes by modelling different sources of error in crucial components of the system. We then investigate in detail the impact of such imperfections on the secret key generation rate of the QKD system, and how one can use the information obtained during entanglement swapping and decoding stages to maximize the rate. For benchmarking purposes, we specify the maximum allowed error rates in different components of the setup below which positive key rates can be obtained., 14 pages, 7 figures

The dynamics of entanglement in `hybrid' non-unitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply \emph{postselection} on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhead. We propose a method to sidestep this issue in a wide class of non-unitary circuits by taking advantage of \emph{spacetime duality}. This method maps the purification dynamics of a mixed state under non-unitary evolution onto a particular correlation function in an associated unitary circuit. This translates to an operational protocol which could be straightforwardly implemented on a digital quantum simulator. We discuss the signatures of different entanglement phases, and demonstrate examples via numerical simulations. With minor modifications, the proposed protocol allows measurement of the purity of arbitrary subsystems, which could shed light on the properties of the quantum error correcting code formed by the mixed phase in this class of hybrid dynamics., 4 pages main text + 9 page supplemental material. v2: added references, expanded supplement, minor modifications to text

We quantify the disturbance of a quantum state undergoing a sequence of observations, and particularly focus on a weak measurement followed by post-selection and compare these results to the projective counterpart. Taking into account the distinguishability of both, the system and the device, we obtain the exact trade-off between the system state disturbance and the change of the device pointer state. We show that for particular post-selection procedures the coupling strength between the system and the device can be significantly reduced without loosing measurement sensitivity, which is directly transferred to a reduced state disturbance of the system. We observe that a weak measurement alone does not provide this advantage but only in combination with post-selection a significant improvement in terms of increased measurement sensitivity and reduced state disturbance is found. We further show that under realistic experimental conditions this state disturbance is small, whereas the exact post-selection probability is considerably larger than the approximate value given by the overlap of the initial and final state when neglecting the system state disturbance.

The weak-value (WV) measurement proposed by Aharonov, Albert, and Vaidman (AAV) has attracted a great deal of interest in connection with quantum metrology. In this paper, we extend the analysis beyond the AAV limit and obtain a few main results. (i) We obtain a nonperturbative result for the signal-to-noise ratio (SNR). In contrast to the AAV prediction, we find that the SNR asymptotically gets worse when the AAV WV ${A}_{w}$ becomes large, i.e., in the case $g|{A}_{w}{|}^{2}\ensuremath{\gg}1$, where $g$ is the measurement strength. (ii) With the increase of $g$ (but also small), we find that the SNR is comparable to the result under the AAV limit, while both can reach---actually the former can slightly exceed---the SNR of the standard measurement. However, with a further increase of $g$, the WV technique will become less efficient than the standard measurement, despite the fact that the postselection probability is increased. (iii) We find that the Fisher information can characterize the estimate precision qualitatively well as the SNR, yet the difference will become more prominent with the increase of $g$. (iv) We carry out analytic expressions of the SNR in the presence of technical noises and illustrate the particular advantage of the imaginary WV measurement. The nonperturbative result of the SNR manifests a favorable range of the noise strength and allows an optimal determination.

In this paper, we propose the generation of hyperentangled photon pairs using type-II spontaneous parametric down-conversion in a biperiod, 5% MgO-doped lithium-niobate ridge waveguide. The photon pairs are entangled in spatial mode and polarization degrees of freedom. A pulsed laser source at 687 nm, having an antisymmetric Hermite-Gaussian HG (1,0) spatial mode, is considered as the pump. Down-converted photon pairs, with the signal being at the telecommunication wavelength of 1550 nm, are characterized through a joint spectral amplitude analysis of their biphoton state.

Flag verification techniques are useful in quantum error correction for detecting critical faults. Here we present an application of flag verification techniques to improving post-selected performance of near-term algorithms. We extend the definition of what constitutes a flag by creating error-detection gadgets based on known transformations of unitary operators. In the case of Clifford or near-Clifford circuits, these unitary operators can be chosen to be controlled Pauli gates, leading to gadgets which require only a small number of additional Clifford gates. We show that such flags can improve circuit fidelities by up to a factor of 2 after post selection, and demonstrate their effectiveness over error models featuring single-qubit depolarizing noise, crosstalk, and two-qubit coherent overrotation., 7 pages, 7 figures

A protocol for remote state preparation is proposed for spin ensembles, where the aim is to prepare a state with a given set of spin expectation values on a remote spin ensemble using entanglement, local spin rotations, and measurements in the Fock basis. The spin ensembles could be realized by thermal atomic ensembles or spinor Bose-Einstein condensates. The protocol works beyond the Holstein-Primakoff approximation, such that spin expectation values for the full Bloch sphere can be prepared. The main practical obstacle is the preparation of the maximally entangled state between the spin ensembles. To overcome this, we examine using states based on the two-axis two-spin (2A2S) Hamiltonian in place of the maximally entangled state and examine its performance. We find that the version of the protocol with 2A2S squeezing well-approximates the maximally entangled state, such that spin averages can be remotely prepared. We evaluate the errors of using 2A2S squeezed states, and find that it decreases with the ensemble size. With post-selection, errors can be systematically decreased further., 12 pages, 6 figures

Many quantum state preparation methods rely on a combination of dissipative quantum state initialization followed by unitary evolution to a desired target state. Here we demonstrate the usefulness of quantum measurement as an additional tool for quantum state preparation. Starting from a pure separable multipartite state, a control sequence, which includes rotation, spin squeezing via one-axis twisting, quantum measurement, and postselection, generates highly entangled multipartite states, which we refer to as projected squeezed (PS) states. Through an optimization method, we then identify parameters required to maximize the overlap fidelity of the PS states with the maximally entangled Greenberger-Horne-Zeilinger (GHZ) states. The method leads to an appreciable decrease in the state preparation time of GHZ states for successfully postselected outcomes when compared to preparation through unitary evolution with one-axis twisting only.

We present a simple extension of the semi-classical model for a two-level system in a cavity, in order to incorporate multiple polarized transitions, such as those appearing in neutral and charged quantum dots (QDs), and two nondegenerate linearly polarized cavity modes. We verify the model by exact quantum master equation calculations, and experimentally using a neutral QD in a polarization non-degenerate micro-cavity, in both cases we observe excellent agreement. Finally, the usefulness of this approach is demonstrated by optimizing a single-photon source based on polarization postselection, where we find an increase in the brightness for optimal polarization conditions as predicted by the model., Comment: 8 pages, for simple code see https://doi.org/10.5281/zenodo.3476660

We introduce a robust scheme for long-distance continuous-variable (CV) measurement-device-independent (MDI) quantum key distribution (QKD) in which we employ post-selection between distant parties communicating through the medium of an untrusted relay. We perform a security analysis that allows for general transmissivity and thermal noise variance of each link, in which we assume an eavesdropper performs a collective attack and controls the excess thermal noise in the channels. The introduction of post-selection enables the parties to sustain a secret key rate over distances exceeding those of existing CV MDI protocols. In the worst-case scenario in which the relay is positioned equidistant between them, we find that the parties may communicate securely over a range of 14 km in standard optical fiber. Our protocol helps to overcome the rate-distance limitations of previously proposed CV MDI protocols while maintaining many of their advantages., 13 pages, 7 figures

Recently, it has become clear that non-hermitian phenomena can be observed not only in open quantum systems experiencing gain and loss but also in equilibrium single-particle properties of strongly correlated systems. However, the circumstances and requirements for the emergence of non-hermitian phenomena in each field are entirely different. While the implementation of postselection is a significant obstacle to observe non-hermitian phenomena in open quantum systems, it is unnecessary in strongly correlated systems. Until now, a relation between both descriptions of non-hermitian phenomena has not been revealed. In this paper, we close this gap and demonstrate that the non-hermitian Hamiltonians emerging in both fields are identical, and we clarify the conditions for the emergence of a non-hermitian Hamiltonian in strongly correlated materials. Using this knowledge, we propose a method to analyze non-hermitian properties without the necessity of postselection by studying specific response functions of open quantum systems and strongly correlated systems., Comment: 5 pages, 3 figures, 6 pages for supplemental materials

Quantum cryptographic conferencing (QCC) holds promise for distributing information-theoretic secure keys among multiple users over a long distance. Limited by the fragility of Greenberger-Horne-Zeilinger (GHZ) states, QCC networks based on directly distributing GHZ states over a long distance still face a big challenge. Another two potential approaches are measurement device-independent QCC and conference-key agreement with single-photon interference, which were proposed on the basis of the postselection of GHZ states and the postselection of the W state, respectively. However, implementations of the former protocol are still heavily constrained by the transmission rate $\ensuremath{\eta}$ of optical channels and the complexity of the setups for postselecting GHZ states. Meanwhile, the latter protocol cannot be cast as a measurement device-independent prepare-and-measure scheme. Combining the idea of postselecting GHZ states and recently proposed twin-field quantum-key-distribution protocols, we report a QCC protocol based on weak coherent-state interferences named ``phase-matching quantum cryptographic conferencing,'' which is immune to all detector side-channel attacks. The proposed protocol can improve the key-generation rate from $O({\ensuremath{\eta}}^{N})$ to $O({\ensuremath{\eta}}^{N\ensuremath{-}1})$ compared with the measurement device-independent QCC protocols. Meanwhile, it can be easily scaled up to multiple parties due to its simple setup.

The existing techniques for measuring high-dimensional pure states of light in the orbital angular momentum (OAM) basis either involve a large number of single-pixel data acquisitions and substantial postselection errors that increase with dimensionality, or involve substantial loss, or require interference with a reference beam of known phase. Here, we propose an interferometric technique that can measure an unknown pure state using only nine multipixel image acquisitions without involving postselection, loss, or a separate reference beam. The technique essentially measures two complex correlation functions of the input field and then employs a recursive postprocessing algorithm to infer the state. We experimentally demonstrate the technique for pure states up to dimensionality of 25, reporting a mean fidelity greater than 90 % up to 11 dimensions. Our technique can significantly improve the performance of OAM-based information processing applications., Comment: 6 pages, 3 figures

We present a protocol to deterministically prepare the electromagnetic field in a large photon number state. The field starts in a coherent state and, through resonant interaction with one or few two-level systems, it evolves into a coherently displaced Fock state without any postselection. We show the feasibility of the scheme under realistic parameters. The presented method opens a door to reach Fock states, with $n\ensuremath{\sim}100$ and optimal fidelities above 70%, blurring the line between macroscopic and quantum states of the field.

We investigate a scheme for topological quantum computing using optical hybrid qubits and make an extensive comparison with previous all-optical schemes. We show that the photon loss threshold reported by Omkar {\it et al}. [Phys. Rev. Lett. 125, 060501 (2020)] can be improved further by employing postselection and multi-Bell-state-measurement based entangling operation to create a special cluster state, known as Raussendorf lattice for topological quantum computation. In particular, the photon loss threshold is enhanced up to $5.7\times10^{-3}$, which is the highest reported value given a reasonable error model. This improvement is obtained at the price of consuming more resources by an order of magnitude, compared to the scheme in the aforementioned reference. Neverthless, this scheme remains resource-efficient compared to other known optical schemes for fault-tolerant quantum computation., Comment: 12 pages, 8 figures

We report the experimental realization of heralded distribution of single-photon path entanglement at telecommunication wavelengths in a repeater-like architecture. The entanglement is established upon detection of a single photon, originating from one of two spontaneous parametric down conversion photon pair sources, after erasing the photon's which-path information. In order to certify the entanglement, we use an entanglement witness which does not rely on post-selection. We herald entanglement between two locations, separated by a total distance of 2 km of optical fiber, at a rate of 1.6 kHz. This work paves the way towards high-rate and practical quantum repeater architectures., Comment: 5+9 pages, 7 figures

Postselected von Neumann measurement characterized by postselection and weak value has been found potential applications in quantum metrology and, solved plenty of fundamental problems in quantum theory. As an application of this new measurement technique in quantum optics, its effects on the features of single-mode radiation fields such as coherent state, squeezed vacuum state and Schrodinger cat sate are investigated by considering full-order effects of unitary evolution. The results show that the conditional probabilities of finding photons, second-order correlation functions, Q-factors and squeezing effects of those states after postselected measurement significantly changed compared with corresponding initial pointer states, respectively., 12 pages, 30 figures

Perfect entanglement swapping, which can be realized without the postselection by using the nonlinear optical technology, provides an important way toward generating the large-scale quantum network. We explore an entanglement-swapping-based dense wavelength division multiplexed network in the experiment. Four users receive single quantum states at different wavelengths, and we perform a time-energy entanglement swapping operation based on the sum-frequency generation to make users fully connected in the network. The results show that the fidelity of the entangled state is larger than 90% and is independent of the number of users. Our Letter demonstrates the feasibility of a proposed multiuser network, and hence paves a route toward a variety of quantum applications, including entanglement-swapping-based quantum direct communication.

In this paper, we explore the possibilities of realizing weak value amplification (WVA) using purely atomic degrees of freedom. Our scheme identifies the internal electronic states and external motional states of a single trapped $^{40}$Ca$^+$ ion as the system degree and pointer degree respectively, and their controllable weak coupling is provided by a bichromatic light field. In our experimental demonstration, by performing appropriate postselection on the internal states, a position displacement of 4 angstroms (in phase space) of the trapped ion is amplified to 10 nanometers. The sensitivity of the amplification effect to the relative phase of the quantum state is also demonstrated. The high operational flexibility of this procedure allows fully exploration of the peculiarities of WVA., 8 pages, 8 figures

Continuous-variable quantum key distribution (CV QKD) protocols with discrete modulation are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks, but their security analysis is less advanced than that of Gaussian modulation schemes. In this work, we apply a numerical method to analyze the security of discrete-modulation protocols against collective attacks in the asymptotic limit, paving the way for a full security proof with finite-size effects. While our method is general for discrete-modulation schemes, we focus on two variants of the CV QKD protocol with quaternary modulation. Interestingly, thanks to the tightness of our proof method, we show that this protocol is capable of achieving much higher key rates over significantly longer distances with experimentally feasible parameters compared with previous security proofs of binary and ternary modulation schemes and also yielding key rates comparable to Gaussian modulation schemes. Furthermore, as our security analysis method is versatile, it allows us to evaluate variations of the discrete-modulated protocols, including direct and reverse reconciliation, and postselection strategies. In particular, we demonstrate that postselection of data in combination with reverse reconciliation can improve the key rates., v1: 15+6 pages, 12 figures, data files uploaded; v2: 23 pages, published version

We present results in structural complexity theory concerned with the following interrelated topics: computation with postselection/restarting, closed timelike curves (CTCs), and approximate counting. The first result is a new characterization of the lesser known complexity class BPP path in terms of more familiar concepts. Precisely, BPP path is the class of problems that can be efficiently solved with a nonadaptive oracle for the approximate counting problem. Similarly, PP equals the class of problems that can be solved efficiently with nonadaptive queries for the related approximate difference problem. Another result is concerned with the computational power conferred by CTCs, or equivalently, the computational complexity of finding stationary distributions for quantum channels. Using the preceding characterization of PP, we show that any poly( n )-time quantum computation using a CTC of O (log n ) qubits may as well just use a CTC of 1 classical bit. This result essentially amounts to showing that one can find a stationary distribution for a poly( n )-dimensional quantum channel in PP.

Weak amplification is an interesting phenomenon. In this paper we show an example that the imaginary weak amplification effect can be only related to the classical probability distribution of the measured quantity. A general result for any two orthogonal postselections and any meter state is also given.

This paper argues that quantum nonlocality (QNL) has not been rigorously proven, despite the existence of recent Einstein-Podolsky-Rosen-Bohm (EPRB) experiments that are claimed to be ‘loophole-free’. First, readers are alerted to rhetorical arguments, which are unfortunately often appealed to in the QNL debate, to empower readers to identify and reject such arguments. Second, logical problems in QNL proofs are described and exemplified by a discussion of the projection postulate problem. Third, experimental issues are described and exemplified by a discussion of the postselection problem. The paper concludes that QNL has not been proven and that locality cannot be excluded.

Weak measurement is studied for a quantum system which is in contact with a thermal reservoir, where pre- and postselection on the quantum system are also performed under the influence of the thermal reservoir. A single parameter which completely characterizes time dependence of statistical properties of weak measurement is derived by means of the projection operator method. The parameter consists of three parts. One is a part that determines the statistical properties when correlation between reservoir’s states before and after the weak measurement and initial correlation between the quantum system and the thermal reservoir are ignored. Another is a correction due to the correlation between the reservoir’s states. The other represents the effect of the initial correlation on the weak measurement. When the reduced time evolution of the quantum system is Markovian, the latter two contributions become negligible. The result shows how to calculate the parameter once a model of a quantum system and a thermal reservoir is given. Furthermore an explicit expression is given for the weak value of an observable influenced by a thermal reservoir.

Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schrodinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entangled states are sensitive to photon loss and a violation of Bell's inequality requires either that the losses are inherently small or that their effects have been minimized using linear optics techniques [M. Micuda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Somewhat surprisingly, the use of the fair sampling assumption is not required for a violation of Bell's inequality despite the use of postselection if the measurements are made in the correct order., 14 pages, 11 figures

Exploiting hyperentanglement of photon pairs, that is, simultaneous entanglement in multiple degrees of freedom(DOFs), increases the dimensionality of Hilbert spaces for quantum information processing. However, generation of hyperentangled photon pairs collinearlly, while produces high brightness, results in a smaller Hilbert space due to the two photons being in the same spatial mode. In this letter, we point out that one can recover the full dimensionality of such hyperentanglement through a simple interference set up, similar to the time-reversed Hong-Ou-Mandel (TR-HOM) process. Different from the standard TR-HOM, we point out a critical phase condition has to be satisfied in order to recover the hyperentanglement. We theoretically analyze the realization of this approach and discuss the feasibility of generating truly hyperentangled photon pairs. Our proposed approach does not require post-selection and hence enables efficient hyper-entangled photon pairs generation for high-dimensional quantum applications., 5 pages, 2 figures, During the preparation of this manuscript, we noticed a similar work posted recently on arXiv:1910.07684. This work is developed independently

Weak values are quantities accessed through quantum experiments involving weak measurements and post-selection. It has been shown that 'anomalous' weak values (those lying beyond the eigenvalue range of the corresponding operator) defy classical explanation in the sense of requiring contextuality [M. F. Pusey, Phys. Rev. Lett. 113, 200401, arXiv:1409.1535]. Here we elaborate on and extend that result in several directions. Firstly, the original theorem requires certain perfect correlations that can never be realised in any actual experiment. Hence, we provide new theorems that allow for a noise-robust experimental verification of contextuality from anomalous weak values, and compare with a recent experiment. Secondly, the original theorem connects the anomaly to contextuality only in the presence of a whole set of extra operational constraints. Here we clarify the debate surrounding anomalous weak values by showing that these conditions are tight -- if any one of them is dropped, the anomaly can be reproduced classically. Thirdly, whereas the original result required the real part of the weak value to be anomalous, we also give a version for any weak value with nonzero imaginary part. Finally, we show that similar results hold if the weak measurement is performed through qubit pointers, rather than the traditional continuous system. In summary, we provide inequalities for witnessing nonclassicality using experimentally realistic measurements of any anomalous weak value, and clarify what ingredients of the quantum experiment must be missing in any classical model that can reproduce the anomaly., 13+12 pages, 4+1 figures, revised abstract, improved presentation

One of the weaknesses of quantum optical state postselection schemes is the low success probability. Typically there is a trade-off between amplifier properties such as success probability and output state fidelity. However, here we present a state comparison amplifier for optical coherent states, which features an active measurement and feedforward mechanism to correct for errors made during the initial amplification. The simple and relatively low latency mechanism allows us to correct for a binary phase alphabet. We demonstrate a significant simultaneous improvement in the amplifier characteristic parameters: output state fidelity, correct state fraction, and success probability. This demonstrates that nondeterministic quantum amplification can be enhanced significantly by measurement and feedforward.

We report an alternative scheme for implementing generalized quantum measurements that does not require the usage of auxiliary system. Our method utilizes solely: (a) classical randomness and post-processing, (b) projective measurements on a relevant quantum system and (c) postselection on non-observing certain outcomes. The scheme implements arbitrary quantum measurement in dimension $d$ with the optimal success probability $1/d$. We apply our results to bound the relative power of projective and generalised measurements for unambiguous state discrimination. Finally, we test our scheme experimentally on IBM's quantum processor. Interestingly, due to noise involved in the implementation of entangling gates, the quality with which our scheme implements generalized qubit measurements outperforms the standard construction using the auxiliary system., 7 + 3 pages, 1 + 2 figures, 1 + 0 tables, comments and suggestions are welcome; v2: improved narrative in the main text, proofs of some technical details were moved to the appendix; v3: changed title, improved narrative in the main text, corrected typos in Appendix (matrix elements of tetrahedral measurement)

We discuss interferometric parameter estimation of the amplitude, instead of the phase, via weak value amplification. The considered weak interaction introduces modulation on the amplitude of the wave function; therefore, the two-party state experiences a nonunitary evolution. With the same pre- and postselection states as those of original weak value amplification, a much larger anomalous amplification factor can be attained. The shift in the intensity profile at the dark port and the signal-to-noise ratio for the parameter of interest get further amplified by the weak value, compared to phase-based weak value amplification. Although the nonunitary evolution introduces loss, more information about the parameter of interest can be extracted. Thus the weak value amplification is extended to measurement of amplitude and nonunitary processes. We also discuss possible applications of this idea for precisely measuring tiny rotations or enhancing the image contrast of transparent objects.

$\mathcal{PT}$-symmetric systems are one of the most interesting research fields in modern quantum physics, where various theoretical and experimental progress has been made. In our work, we experimentally demonstrate how to realize a general $\mathcal{PT}$-symmetric two-level operation in a quantum computation frame with a universal circuit model. It is based on enlarging the system with ancillary qubits and encoding the subsystem with the non-Hermitian Hamiltonian with postselection. Furthermore, we use the general formula to demonstrate one particular interesting issue, entanglement restoration induced by local $\mathcal{PT}$-symmetric operation in our four-qubit liquid nuclear magnetic resonance platform, and a theoretical explanation for the physical characteristics has been proposed. We also extend the protocol to the realization of an arbitrary two-level Hamiltonian evolution without a Hermitian restriction by an appropriate modification of the original quantum circuit. Our work lays the foundation for quantum simulation of the general $\mathcal{PT}$-symmetric problem in realistic quantum simulators, and the scheme can be extended to other quantum computation platforms.

The measurement of a quantum state wave function not only acts as a fundamental part in quantum physics but also plays an important role in developing practical quantum technologies. Conventional quantum state tomography has been widely used to estimate quantum wave functions, which usually requires complicated measurement techniques. The recent weak-value-based quantum measurement circumvents this resource issue but relies on an extra pointer space. Here, we theoretically propose and then experimentally demonstrate a direct and efficient measurement strategy based on a δ-quench probe: by quenching its complex probability amplitude one by one (δ quench) in the given basis, we can directly obtain the quantum wave function of a pure ensemble by projecting the quenched state onto a postselection state. We confirm its power by experimentally measuring photonic complex temporal wave functions. This new method is versatile and can find applications in quantum information science and engineering.

A solid state spin is an attractive system with which to realize an ultra-sensitive magnetic field sensor. A spin superposition state will acquire a phase induced by the target field, and we can estimate the field strength from this phase. Recent studies have aimed at improving sensitivity through the use of quantum error correction (QEC) to detect and correct any bit-flip errors that may occur during the sensing period. Here, we investigate the performance of a two-qubit sensor employing QEC and under the effect of energy relaxation. Surprisingly, we find that the standard QEC technique to detect and recover from an error does not improve the sensitivity compared with the single-qubit sensors. This is a consequence of the fact that the energy relaxation induces both a phase-flip and a bit-flip noise where the former noise cannot be distinguished from the relative phase induced from the target fields. However, we have found that we can improve the sensitivity if we adopt postselection to discard the state when error is detected. Even when quantum error detection is moderately noisy, and allowing for the cost of the postselection technique, we find that this two-qubit system shows an advantage in sensing over a single qubit in the same conditions.

Protecting quantum information from errors is essential for large-scale quantum computation. Quantum error correction (QEC) encodes information in entangled states of many qubits, and performs parity measurements to identify errors without destroying the encoded information. However, traditional QEC cannot handle leakage from the qubit computational space. Leakage affects leading experimental platforms, based on trapped ions and superconducting circuits, which use effective qubits within many-level physical systems. We investigate how two-transmon entangled states evolve under repeated parity measurements, and demonstrate the use of hidden Markov models to detect leakage using only the record of parity measurement outcomes required for QEC. We show the stabilization of Bell states over up to 26 parity measurements by mitigating leakage using postselection, and correcting qubit errors using Pauli-frame transformations. Our leakage identification method is computationally efficient and thus compatible with real-time leakage tracking and correction in larger quantum processors., 22 pages, 15 figures

Memory effects can be studied through a conditional past-future correlation, which measures departure with respect to a conditional past-future independence valid in a memoryless Markovian regime. In a quantum regime this property leads to an operational definition of quantum non-Markovianity based on three consecutive system measurement processes and postselection [Budini, Phys. Rev. Lett. 121, 240401 (2018)]. Here, we study the conditional past-future correlation for a qubit system coupled to different dephasing environments. Exact solutions are obtained for a quantum spin bath as well as for classically fluctuating random Hamiltonian models. The developing of memory effects and departures from Born-Markov or white-noise approximations are related to a measurement back action that changes the system dynamics between consecutive measurements. It is shown that this effect may develop even when the former system evolution is given by a time-independent Lindblad equation. This unusual non-Markovian case arises when the characteristic parameters of the dynamics become Lorentzian random distributed variables., Comment: 12 pages, 7 figures