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Knill, Laflamme, and Milburn showed that linear optics techniques could be used to implement a nonlinear sign gate. They also showed that two of their nonlinear sign gates could be combined to implement a controlled-phase gate, which has a number of practical applications. Here we describe an alternative implementation of a controlled-phase gate for a single-rail target qubit that only requires the use of a single nonlinear sign gate. This gives a much higher average probability of success when the required ancilla photons are generated using heralding techniques. This implementation of a controlled-phase gate destroys the control qubit, which is acceptable in a number of applications where the control qubit would have been destroyed in any event, such as in a postselection process.

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

Quantum computing potentially offers exponential speed-ups over classical computing for certain tasks. A central, outstanding challenge to making quantum computing practical is to achieve fault tolerance, meaning that computations of any length or size can be realised in the presence of noise. The Gottesman-Kitaev-Preskill code is a promising approach towards fault-tolerant quantum computing, encoding logical qubits into grid states of harmonic oscillators. However, for the code to be fault tolerant, the quality of the grid states has to be extremely high. Approximate grid states have recently been realized experimentally, but their quality is still insufficient for fault tolerance. Current implementable protocols for generating grid states rely on measurements of ancillary qubits combined with either postselection or feed forward. Implementing such measurements take up significant time during which the states decohere, thus limiting their quality. Here we propose a measurement-free preparation protocol which deterministically prepares arbitrary logical grid states with a rectangular or hexagonal lattice. The protocol can be readily implemented in trapped-ion or superconducting-circuit platforms to generate high-quality grid states using only a few interactions, even with the noise levels found in current systems., Comment: 13 pages, 7 figures

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.

We propose schemes for preparing W and GHZ photonic states entangled in polarization via quantum walks, where the trajectory exchanging of identical photons plus postselection induces the coupling between their polarization degrees of freedom. Being different from the polarization beam splitter-based approach, the indistinguishability of identical photons provides an alternative for coupling photons, which is more phase stable and may induce richer actions than the traditional polarization beam splitter on input photons. Our schemes demonstrate that this new coupling mechanism for photons is originated from the fact that trajectory-exchanging operation plus postselection can extract entangled states from the initially product states, and this new coupling mechanism may find considerable potential applications in both quantum communication and quantum computation.

A conditional average of an observable is considered for a quantum system, where measurement on a system is performed between an initial preparation and a postselection. It is shown that when the effect of measurement performed on a system can be described only in terms of eigenprojectors of a measured observable, the conditional average is represented by a mixture of the strong and weak values of the observable. Furthermore, a measurement process is constructed which provides the conditional average from measurement outcomes of pointer observables of an apparatus. In particular, when a qubit system is considered, the measurement apparatus consists of a lossless beam splitter, a single-qubit unitary gate and two controlled NOT gates.

We present two nonlocal entanglement concentration protocols (ECPs) to distill a subset of N-photon systems in a Greenberger-Horne-Zeilinger (GHZ) state or a W state from a set of photon systems in a partially entangled GHZ-like pure state or a less-entangled W-like state with known parameter, respectively. Our ECPs have some advantages. First, our ECPs work in a heralded way with linear-optical elements only, without the postselection based on nonlinear optics, far different from the previous ECPs. Second, they require only a copy of the less-entangled photon system in each round of the entanglement concentration process, not two copies, which decreases the difficulty of their implementation in experiment largely. Third, our ECPs avoid checking the photon number in the output modes of linear-optical elements with the sophisticated single-photon detectors. Moreover, all parties can operate the process for concentration simultaneously and independently, which leads to flexible operations and improves the performance greatly in experiment. These advantages make our ECPs useful in practical applications in long-distance quantum communication network.

We propose a simple implementation scheme of quantum delayed-choice experiment in linear optical system without initial entanglement resource. By choosing different detecting devices, one can selectively observe the photon’s different behaviors after the photon has been passed the Mach-Zehnder interferometer. The scheme shows that the photon’s wave behavior and particle behavior can be observed with a single experimental setup by postselection, that is, the photon can show the superposition behavior of wave and particle. Especially, we compare the wave-particle superposition behavior and the wave-particle mixture behavior in detail, and find the quantum interference effect between wave and particle behavior, which may be helpful to reveal the nature of photonessentially.

We introduce a modular-value two-qubit gate and explore its advantages in experimentally-limited situations. The gate is defined such that the final state of a target qubit is fully controlled by a pre- and post-selection procedure in a control qubit given an (imperfect or technically limited) intermediate conditional qubit-qubit interaction. As an example of the gate and its benefit, we make the connection to a postselected cross phase modulation scenario when a undesired absorption is present. Probabilistic amplification of a small cross phase while mitigating relative absorption is possible, and a complementary behaviour between phase and amplitude emerges.

We study the entanglement dynamics for two coupled multi-excitation cavity fields, each independently interacting with a two-level atom. We find that even when the atom-field system is initially not entangled, the fields can become heavily entangled through postselecting of the atomic state. The field entanglement entropy is dependent on the total excitation number but independent of the coherent photon hopping strength.

We examine some variants of computation with closed timelike curves (CTCs), where various restrictions are imposed on the memory of the computer, and the information carrying capacity and range of the CTC. We give full characterizations of the classes of languages decided by polynomial time probabilistic and quantum computers that can send a single classical bit to their own past. We show that, given a time machine with constant negative delay, one can implement CTC-based computations without the need to know about the runtime beforehand. Chaining multiple instances of such fixed-length CTCs, the power of postselection can be endowed to deterministic computers, all languages in $$\mathsf{NP} \cup \mathsf{coNP}$$ can be decided with no error in worst-case polynomial time, and all Turing-decidable languages can be decided in constant expected time. We provide proofs of the following facts for weaker models: Augmenting probabilistic computers with a single CTC leads to an improvement in language recognition power. Quantum computers under these restrictions are more powerful than their classical counterparts. Some deterministic models assisted with multiple CTCs are more powerful than those with a single CTC.

We propose a linear optical protocol for teleporting a multi(W)-photon Greenberger-Horne-Zeilinger (GHZ) polarization-entangled state from a sender to a receiver under control of a number of controllers in terms of optical elements. We show that the protocol can be successfully realized with a certain probability. This protocol has the advantage of transmitting much less particles and classical information for teleporting the W-photon GHZ polarization-state than others, and the protocol is based on linear optical elements and postselection strategy, which are feasible with existing experimental technology.

A major hurdle in building a quantum computer is overcoming noise, since quantum superpositions are fragile. Developed over the last couple of years, schemes for achieving fault tolerance based on error detection, rather than error correction, appear to tolerate as much as 3–6% noise per gate—an order of magnitude higher than previous procedures. However, proof techniques could not show that these promising fault-tolerance schemes tolerated any noise at all; the distribution of errors in the quantum state has correlations that conceivably could grow out of control. With an analysis based on decomposing complicated probability distributions into mixtures of simpler ones, we rigorously prove the existence of constant tolerable noise rates (“noise thresholds”) for error-detection-based schemes. Numerical calculations indicate that the actual noise threshold this method yields is lower-bounded by 0.1% noise per gate.

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