Generation of nonclassical states in a large detuning cavity

A central question in information theory is to determine the maximum success probability that can be achieved in sending a fixed number of messages over a noisy channel. This was first studied in the pioneering work of Shannon who established a simple expression characterizing this quantity in the limit of multiple independent uses of the channel. Here we consider the general setting with only one use of the channel. We observe that the maximum success probability can be expressed as the maximum value of a submodular function. Using this connection, we establish the following results: 1. There is a simple greedy polynomial-time algorithm that computes a code achieving a (1-1/e)-approximation of the maximum success probability. Moreover, for this problem it is NP-hard to obtain an approximation ratio strictly better than (1-1/e). 2. Shared quantum entanglement between the sender and the receiver can increase the success probability by a factor of at most 1/(1-1/e). In addition, this factor is tight if one allows an arbitrary non-signaling box between the sender and the receiver. 3. We give tight bounds on the one-shot performance of the meta-converse of Polyanskiy-Poor-Verdu.

Channel simulation using coherence, which refers to realizing a target channel with coherent states and free operations, is a fundamental problem in the quantum resource theory of coherence. The limitations of the accuracy of deterministic channel simulation motivate us to consider the more general probabilistic framework. In this paper, we develop the framework for probabilistic channel simulation using coherence with free operations. When the chosen set of free operations is the maximally incoherent operations, we provide an efficiently computable semidefinite program (SDP) to calculate the maximal success probability and derive the analytic expression of success probability for some special cases. When the chosen set of free operations is the dephasing-covariant incoherent operations (DIO), we show that if the target channel is not a resource nonactivating channel then one cannot simulate it exactly both deterministically and probabilistically. The SDP for maximal success probability of simulating a channel by DIO is also given correspondingly. Published by the American Physical Society 2024

The main contributions of this paper are two-fold.Firstly, we present a novel direction in the cryptanalysis of the cryptographic hash function SHA-1. Our work builds on previous cryptanalytic efforts on SHA-1 based on combinations of local collisions. Due to dependencies, previous approaches used heuristic corrections when combining the success probabilities and message conditions of the individual local collisions. Although this leads to success probabilities that are seemingly sufficient for feasible collision attacks, this approach most often does not lead to the maximum success probability possible as desired. We introduce novel techniques that enable us to determine the theoretical maximum success probability for a given set of (dependent) local collisions, as well as the smallest set of message conditions that attains this probability. We apply our new techniques and present an implemented open-source near-collision attack on SHA-1 with a complexity equivalent to 257.5 SHA-1 compressions.Secondly, we present an identical-prefix collision attack and a chosen-prefix collision attack on SHA-1 with complexities equivalent to approximately 261 and 277.1 SHA-1 compressions, respectively.

Macroscopic cat states have been widely studied to illustrate fundamental principles of quantum physics as well as their applications in quantum information processing. In this paper, we propose a quantum speed-up method for the creation of cat states in a Kerr nonlinear resonator (KNR) via optimal adiabatic control. By simultaneously adiabatic tuning the cavity-field detuning and driving field strength, the width of the minimum energy gap between the target trajectory and non-adiabatic trajectory can be widened, which allows us to accelerate the evolution along the adiabatic path. Compared with the previous proposal, preparing cat states only by controlling two-photon pumping strength, our method can prepare the target state with a shorter time, a high-fidelity and a large non-classical volume. It is worth noting that the cat state prepared here is also robust against single-photon loss. Moreover, when we consider the KNR with a large initial detuning, our proposal will create a large-size cat state successfully. This proposal for preparing cat states can be implemented in superconducting quantum circuits, which provides a quantum state resource for quantum information encoding and fault-tolerant quantum computing.

The ability to distill quantum coherence is pivotal for optimizing the performance of quantum technologies; however, such a task cannot always be accomplished with certainty. Here we develop a general framework of probabilistic distillation of quantum coherence in a one-shot setting, establishing fundamental limitations for different classes of free operations. We first provide a geometric interpretation for the maximal success probability, showing that under maximally incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO) the problem can be simplified into efficiently computable semidefinite programs. Exploiting these results, we find that DIO and its subset of strictly incoherent operations have equal power in the probabilistic distillation of coherence from pure input states, while MIO are strictly stronger. We then prove a fundamental no-go result: Distilling coherence from any full-rank state is impossible even probabilistically. We further find that in some conditions the maximal success probability can vanish suddenly beyond a certain threshold in the distillation fidelity. Finally, we consider probabilistic coherence distillation assisted by a catalyst and demonstrate, with specific examples, its superiority to the unassisted and deterministic cases.

Assume that the probability of success is unimodal as a function of dose. Take the response to be binary and the possible treatment space to be a lattice. The Optimizing Up-and-Down Design allocates treatments to pairs of subjects in a way that causes the treatment distribution to cluster around the treatment with maximum success probability. This procedure is constructed to use accruing information to limit the number of patients that are exposed to doses with high probabilities of failure. The Optimizing Up-and-Down Design is motivated by Kiefer and Wolfowitz’s stochastic approximation procedure. In this paper, we compare its performance to stochastic approximation. As an estimator of the best dose, simulation studies demonstrate that the mode of the empirical treatment distribution using the Optimizing Up-and-Down Design converges faster than does the usual estimator using stochastic approximation.Keywordsconstant gain stochastic algorithmMarkov chainsphase I/II clinical trialrandom walk designsstationary treatment distributionstochastic approximation

A cat-state is a superposition of two coherent states with amplitudes\n$\\alpha_{0}$ and $-\\alpha_{0}$. Recent experiments create cat states in a\nmicrowave cavity field using superconducting circuits. As with degenerate\nparametric oscillation (DPO) in an adiabatic and highly nonlinear limit, the\nstates are formed in a signal cavity mode via a two-photon dissipative process\ninduced by the down conversion of a pump field to generate pairs of signal\nphotons. The damping of the signal and the presence of thermal fluctuations\nrapidly decoheres the state, and the effect on the dynamics is to either\ndestroy the possibility of a cat state, or else to sharply reduce the lifetime\nand size of the cat-states that can be formed. In this paper, we study the\neffect on both the DPO and microwave systems of a squeezed reservoir coupled to\nthe cavity. While the threshold nonlinearity is not altered, we show that the\nuse of squeezed states significantly lengthens the lifetime of the cat states.\nThis improves the feasibility of generating cat states of large amplitude and\nwith a greater degree of quantum macroscopic coherence, which is necessary for\nmany quantum technology applications. Using current experimental parameters for\nthe microwave set-up, which requires a modified Hamiltonian, we further\ndemonstrate how squeezed states enhance the quality of the cat states that\ncould be formed in this regime. Squeezing also combats the significant\ndecoherence due to thermal noise, which is relevant for microwave fields at\nfinite temperature. By modeling a thermal squeezed reservoir, we show that the\nthermal decoherence of the dynamical cat states can be inhibited by a careful\ncontrol of the squeezing of the reservoir. To signify the quality of the cat\nstate, we consider different signatures including fringes and negativity, and\nthe $C_{l_{1}}$ measure of quantum coherence.\n

We present some different hyperentanglement concentration protocols (hyper-ECPs) for nonlocal N-photon systems in partially polarization-spatial hyperentangled states with known parameters, resorting to linear optical elements only, including those for hyperentangled Greenberger---Horne---Zeilinger-class states and the ones for hyperentangled cluster-class states. Our hyper-ECPs have some interesting features. First, they require only one copy of nonlocal N-photon systems and do not resort to ancillary photons. Second, they work with linear optical elements, neither Bell-state measurement nor two-qubit entangling gates. Third, they have the maximal success probability with only a round of entanglement concentration, not repeating the concentration process some times. Fourth, they resort to some polarizing beam splitters and wave plates, not unbalanced beam splitters, which make them more convenient in experiment.

We propose an optimal entanglement concentration protocol (ECP) for nonlocal \(N\)-electron systems in a partially entangled Greenberger–Horne–Zeilinger (GHZ) pure state, resorting to charge detection and the projection measurement on an additional electron. For each nonlocal \(N\)-electron system in a partially entangled GHZ state, one party in quantum communication, say Alice first entangles it with an additional electron, and then, she projects the additional electron into an orthogonal basis for dividing the \(N\)-electron systems into two groups. In the first group, the \(N\) parties obtain a subset of \(N\)-electron systems in a maximally entangled state directly. In the second group, they obtain some less-entangled \(N\)-electron systems which are the resource for the entanglement concentration in the next round. By iterating the entanglement concentration process several times, the present ECP has the maximal success probability, the theoretical limit of an ECP as it just equals to the entanglement of the partially entangled state, far higher than others. Moreover, this ECP for an \(N\)-electron GHZ-type state requires only one additional electron, not two or more, and it does not resort to a collective unitary evolution, far different from others, which may decrease the difficulty for its implementation in experiment. When it is used for an \(N\)-electron W-type state, \(N-1\) additional electrons are required only.

We propose an optimal nonlocal entanglement concentration protocol (ECP) for\nmulti-photon systems in a partially entangled pure state, resorting to the\nprojection measurement on an additional photon. One party in quantum\ncommunication first performs a parity-check measurement on her photon in an\nN-photon system and an additional photon, and then she projects the additional\nphoton into an orthogonal Hilbert space for dividing the original $N$-photon\nsystems into two groups. In the first group, the N parties will obtain a subset\nof $N$-photon systems in a maximally entangled state. In the second group, they\nwill obtain some less-entangled N-photon systems which are the resource for the\nentanglement concentration in the next round. By iterating the entanglement\nconcentration process several times, the present ECP has the maximal success\nprobability which is just equivalent to the entanglement of the partially\nentangled state. That is, this ECP is an optimal one.\n

Hyperentanglement has attracted much attention due to its fascinating applications in quantum communication. However, it is impossible to purify a pair of photon systems in a mixed hyperentangled state with errors in two degrees of freedom using linear optical elements only, far different from all the existing entanglement purification protocols in a degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of purifying a spatial-polarization mixed hyperentangled Bell state with the errors in both the spatial-mode and polarization DOFs, resorting to the nonlinear optics of a nitrogen-vacancy (NV) center in a diamond embedded in a photonic crystal cavity coupled to a waveguide. We present the first hyperentanglement purification protocol for purifying a pair of two-photon systems in a mixed hyperentangled Bell state with the errors in two DOFs. We also propose an efficient hyperentanglement concentration protocol for a partially hyperentangled Bell pure state, which has the maximal success probability in principle. These two protocols are useful in long-distance quantum communication with hyperentanglement.

In this work, the authors propose a novel technique to extend the scope of cognitive radio (CR) networks to multiple source–destination pairs. To accomplish this, a simplified feasible path set is formed and then three types of criteria or methods are employed to reach a solution for the best path for each pair. This set is defined by non‐intersecting paths which do not share any relay nodes. This not only solves the problem at hand but also greatly reduces the complexity which leads to a fast solution. The first method uses the maximum probability of success as a means for selecting the best path. In the second method, a fast and simple technique is used by choosing the minimum number of overall hops for path selection. The element with the minimum overall transmission time is selected for data transmission in the third technique. Finally, the proposed methods are compared through simulation to a unicast single user case in terms of throughput and packet delivery rate. The simulation results show that the first method has the best performance while the second method is slightly worse but faster.

We consider the effect of a thermal bath on quantum correlations induced by the gravitational interaction in the weak field limit between two massive cat states, called gravitational cat (gravcat) states. The main goal of this paper is to provide a good understanding of the effects of temperature and several parameters in the entanglement (measured by the concurrence) and quantum coherence (measured by the l1-norm that is defined from the minimal distance between the quantum state and the set of incoherent states) which are derived from the thermal quantum density operator. Our results show that the thermal concurrence and l1-norm can be significantly optimized by increasing the masses or decreasing the distance between them. We investigate and discuss the behavior of these quantities under temperature variations in different regimes, including some that are expected to be experimentally feasible in the future. In particular, we observe that thermal fluctuations raise non-entangled quantum correlations when entanglement suddenly drops.

This paper has been motivated by a recent paper by Dey [Phys. Rev. D 91, 044024 (2015)] on the known Arik-Coon $q$ oscillator. We construct $q$ coherent, even and odd $q$-cat states in Fock representation for the Biedenharn-Macfarlane $q$ oscillator with $q>1$ and study their nonclassical properties. The $q$-coherent states minimize the Heisenberg uncertainty relation between the generalized position and momentum operators as well as the $x$ and $y$ components of a $q$-deformed $\text{su}(1,1)$ algebra in the Schwinger boson representation. The latter is also minimized by the even and odd $q$-cat states. We show that, contrary to the undeformed harmonic oscillator, the squeezing effect in both position and momentum operators can be exhibited by odd $q$-cat states. It is also violated by even $q$-cat states. Furthermore, it is shown that the antibunching effect and sub-Poissonian or super-Poissonian statistics can simultaneously appear by each of the even or odd $q$-cat states. Finally, a unitary Fock representation of the $q$-deformed $\text{su}(1,1)$ algebra is obtained by the $q$-deformed Bargmann-Fock realization.

Spin cat states are superpositions of two or more coherent spin states (CSSs) that are distinctly separated over the Bloch sphere. Additionally, the nuclei with angular momenta greater than 1/2 possess a quadrupolar charge distribution. At the intersection of these two phenomena, we devise a simple scheme for generating various types of nuclear-spin cat states. The native biaxial electric quadrupole interaction that is readily available in strained solid-state systems plays a key role here. However, the fact that built-in strain cannot be switched off poses a challenge for the stabilization of target cat states once they are prepared. We remedy this by abruptly diverting via a single rotation pulse the state evolution to the neighborhood of the fixed points of the underlying classical Hamiltonian flow. Optimal process parameters are obtained as a function of electric field gradient biaxiality and nuclear-spin angular momentum. The overall procedure is seen to be robust under 5% deviations from optimal values. We show that higher-level cat states with four superposed CSS can also be formed using three rotation pulses. Finally, for open systems subject to decoherence we extract the scaling of cat-state fidelity damping with respect to the spin quantum number. This reveals rates greater than the dephasing of individual CSSs. Yet, our results affirm that these cat states can preserve their fidelities for practically useful durations under the currently attainable decoherence levels.