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Quantum algorithms can greatly speed up computation in solving some classical problems, while the computational power of quantum computers should also be restricted by laws of physics. Due to quantum time-energy uncertainty relation, there is a lower limit of the evolution time for a given quantum operation, and therefore the time complexity must be considered when the number of serial quantum operations is particularly large. When the key length is about at the level of KB (encryption and decryption can be completed in a few minutes by using standard programs), it will take at least 50-100 years for NTC (Neighbor-only, Two-qubit gate, Concurrent) architecture ion-trap quantum computers to execute Shor’s algorithm. For NTC architecture superconducting quantum computers with a code distance 27 for error-correcting, when the key length increased to 16 KB, the cracking time will also increase to 100 years that far exceeds the coherence time. This shows the robustness of the updated RSA against practical quantum computing attacks.

To improve the maximal transmission distance and the maximal error rate tolerance, we apply the advantage distillation technology to analyze security of the practical decoy-sate quantum key distribution system. Based on the practical experimental parameters, the device-dependent quantum key distribution protocols and the measurement-device-independent quantum key distribution protocols have been respectively analyzed, and our analysis results demonstrate that the advantage distillation technology can significantly improve the performance of different quantum key distribution protocols. In the four-state and six-state device-dependent quantum key distribution protocols, we prove that the maximal transmission distance can be improved from 142 km to 180 km and from 146 km to 187 km respectively. In the four-state and six-state measurement-device-independent quantum key distribution protocols, we prove that the maximal transmission distance can be improved from 195 km to 273 km and from 200 km to 282 km respectively. More interestingly, the advantage distillation technology does not need to change the hardware devices about the quantum step, thus it can be conveniently to be applied in various practical quantum key distribution systems.

Recently, Ye et al. (Int. J. Theor. Phys. 56, 1517–1529, 2017) proposed a quantum private comparison (QPC) protocol based on five-qubit entanglement state. Two parties can verify that their secret information is equal or not with the help of the semi-honest third party (TP). However, in this paper we will point out the Ye et al.’s initial protocol is not safe under a special participant attack. That is a malicious participant can get the other party’s secret input information illegally under the forgery attack. Furthermore, we give two possible improvement protocols, which can perform this protocol secure against this kind of attack.

Quantum machine learning based on quantum algorithms may achieve an exponential speedup over classical algorithms in dealing with some problems such as clustering. In this paper, we use the method of training the lower bound of the average log likelihood function on the quantum Boltzmann machine (QBM) to recognize the handwritten number datasets and compare the training results with classical models. We find that, when the QBM is semi-restricted, the training results get better with fewer computing resources. This shows that it is necessary to design a targeted algorithm to speed up computation and save resources.

The security of the perfect quantum key distribution protocol can be guaranteed by applying the fundamental laws of quantum mechanics, but the practical quantum key distribution system may be attacked by utilizing imperfect state preparation and measurement devices. In this work, we analyze the security of the practical quantum key distribution system with weak-randomness basis selection, where the basis selection may be partly controlled by the eavesdropper due to the imperfect quantum devices. We propose the parameter $\ensuremath{\epsilon}$ to quantify the deviation value between the practical basis selection probability and the perfect basis selection probability, and the secret key rate of the practical quantum key distribution system is obtained under different $\ensuremath{\epsilon}$ values. By applying the practical experimental parameters, the analysis result demonstrates that the maximal transmission distance will be reduced from 142 to 139 km if $\ensuremath{\epsilon}\ensuremath{\le}0.1$, but no secret key can be generated in the case of $\ensuremath{\epsilon}\ensuremath{\ge}0.34$.

Information is physical, it cannot simply disappear in any physical process. This basic principle of information science constitutes one of the most important elements for the very foundation to our daily life and to our understanding of the universe. However, this fundamental principle is challenged by the physics of black holes. Classic black holes was viewed as only capable of absorbing but not emitting particles, so black holes look completely black. All matter that falls into the black hole will be stored in the black hole forever, and the information carry by these matter will always be stored in the black hole. Although the information in the black hole cannot be seen, we know that the information has not been lost. After considering the quantum effect, the black hole is no longer completely black. By considering quantum effect of black hole, Hawking shows that black holes emit thermal radiation like ordinary hot bodies. It is well known that there is no correlation between thermal radiation, therefore no information can be carried out by Hawking radiation. With the black hole evaporating, the information inside the black hole will gradually be lost. However, the unitary property of quantum mechanics indicates that information is conserved, therefore, the loss of black hole information conflicts with the unitary of quantum mechanics, this is the so-called mystery of black hole information loss. This problem reflects the conflict between gravitational theory and quantum theory, and attracts wide attention of scientists. Whether there is a correlation between Hawking radiation is the key to solving the problem of black hole information loss. Without considering the self-gravitating of the radiating particles in Hawkings initial calculations, he obtained the results of the pure thermal spectrum, so his result is inconsistent with energy conservation. Kraus and Wilczek show that the thermal spectrum may be corrected if the self-gravitating of the radiant particles is taken into account, thus Hawking radiations must be correlated, and their correlations can carry away information encoded within. This paper firstly introduced the black hole radiation non-thermal spectrum obtained by Parikh and Wilczek, who use the method of quantum tunneling after counting the self-gravitating of radiation particles; then it also introduced the research of Zhang et al., which proves that the entropy is conservation during black hole radiation process based on the non-thermal spectrum obtained by Parikh and Wilczek; and finally we proposed a possible physical mechanism for the correlation between black hole radiation, which shows that the gravitational correlation between the black hole radiation particles can carry information, so that the information is conserved during the black hole radiation process. The series of research on black hole information loss problem reveals that information conservation remains true when gravitational correlations among Hawking radiations are properly taken into account. Information conservation principle thus states Hawking radiation is unitary, which shows that the dynamics of a black hole obey the laws of quantum mechanics. Since a black hole is a result of general relativity, the unitarity of a black hole definitely indicates the possibility of a unified gravity and quantum mechanics.

Quantum public key encryption system provides information confidentiality using quantum mechanics. This paper presents a quantum public key cryptosystem (QPKC) based on the Bell states. By Holevo’s theorem, the presented scheme provides the security of the secret key using one-wayness during the QPKC. While the QPKC scheme is information theoretic security under chosen plaintext attack (CPA). Finally some important features of presented QPKC scheme can be compared with other QPKC scheme.

Classical public key cryptosystems (P K C), such as R S A, E I G a m a l, E C C, are no longer secure in quantum algorithms, and quantum cryptography has become a novel research topic. In this paper we present a quantum asymmetrical cryptosystem i.e. quantum public key cryptosystem (Q P K C) based on the Bell states. In particular, in the proposed QPKC the public key are given by the first n particles of Bell states and generalized Pauli operations. The corresponding secret key are the last n particles of Bell states and the inverse of generalized Pauli operations. The proposed QPKC encrypts the message using a public key and decrypts the ciphertext using a private key. By H o l e v o ′ s theorem, we proved the security of the secret key and messages during the QPKC.

Quantum key distribution protocol requires true random numbers to prepare and measure quantum states, but the randomness may be weakened by applying the imperfect input random numbers or imperfect quantum devices. In this work, we propose the randomness attack model in the practical quantum key distribution system, and we analyze the final secret key rate under the randomness attack. The security analysis result demonstrates that the imperfect randomness can be amplified by considering the signal loss, thus the quantum key distribution system may be attacked even if the randomness has very small part of imperfection. Combining the practical experimental parameters with the small nonrandom probability parameters $0.1%$ and $1%$, we prove that the maximal transmission distance will be sharply reduced from 140 km to 60 and 12 km, respectively.

In this paper, we study the changes of quantum effects of a growing universe by using Wheeler-DeWitt equation (WDWE) together with de Broglie-Bohm quantum trajectory approach. From WDWE, we obtain the quantum modified Friedmann equations which have additional terms called quantum potential compared to standard Friedmann equations. The quantum potential governs the behavior of the early universe, providing energy for inflation, while it decreases rapidly as the universe grows. The quantum potential of the grown-up universe is much smaller than that required for accelerating expansion. This indicates that quantum effects of our universe cannot be treated as a candidate for dark energy., Comment: Any comments are welcome!

It seems there is a large gap between quantum cloning and classical duplication since quantum mechanics forbid perfect copies of unknown quantum states. In this paper, we prove that a classical duplication process can be realized by using a universal quantum cloning machine (QCM). A classical bit is encoded not on a single quantum state, but on a large number of single identical quantum states. Errors are inevitable when copying these identical quantum states due to the quantum no-cloning theorem. When a small part of errors are ignored, i.e., errors as the minority are automatically corrected by the majority, the fidelity of duplicated copies of classical information will approach unity infinitely. In this way, the classical bits can be duplicated precisely with a universal QCM, which presents a natural transition from quantum cloning to classical duplication. The implement of classical duplication by using QCM shines new lights on the universality of quantum mechanics.

We propose a scheme to enhance the fidelity of a symmetric quantum cloning machine via weak measurements. By adjusting the intensity of the weak measurement parameter $p$, we obtain copies of initial states with different values of fidelity. Choosing a proper value of $p$, we can obtain perfect copies. In this paper, we focus on $1\ensuremath{-}2$ quantum cloning for two nonorthogonal states. Sets containing more than two linear independent states are also briefly discussed. Due to the probabilistic nature of weak measurements, we obtain high-fidelity copies probabilistically. If the weak measurement is a success, we do subsequent operations to obtain high-fidelity copies; otherwise, the cloning process fails and we quit. From this perspective, the scheme we propose is economical for saving quantum resources and time. Our scheme may be very useful in quantum information processing.

The back reactions of Hawking radiation allow nontrivial correlations between consecutive Hawking quanta, which gives a possible way of resolving the paradox of black hole information loss known as the hidden messenger method. In a recent work of Ma {\it et al} [arXiv:1711.10704], this method is enhanced by a general derivation using small deviations of the states of Hawking quanta off canonical typicality. In this paper, we use this typicality argument to study the effects of generic back reactions on the quantum geometries described by spin network states, and discuss the viability of entropy conservation in loop quantum gravity. We find that such back reactions lead to small area deformations of quantum geometries including those of quantum black holes. This shows that the hidden-messenger method is still viable in loop quantum gravity, which is a first step towards resolving the paradox of black hole information loss in quantum gravity., Comment: 13 pages

We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions including the exponential expansion solutions of the scalar factor $a$ for the bubble. We show that exponential expansion of the bubble continues with a short period (about a Planck time $t_p$), no matter whether the bubble is closed, flat or open. The exponential expansion ends spontaneously when the bubble becomes large, i.e., the scalar factor $a$ of the bubble approaches a Planck length $l_p$. We show that it is quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe., Final version

We study the Hawking radiation of black holes by considering the canonical typicality. For the universe consisting of black holes and their outer part, we directly obtain a non-thermal radiation spectrum of an arbitrary black hole from its entropy, which only depends on a few external qualities (known as hairs), such as mass, charge, and angular momentum. Our result shows that the spectrum of the non-thermal radiation is independent of the detailed quantum tunneling dynamics across black hole horizon. We prove that the black hole information paradox is naturally resolved by taking account the correlation between black hole and its radiation in our approach., 5 pages, 1 figure, pulished on Europhysics Letters, comments are welcomes

Finding the complete quantum gravity theory is the most important and frontal subject in theoretical physics, and the black hole thermodynamics and using quantum interferometer to test gravitational effect are considered as two significant “probing fields” for the coming quantum gravity theory. The two fields represent two respective ends of modern research into quantum gravity: one introduces quantum mechanics into a gravitational system, while the other attempts to incorporate gravity with a quantum system through observing the evolution of the quantum system in the gravitational background. For the former, the unitarity of quantum mechanics will meet a great challenge, while for the latter, the equivalence principle of general relativity will be probed more and more rigorously in experiments done with microscopical particles. Now the Hawking radiation of black holes has been found in the atomic, molecular and optic experiments, but its mechanism is unclear. In particular, whether the phenomenon could be explained within the current theories or needs the new physics is also unclear. However, it is very significant to get insight into some possible elements about quantum gravity through these experiments. On the other hand, the gravitational effects can be measured by quantum systems, which provides not only the convenience to study the influence of gravitational effects on quantum systems, but also a possible entrance to study the incorporation of quantum mechanics and gravity. In the review, we will discuss all these based on the interdiscipline of atom-molecule-optics and gravity, and our recent works related to the incorporation of quantum mechanics and gravity.

Information about the collapsed matter in black holes will be lost with thermal Hawking radiations. Recently, it has been proved that information is conserved in Hawking radiation from stationary black holes with the nonthermal spectrum discovered by Parikh and Wilczek. In this paper, we study the information loss problem for spherically symmetric nonstationary black holes. We prove that information can be recovered even with Hawking radiations from dynamical horizons.

Recently, He proposed a novel quantum private comparison protocol without a third party (G. P. He, Int. J. Quantum Inf. 15(2) (2016) 1750014). This paper points out that two security loopholes in He’s protocol are existent. And a new QPC protocol which can avoid these loopholes is proposed without the help of a third party in this paper.

When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by E. Verlinde's paper, we first calculate the entropy change of a system when gravity does positive work on this system. Based on the concept of gravitational correlation entropy, we prove that the entropy of a Schwarzschild black hole originates from the gravitational correlations between the interior matters of the black hole. By analyzing the gravitational correlation entropies in the process of Hawking radiation in a general context, we prove that the reduced entropy of a black hole is exactly carried away by the radiation and the gravitational correlations between these radiating particles, and the entropy or information is conserved at all times during Hawking radiation. Finally, we attempt to give a unified description of the non-extensive black-hole entropy and the extensive entropy of ordinary matter., 8 pages,1 figures

Recently, Lucamarini et al. proposed the device-independent entanglement-based Bennett 1992 protocol [Phys. Rev. A 86, 032325 (2012)]. By exploiting the results in device-independent quantum key distribution with the Clauser-Horne-Shimony-Holt inequality, they claimed the security of their protocol. We will show, however, the way of encoding and the process for the latent eavesdropper to obtain the illegal information are different in these two protocols. Thus the security of their protocol cannot rely on Bell's theorem only.

Shock wave focusing by an ellipsoidal reflector can produce higher pressure in the focal region. The focusing process of shock wave was studied by theory analyses and numerical results. Base on the experimental observation the shock wave source is equivalent to the explosion of an underwater explosive. A finite element model was set up to investigate the shock wave focusing behaviors. Both the pressure-time history and the peak pressure along the axial position were presented. The shock wave focusing process was shown. The interactions of waves in the focal region are shown. A modified EOS of water was applied, which can be used to analyze the negative pressure observed; the numerical results based on the modified EOS agree well with the experimental data.

The passive decoy state quantum key distribution (QKD) protocol is practically interesting for its longer transmission distance and convenience on the decoy states choice. In this paper, its unconditional security with finite length of the key bits is guaranteed. And its performances under this practical condition are demonstrated.

In this paper, we consider the controllably secure quantum key distribution (QKD) with coherent source, i.e., the practical decoy state QKD with finite resource is studied within the scope of some controllable security parameters. Our simulation shows the controllably secure QKD is more resource-consuming compared with the practical decoy QKD with relatively statistical fluctuation. However, further numerically solutions show that both protocols agree well with each other in the asymptotic limit, where the resource is large enough but not infinite. Our work shows the dark counts will contribute apparently to the transmission distance when communication distance approaches to the asymptotic limit. It also shows that both the secure transmission distance and the rate of the secure final key can be increased apparently when the security estimation parameters are not fixed but numerically optimized.

It seems that quantum key distribution (QKD) may be completely insecure when the message sender Alice always encodes her key bits in a fixed basis. In this paper, we present a QKD protocol with classical Alice, i.e. Alice always encodes her key bit in the {|0〉,|1〉} basis (we call it classical {0,1} basis) and the eavesdropper Eve knows this fact. We prove that our protocol is completely robust against any eavesdropping attack and present the amount of tolerable noise against Eve's individual attack. Next, we present a QKD protocol to demonstrate that secure key bits can be distributed even if neither Alice nor Bob has quantum capacities, and extend this idea to a QKD network protocol with numerous parties who have only classical capacities. Finally, we discuss that quantum is necessary in QKD for security reasons, but both Alice and Bob may be classical.

We show that the first law of the black hole thermodynamics can lead to the tunneling probability through the quantum horizon by calculating the change of entropy with the quantum gravity correction and the change of surface gravity is presented clearly in the calculation. The method is also applicable to the general situation which is independent on the form of black hole entropy and this verifies the connection of black hole tunneling with thermodynamics further. In the end we discuss the crucial role of the relation between the radiation temperature and surface gravity in this derivation., To appear in Phys Lett B

Because of the monogamy of entanglement, the measurement-device-independent quantum key distribution is immune to the side-information leaking of the measurement devices. When the correlated measurement outcomes are generated from the dark counts, no entanglement is actually obtained. However, secure key bits can still be proven to be generated from these measurement outcomes. Especially, we will give numerical studies on the contributions of dark counts to the key generation rate in practical decoy state MDI-QKD where a signal source, a weaker decoy source and a vacuum decoy source are used by either legitimate key distributer.

a b s t r a c t In this paper, we study the physical meaning of the wavefunction of the universe. With the continuity equation derived from the Wheeler-DeWitt (WDW) equation in the minisuperspace model, we show that the quantity ρ(a) =| ψ(a)| 2 for the universe is inversely proportional to the Hubble parameter of the universe. Thus, ρ(a) represents the probability density of the universe staying in the state a during its evolution, which we call the dynamical interpretation of the wavefunction of the universe. We demonstrate that the dynamical interpretation can predict the evolution laws of the universe in the classical limit as those given by the Friedmann equation. Furthermore, we show that the value of the operator ordering factor p in the WDW equation can be determined to be p =− 2.

Recently, it was proposed that a small true vacuum universe can inflate spontaneously, in principle. Furthermore, there should be matter creation in vacuum inflation due to quantum fluctuations, and the matter created will influence the inflation simultaneously. In this paper, scalar and tensor perturbations in this model are analyzed and confronted with recent observations. These perturbations are derived and expressed with Hubble flow-functions. By comparing our calculations with experimental results, we can determine all the parameters in this model. Finally, with the determined parameters, we compute the evolution of the matter density and show that the matter produced in inflation roughly fits the observations at present.

An interesting idea is that the universe could be spontaneously created from nothing, but no rigorous proof has been given. In this paper, we present such a proof based on the analytic solutions of the Wheeler-DeWitt equation (WDWE). Explicit solutions of the WDWE for the special operator ordering factor p=-2 (or 4) show that, once a small true vacuum bubble is created by quantum fluctuations of the metastable false vacuum, it can expand exponentially no matter whether the bubble is closed, flat or open. The exponential expansion will end when the bubble becomes large and thus the early universe appears. With the de Broglie-Bohm quantum trajectory theory, we show explicitly that it is the quantum potential that plays the role of the cosmological constant and provides the power for the exponential expansion of the true vacuum bubble. So it is clear that the birth of the early universe completely depends on the quantum nature of the theory., The problem of singularity can be avoided naturally as the universe can be spontaneously created from nothing

Since the discovery of Hawking radiation, its consistency with quantum theory has been widely questioned. In the widely described picture, irrespective of what initial state a black hole starts with before collapsing, it eventually evolves into a thermal state of Hawking radiations after the black hole is exhausted. This scenario violates the principle of unitarity as required for quantum mechanics and leads to the acclaimed "information loss paradox". This paradox has become an obstacle or a reversed touchstone for any possible theory to unify the gravity and quantum mechanics. Based on the results from Hawking radiation as tunneling, we recently show that Hawking radiations can carry off all information about the collapsed matter in a black hole. After discovering the existence of information-carrying correlation, we show in great detail that entropy is conserved for Hawking radiation based on standard probability theory and statistics. We claim that information previously considered lost remains hidden inside Hawking radiation. More specifically, it is encoded into correlations between Hawking radiations. Our study thus establishes harmony between Harking radiation and the unitarity of quantum mechanics, which establishes the basis for a significant milestone towards resolving the long-standing information loss paradox. The paper provides a brief review of the exciting development on Hawking raidation. In addition to summarize our own work on this subject, we compare and address other related studies.

We revisit the tunneling process from a Schwarzschild black hole in the noncommutative spacetime and obtain the non-thermal tunneling probability. In such non-thermal spectrum, the correlations are discovered, which can carry the information about the noncommutativity. Thus this enlightens a way to find the noncommutative information in the Hawking radiation. The entropy is also shown to be conserved in the whole radiation process, which implies that the unitarity is held even for the Hawking radiation from noncommutative black holes.

The crucial issue of quantum communication protocol is its security. In this Letter, we show that all the deterministic and direct two-way quantum communication protocols, sometimes called ping-pong (PP) protocols, are insecure when an eavesdropper uses the invisible photon to eavesdrop on the communication. With our invisible photon eavesdropping (IPE) scheme, the eavesdropper can obtain full information of the communication with zero risk of being detected. We show that this IPE scheme can be implemented experimentally with current technology. Finally, a possible improvement of PP communication protocols security is proposed. (c) 2005 Elsevier B.V. All rights reserved.

Gravitational information is incorporated into an atomic state by correlation of the internal and external degrees of freedom of the atom, in the present study of the atomic interferometer. Thus it is difficult to transfer information by using a standard teleportation scheme. In this paper, we propose a novel scheme for the transfer of gravitational information through a quantum channel provided by the entangled atomic state. Significantly, the existence of a quantum channel suppresses phase noise, improving the sensitivity of the atomic interferometer. Thus our proposal provides novel readout mechanism for the interferometer with an improved signal-to-noise ratio.

Information about the collapsed matter in a black hole will be lost if Hawking radiations are truly thermal. Recent studies discover that information can be transmitted from a black hole by Hawking radiations, due to their spectrum deviating from exact thermality when back reaction is considered. In this paper, we focus on the spectroscopic features of Hawking radiation from a Schwarzschild black hole, contrasting the differences between the nonthermal and thermal spectra. Of great interest, we find that the energy covariances of Hawking radiations for the thermal spectrum are exactly zero, while the energy covariances are non-trivial for the nonthermal spectrum. Consequently, the nonthermal spectrum can be distinguished from the thermal one by counting the energy covariances of successive emissions, which provides an avenue towards experimentally testing the long-standing "information loss paradox"., Published version. 6 figures

In both classical and quantum world, information cannot appear or disappear. This fundamental principle, however, is questioned for a black hole, by the acclaimed "information loss paradox". Based on the conservation laws of energy, charge, and angular momentum, we recently show the total information encoded in the correlations among Hawking radiations equals exactly to the same amount previously considered lost, assuming the non-thermal spectrum of Parikh and Wilczek. Thus the information loss paradox can be falsified through experiments by detecting correlations, for instance, through measuring the covariances of Hawking radiations from black holes, such as the manmade ones speculated to appear in LHC experiments. The affirmation of information conservation in Hawking radiation will shine new light on the unification of gravity with quantum mechanics., Comment: First Award in the 2013 Awards for Essays on Gravitation

In a two-way deterministic quantum key distribution (DQKD) protocol, Bob randomly prepares qubits in one of four states and sends them to Alice. To encode a bit, Alice performs an operation on each received qubit and returns it to Bob. Bob then measures the backward qubits to learn about Alice's operations and hence the key bits. Recently, we proved the unconditional security of the final key of this protocol in the ideal device setting. In this paper, we prove that two-way DQKD protocols are immune to all detector side channel attacks at Bob's side, while we assume ideal detectors at Alice's side for error testing. Our result represents a step forward in making DQKD protocols secure against general detector side channel attacks., Comment: Published version

Privacy amplification (PA) is an essential post-processing step in quantum key distribution (QKD) for removing any information an eavesdropper may have on the final secret key. In this paper, we consider delaying PA of the final key after its use in one-time pad encryption and prove its security. We prove that the security and the key generation rate are not affected by delaying PA. Delaying PA has two applications: it serves as a tool for significantly simplifying the security proof of QKD with a two-way quantum channel, and also it is useful in QKD networks with trusted relays. To illustrate the power of the delayed PA idea, we use it to prove the security of a qubit-based two-way deterministic QKD protocol which uses four states and four encoding operations., Comment: 11 pages, 3 figures

We investigate the meaning of the entropy carried away by Hawking radiations from a black hole. We propose that the entropy for a black hole measures the uncertainty of the information about the black hole forming matter's precollapsed configurations, self-collapsed configurations, and inter-collapsed configurations. We find that gravitational wave or gravitational radiation alone cannot carry all information about the processes of black hole coalescence and collapse, while the total information locked in the hole could be carried away completely by Hawking radiation as tunneling.

In a deterministic quantum key distribution (DQKD) protocol with a two-way quantum channel, Bob sends a qubit to Alice who then encodes a key bit onto the qubit and sends it back to Bob. After measuring the returned qubit, Bob can obtain Alice's key bit immediately, without basis reconciliation. Since an eavesdropper may attack the qubits traveling on either the Bob-Alice channel or the Alice-Bob channel, the security analysis of DQKD with a two-way quantum channel is complicated and its unconditional security has been controversial. This paper presents a security proof of a single-photon four-state DQKD against general attacks., Comment: Publication version