Feasibility of 300 km Quantum Key Distribution with Entangled States
Thomas Scheidl, Rupert Ursin, Alessandro Fedrizzi, Sven Ramelow, Xiao-Song Ma, Thomas Herbst, Robert Prevedel, Lothar Ratschbacher, Johannes Kofler, Thomas Jenn… 展开作者
Thomas Scheidl, Rupert Ursin, Alessandro Fedrizzi, Sven Ramelow, Xiao-Song Ma, Thomas Herbst, Robert Prevedel, Lothar Ratschbacher, Johannes Kofler, Thomas Jennewein, Anton Zeilinger
A significant limitation of practical quantum key distribution (QKD) setups is currently their limited operational range. It has recently been emphasized (X. Ma, C.-H. F. Fung, and H.-K. Lo., Phys. Rev. A, 76:012307, 2007) that entanglement-based QKD systems can tolerate higher channel losses than systems based on weak coherent laser pulses (WCP), in particular when the source is located symmetrically between the two communicating parties, Alice and Bob. In the work presented here, we experimentally study this important advantage by implementing different entanglement-based QKD setups on a 144~km free-space link between the two Canary Islands of La Palma and Tenerife. We established three different configurations where the entangled photon source was placed at Alice's location, asymmetrically between Alice and Bob and symmetrically in the middle between Alice and Bob, respectively. The resulting quantum channel attenuations of 35~dB, 58~dB and 71~dB, respectively, significantly exceed the limit for WCP systems. This confirms that QKD over distances of 300~km and even more is feasible with entangled state sources placed in the middle between Alice and Bob.
Entangled photon pairs have been promised to deliver a substantial quantum advantage for two-photon absorption spectroscopy. However, recent work has challenged the previously reported magnitude of quantum enhancement in two-photon absorption. Here, we present an experimental comparison of sum-frequency generation and molecular absorption, each driven by isolated photon pairs. We establish an upper bound on the enhancement for entangled-two-photon absorption in Rhodamine-6G, which lies well below previously reported values.
We study the feasibility of nonlocally compensating for polarization mode dispersion (PMD), when polarization entangled photons are distributed in fiber-optic channels.We quantify the effectiveness of nonlocal compensation while taking into account the possibility that entanglement is generated through the use of a pulsed optical pump signal.
Entanglement distillation aims at preparing highly entangled states out of a supply of weakly entangled pairs, using local devices and classical communication only. In this note we discuss the experimentally feasible schemes for optical continuous-variable entanglement distillation that have been presented in [D.E. Browne, J. Eisert, S. Scheel, and M.B. Plenio, Phys. Rev. A 67, 062320 (2003)] and [J. Eisert, D.E. Browne, S. Scheel, and M.B. Plenio, Annals of Physics (NY) 311, 431 (2004)]. We emphasize their versatility in particular with regards to the detection process and discuss the merits …
An entanglement concentration scheme for unknown atomic entanglement states is proposed via entanglement swapping in cavity QED. Because the interaction used here is a large-detuned one between two driven atoms and a quantized cavity mode, the effects of the cavity decay and thermal field have been eliminated. These advantages can warrant the experimental feasibility of the current scheme.
We show the enhancement of distillable key rate for quantum key distribution(QKD), by local filtering, for several bound entangled states. Through our work it becomes evident that the local filtration operations, while transforming one bound entangled state to another, have the potential to increase the utility of the new state for QKD. We demonstrate three examples of `one way distillable key rate' enhancement by local filtering and in this process, discover new bound entangled states which are key distillable.
We propose and analyze a new method to produce single and entangled photons which does not require cavities. It relies on the collective enhancement of light emission as a consequence of the presence of entanglement in atomic ensembles. Light emission is triggered by a laser pulse, and therefore our scheme is deterministic. Furthermore, it allows one to produce a variety of photonic entangled states by first preparing certain atomic states using simple sequences of quantum gates. We analyze the feasibility of our scheme, and particularize it to: ions in linear traps, atoms in optical lattices,…
In this paper, we present sufficient conditions for states to have positive distillable key rate. Exploiting the conditions, we show that the bound entangled states given by Horodecki et al. [Phys. Rev. Lett. 94, 160502 (2005), quant-ph/0506203] have nonzero distillable key rate, and finally exhibit a new class of bound entangled states with positive distillable key rate, but with negative Devetak-Winter lower bound of distillable key rate for the ccq states of their privacy squeezed versions.
A two-step quantum key distribution protocol using frequency and polarization doubly entangled photons is proposed. In this protocol, information is encoded by a unitary operation on each of the two doubly entangled photons and sent from Alice to Bob in two steps. State measurement device is designed. The security of the communication is analyzed.
Recently, Boyer et al. presented a novel semiquantum key distribution protocol [M. Boyer, D. Kenigsberg, and T. Mor, Phys. Rev. Lett. 99, 140501 (2007)], by using four quantum states, each of which is randomly prepared by Z basis or X basis. Here we present a semiquantum key distribution protocol by using entangled states in which quantum Alice shares a secret key with classical Bob. We also show the protocol is secure against eavesdropping.
We construct multipartite entangled states with underlying W-type structure satisfying positive partial transpose (PPT) condition under any (N-1)|1 partition. Then we show how to distill N-partite secure key form the states using two different methods: direct application of local filtering and novel random key distillation scheme in which we adopt the idea form recent results on entanglement distillation. Open problems and possible implications are also discussed.
We study the feasibility of extracting a pure entangled state of non-complementary, and potentially well separated, regions of a quantum many-body system. It is shown that this can indeed be accomplished in non-equilibrium scenarios as well as the ground state of the considered spin chain models when one locally measures observables such as magnetization in separated blocks of spins. A general procedure is presented, which can search for the optimal way to extract a pure entangled state through local projections. Our results indicate a connection of the projective extraction of entanglement to…
We present a scheme to realize a quantum key distribution using vacuum-one photon entangled states created both from Alice and Bob. The protocol consists in an exchange of spatial modes between Alice and Bob and in a recombination which allows one of them to reconstruct the bit encoded by the counterpart in the phase of the entangled state. The security of the scheme is analyzed against some simple kind of attack. The model is shown to reach higher efficiency with respect to prior schemes using phase encoding methods.
Efficiency is a key issue in any real implementation of a cryptographic protocol since the physical resources are not unlimited. We will first show that Quantum Key Distribution is possible with an "Entanglement based" scheme with NPPT symmetric Gaussian states in spite of the fact that these systems cannot be distilled with Gaussian operations (they are all bound entangled). In this work we analyze the secrecy properties of Gaussian states under Gaussian operations. Although such operations are useless for quantum distillation, we prove that it is possible to distill efficiently a secret key …
We present three quantum key distribution protocols using entangled state. In the first two protocols, all Einstein-Podolsky-Rosen pairs are used to distribute a secret key except those chosen for eavesdropping check, because the communication parties measure each of their particles in an invariable measuring basis. The first protocol is based on the ideal of qubit transmission in blocks. Although it need quantum memory, its theoretic efficiency approximates to 100%. The second protocol does not need quantum memory and its efficiency for qubits can achieve 100%. In the third protocol, we prese…
We report on a complete experimental implementation of a quantum key distribution protocol through a free space link using polarization-entangled photon pairs from a compact parametric down-conversion source. Over 10 hours of uninterrupted communication between sites 1.5 km apart, we observe average key generation rates of 630 per second after error correction and privacy amplification. Our scheme requires no specific hardware channel for synchronization apart from a classical wireless link, and no explicit random number generator.
We present an entangled-state quantum cryptography system that operated for the first time in a real world application scenario. The full key generation protocol was performed in real time between two distributed embedded hardware devices, which were connected by 1.45 km of optical fiber, installed for this experiment in the Vienna sewage system. The generated quantum key was immediately handed over and used by a secure communication application.
Recently, a quantum key exchange protocol has been described, which served as basis for securing an actual bank transaction by means of quantum cryptography [quant-ph/0404115]. Here we show, that the authentication scheme applied is insecure in the sense that an attacker can provoke a situation where initiator and responder of a key exchange end up with different keys. Moreover, it may happen that an attacker can decrypt a part of the plaintext protected with the derived encryption key.
We present a full implementation of a quantum key distribution system using energy-time entangled photon pairs and functioning with a 30km standard telecom fiber quantum channel. Two bases of two orthogonal states are implemented and the setup is quite robust to environmental constraints such as temperature variation. Two different ways to manage chromatic dispersion in the quantum channel are discussed.
We establish a security proof of frequency-time coding quantum key distribution (FT-QKD) protocol by showing its connection to the squeezed state quantum key distribution protocol, which has been proven to be unconditionally secure. We also extend the prepare-and-measure FT-QKD protocol to an entanglement based FT-QKD protocol which is more appealing in practice. Furthermore, we propose a correlated frequency measurement scheme of entangled photon pair by using time resolving single photon detector. Simulation results show that the FT-QKD protocol can be implemented with today's technology.
We present a practical method that can make quantum key distribution (QKD), for the first time, both ultra-long-distance and immune to all attacks in the detection system. This method is an important extension of the measurement-device-independent QKD (MDI-QKD) - MDI-QKD with entangled photon sources in the middle. By proposing a general model and simulating an entanglement based QKD experiment, we find that MDI-QKD with one entangled photon source in the middle can practically tolerate 77 dB combined loss (367km standard telecom fiber) in the asymptotic limit, and it can still tolerate 60 dB …
We introduce a novel time-frequency quantum key distribution (TFQKD) scheme based on photon pairs entangled in these two conjugate degrees of freedom. The scheme uses spectral detection and phase modulation to enable measurements in the temporal basis by means of time-to-frequency conversion. This allows large-alphabet encoding to be implemented with realistic components. A general security analysis for TFQKD with binned measurements reveals a close connection with finite-dimensional QKD protocols and enables analysis of the effects of dark counts on the secure key size.
We suggest a quantum cryptographic scheme using continuous EPR-like correlations of bright optical beams. For binary key encoding, the continuous information is discretized in a novel way by associating a respective measurement, amplitude or phase, with a bit value "1" or "0". The secure key distribution is guaranteed by the quantum correlations. No pre-determined information is sent through the quantum channel contributing to the security of the system.
We propose an efficient quantum key distribution scheme based on entanglement. The sender chooses pairs of photons in one of the two equivalent nonmaximally entangled states randomly, and sends a sequence of photons from each pair to the receiver. They choose from the various bases independently but with substantially different probabilities, thus reducing the fraction of discarded data, and a significant gain in efficiency is achieved. We then show that such a refined data analysis guarantees the security of our scheme against a biased eavesdropping strategy.
Hereunder, we study the class of irreducible private states that are private states from which all the secret content is accessible via measuring their key part. We provide the first protocol which distills key not only from the key part, but also from the shield if only the state is reducible. We prove also a tighter upper bound on the performance of that protocol, given in terms of regularized relative entropy of entanglement instead of relative entropy of entanglement previously known. This implies in particular that the irreducible private states are all strictly irreducible if and only if…
In this paper, we present the first experimental demonstration on continuous variable quantum key distribution using determinant Einstein-Podolsky-Rosen entangled states of optical field. By means of the instantaneous measurements of the quantum fluctuations of optical modes respectively distributed at sender and receiver, the random bits of secret key are obtained without the need for signal modulation. The post-selection boundaries for the presented entanglement-based scheme against both Gaussian collective and individual attacks are theoretically concluded. The final secret key rates of 84 …
Random generation and confidential distribution of cryptographic keys are fundamental building blocks of secure communication. Using quantum states in which the transmitted quantum bit is entangled with a stationary memory quantum bit allows the secure generation and distribution of keys to be based on fundamental properties of quantum mechanics. At the same time, the reach of secure communication networks can be enhanced, in particular, since this architecture would be compatible with quantum repeaters which are an integral part for scaling quantum networks. Here, we realize a true single-pho…
Suppose Alice and Bob try to transform an entangled state shared between them into another one by local operations and classical communications. Then in general a certain amount of entanglement contained in the initial state will decrease in the process of transformation. However, an interesting phenomenon called partial entanglement recovery shows that it is possible to recover some amount of entanglement by adding another entangled state and transforming the two entangled states collectively. In this paper we are mainly concerned with the feasibility of partial entanglement recovery. The bas…
Generation of polarization-entangled photons from quantum dots via the biexciton-exciton recombination cascade is complicated by the presence of an energy spitting between the intermediate excitonic levels, which severely degrades the quality of the entangled photon source. In this paper we present a novel, conceptually simple and straightforward proposal for restoring the entanglement of said source by applying a cascade of time-dependent operations on the emitted photons. This is in striking contrast with the techniques usually employed, that act on the quantum emitter itself in order to rem…
We show that non-maximally entangled states can be used to build a quantum key distribution (QKD) scheme whose security and key rate transmission is nearly equivalent to those of standard QKD protocols. These aspects can be controlled by using the new free parameter in the present scheme, namely, the degree of partial entanglement. Furthermore, we discuss how to build a controlled QKD scheme, also based on partially entangled states, where a third party can decide whether or not Alice and Bob are allowed to share a key.
We investigate a quantum key distribution (QKD) scheme which utilizes a biased basis choice in order to increase the efficiency of the scheme. The optimal bias between the two measurement bases, a more refined error analysis, and finite key size effects are all studied in order to assure the security of the final key generated with the system. We then implement the scheme in a local entangled QKD system that uses polarization entangled photon pairs to securely distribute the key. A 50/50 non-polarizing beamsplitter with different optical attenuators is used to simulate a variable beamsplitter …
States with private correlations but little or no distillable entanglement were recently reported. Here, we consider the secure distribution of such states, i.e., the situation when an adversary gives two parties such states and they have to verify privacy. We present a protocol which enables the parties to extract from such untrusted states an arbitrarily long and secure key, even though the amount of distillable entanglement of the untrusted states can be arbitrarily small.
Quantum key distribution (QKD) refers to specific quantum strategies which permit the secure distribution of a secret key between two parties that wish to communicate secretly. Quantum cryptography has proven unconditionally secure in ideal scenarios and has been successfully implemented using quantum states with finite (discrete) as well as infinite (continuous) degrees of freedom. Here, we analyze the efficiency of QKD protocols that use as a resource entangled gaussian states and gaussian operations only. In this framework, it has already been shown that QKD is possible (M. Navascués et al.…
Using the previously shared Einstein-Podolsky-Rosen pairs, a proposal which can be used to distribute a quantum key and identify the user's identification simultaneously is presented. In this scheme, two local unitary operations and the Bell state measurement are used. Combined with quantum memories, a cryptographic network is proposed. One advantage is no classical communication is needed, which make the scheme more secure. The secure analysis of this scheme is shown.
We discuss a cavity-QED scheme to deterministically generate entangled photons pairs by using a three-level atom successively coupled to two single longitudinal mode high-Q cavities presenting polarization degeneracy. The first cavity is prepared in a well defined Fock state with two photons with opposite circular polarizations while the second cavity remains in the vacuum state. A half-of-a-resonant Rabi oscillation in each cavity transfers one photon from the first to the second cavity, leaving the photons entangled in their polarization degree of freedom. The feasibility of this implementat…
In view of real world applications of quantum information technologies, the combination of miniature quantum resources with existing fibre networks is a crucial issue. Among such resources, on-chip entangled photon sources play a central role for applications spanning quantum communications, computing and metrology. Here, we use a semiconductor source of entangled photons operating at room temperature in conjunction with standard telecom components to demonstrate multi-user quantum key distribution, a core protocol for securing communications in quantum networks. The source consists of an AlGa…
So far, various multi-photon entangled states have been observed experimentally by using different experimental set-ups. Here, we present a scheme to realize many SLOCC-inequivalent states of three and four qubits via projective measurements on suitable entangled states. We demonstrate how these states can be observed experimentally in a single set-up and study the feasibility of the implementation with present-day technology.
Frequency-Resolved Simulations of Highly Entangled Biphoton States: Beyond the Single-Pair Approximation. II. Application to Entanglement-based Quantum Key Distribution
In this paper, we put forward a novel single-state three-party semiquantum key agreement (SQKA) protocol with three-particle GHZ entangled states first. Different with previous quantum key agreement (QKA) protocols, the proposed single-state three-party SQKA protocol can realize the goal that a quantum party and two classical parties who only possess limited quantum capabilities equally contribute to the generation of a shared private key over quantum channels. Detailed security analysis turns out that the proposed single-state three-party SQKA protocol is secure against several famous attacks…
By realizing a quantum cryptography system based on polarization entangled photon pairs we establish highly secure keys, because a single photon source is approximated and the inherent randomness of quantum measurements is exploited. We implement a novel key distribution scheme using Wigner's inequality to test the security of the quantum channel, and, alternatively, realize a variant of the BB84 protocol. Our system has two completely independent users separated by 360 m, and generates raw keys at rates of 400 - 800 bits/second with bit error rates arround 3 percent.
In general, the state of a quantum system represented by density operator and its determination is a fundamental problem in quantum mechanics. A method of direct measurement of matrix element of density operator of a single two dimensional quantum system using weak measurement was theoretically proposed[Phys. Rev. Lett. 134, 070402(2012)] and experimentally demonstrated[Phys. Rev. Lett. 117, 120401(2016)] by Lundeen et al. Furthermore, recently the Guo-Guang Can et al.[Phys. Rev. Lett. 123, 150402(2019)] investigated the method of direct measurement of a nonlocal entangled quantum state. Howev…
We report on the first real-time implementation of a quantum key distribution (QKD) system using entangled photon pairs that are sent over two free-space optical telescope links. The entangled photon pairs are produced with a type-II spontaneous parametric down-conversion source placed in a central, potentially untrusted, location. The two free-space links cover a distance of 435 m and 1,325 m respectively, producing a total separation of 1,575 m. The system relies on passive polarization analysis units, GPS timing receivers for synchronization, and custom written software to perform the compl…
The study of quantum cryptography and quantum non-locality have traditionnally been based on two-level quantum systems (qubits). In this paper we consider a generalisation of Ekert's cryptographic protocol [Ekert] where qubits are replaced by qutrits. The security of this protocol is related to non-locality, in analogy with Ekert's protocol. In order to study its robustness against the optimal individual attacks, we derive the information gained by a potential eavesdropper applying a cloning-based attack.
We here present the rate analysis and a proof of principle realization of a device-independent quantum key distribution (QKD) protocol requiring the lowest detection efficiency necessary to achieve a secure key compared to device-independent protocols known so far. The protocol is based on non-maximally entangled state and its experimental realization has been performed by two-photon bipartite entangled states. The improvement with respect to protocols involving maximally entangled states has been estimated.
In this paper we present a novel analysis of the feasibility of quantum key distribution between a LEO satellite and a ground station. First of all, we study signal propagation through a turbulent atmosphere for uplinks and downlinks, discussing the contribution of beam spreading and beam wandering. Then we introduce a model for the background noise of the channel during night-time and day-time, calculating the signal-to-noise ratio for different configurations. We also discuss the expected error-rate due to imperfect polarization-compensation in the channel. Finally, we calculate the expected…
Now that fundamental quantum principles of indeterminacy and measurement have become the basis of new technologies that provide secrecy between two communicating parties, there is a need to provide teaching laboratories that illustrate how these technologies work. In this article we describe a laboratory exercise in which students perform quantum key distribution with single photons, and see how the secrecy of the communication is ensured by the principles of quantum superposition and state projection. We used a table-top apparatus, similar to those used in correlated-photon undergraduate labo…
We revisit the practical implementation of high-dimensional quantum key distribution protocol using path entanglement reported in [Phys.Rev.Lett.~127,~110505,~2021]. Here we refine the noise robustness analysis performed there by simulating the effect of different types of channel noise on the noiseless experimental data. Further, we extend the analysis to two kinds of asymmetric scenarios. In the first scenario the entanglement source is placed in Alice's lab and thus Only one noisy channel has to be considered. In the second scenario, Bob's detectors are placed at different physical location…
This paper presents the feasibility study of deploying Quantum Key Distribution (QKD) from High Altitude Platforms (HAPs), as a way of securing future communications applications and services. The paper provides a thorough review of the state of the art HAP technologies and summarises the benefits that HAPs can bring to the QKD services. A detailed link budget analysis is presented in the paper to evaluate the feasibility of delivering QKD from stratospheric HAPs flying at 20 km altitude. The results show a generous link budget under most operating conditions which brings the possibility of us…
We present a scheme for an integrated four-wave mixing source of narrow-band path-entangled photon pairs with efficient spatial pump self-rejection. The scheme is based on correlated loss in a system of waveguides in Kerr nonlinear media. We demonstrate that this setup allows for upwards of 100dB pump rejection, without additional filtering. The effect is reached by driving the symmetric collective mode that is strongly attenuated by an engineered dissipation, while photon pairs are born in the antisymmetric mode. A similar set-up can additionally be realized for generation of two-photon NOON …
Quantum networks are essential for realising distributed quantum computation and quantum communication. Entangled photons are a key resource, with applications such as quantum key distribution, quantum relays, and quantum repeaters. All components integrated in a quantum network must be synchronised and therefore comply with a certain clock frequency. In quantum key distribution, the most mature technology, clock rates have reached and exceeded 1GHz. Here we show the first electrically pulsed sub-Poissonian entangled photon source compatible with existing fiber networks operating at this clock…
Recently, Boyer et al. presented a novel semiquantum key distribution protocol [M. Boyer, D. Kenigsberg, and T. Mor, Phys. Rev. Lett. 99, 140501 (2007)], in which quantum Alice shares a secret key with classical Bob. Li et al. proposed two semiquantum secret sharing protocols [Q. Li, W. H. Chan, and D. Y. Long, Phys. Rev. A 82, 022303 (2010)] by using maximally entangled Greenberger-Horne-Zeilinger states. In this paper, we present a semiquantum secret sharing protocol by using two-particle entangled states in which quantum Alice shares a secret key with two classical parties, Bob and Charlie.…
