We present a protocol for deterministic and highly efficient quantum cryptography with entangled photon pairs in a 4x4-dimentional Hilbert space. Two communicating parties, Alice and Bob first share a both polarization- and path-entangled photon pair, and then each performs a complete Bell-state measurement on their own photon in one of two complementary Bell-state bases. It is demonstrated that each measurement in which both Alice and Bob register a photon can build certain perfect correlation and generate 1.5 key bits on average. The security of our protocol is guaranteed by the non-cloning theorem.
Recently the explicit applicability of bound entanglement in quantum cryptography has been shown. In this paper some of recent results respecting this topic are reviewed. In particular relevant notions and definitions are reminded. The new construction of bound entangled states containing secure correlations is presented. It provides low dimensional 6\otimes6 bound entangled states with nonzero distillable key.
A photon source based on postselection from entangled photon pairs produced by parametric frequency down-conversion is suggested. Its ability to provide good approximations of single-photon states is examined. Application of this source in quantum cryptography for quantum key distribution is discussed. Advantages of the source compared to other currently used sources are clarified. Future prospects of the photon source are outlined.
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.
Using polarization-entangled photons from spontaneous parametric downconversion, we have implemented Ekert's quantum cryptography protocol. The near-perfect correlations of the photons allow the sharing of a secret key between two parties. The presence of an eavesdropper is continually checked by measuring Bell's inequalities. We investigated several possible eavesdropper strategies, including pseudo-quantum non-demolition measurements. In all cases, the eavesdropper's presence was readily apparent. We discuss a procedure to increase her detectability.
We present a setup for quantum cryptography based on photon pairs in energy-time Bell states and show its feasability in a laboratory experiment. Our scheme combines the advantages of using photon pairs instead of faint laser pulses and the possibility to preserve energy-time entanglement over long distances. Moreover, using 4-dimensional energy-time states, no fast random change of bases is required in our setup : Nature itself decides whether to measure in the energy or in the time base.
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.
Real sources of entangled photon pairs (like parametric down conversion) are not perfect. They produce quantum states that contain more than only one photon pair with some probability. In this paper it is discussed what happens if such states are used for the purpose of quantum key distribution. It is shown that the presence of "multi-pair" signals (together with low detection efficiencies) causes errors in transmission even if there is no eavesdropper. Moreover, it is shown that even the eavesdropping, that draws information only from these "multi-pair" signals, increases the error rate. Info…
We describe how to modify the BB84 protocol for quantum cryptography in order to make it deterministic. We study both theoretical and experimental aspects of this issue, showing that the new scheme is as secure as the old one, more efficient on small-scale distances, and within the range of current technology.
We propose a quantum transmission based on bi-photons which are doubly-entangled both in polarisation and phase. This scheme finds a natural application in quantum cryptography, where we show that an eventual eavesdropper is bound to introduce a larger error on the quantum communication than for a single entangled bi-photon communication, when steeling the same information.
A new quantum cryptography implementation is presented that combines one-way operation with an autocompensating feature that has hitherto only been available in implementations that require the signal to make a round trip between the users. Using the concept of advanced waves, it is shown that this new implementation is related to the round-trip implementations in the same way that Ekert's two-particle scheme is related to the original one-particle scheme of Bennett and Brassard. The practical advantages and disadvantages of the proposed implementation are discussed in the context of existing …
Quantum-cryptography key distribution (QCKD) experiments have been recently reported using polarization-entangled photons. However, in any practical realization, quantum systems suffer from either unwanted or induced interactions with the environment and the quantum measurement system, showing up as quantum and, ultimately, statistical noise. In this paper, we investigate how ideal polarization entanglement in spontaneous parametric downconversion (SPDC) suffers quantum noise in its practical implementation as a secure quantum system, yielding errors in the transmitted bit sequence. Because al…
We propose a novel double-entanglement-based quantum cryptography protocol that is both efficient and deterministic. The proposal uses photon pairs with entanglement both in polarization and in time degrees of freedom; each measurement in which both of the two communicating parties register a photon can establish one and only one perfect correlation and thus deterministically create a key bit. Eavesdropping can be detected by violation of local realism. A variation of the protocol shows a higher security, similarly to the six-state protocol, under individual attacks. Our scheme allows a robust…
In this paper we analyze the security of the so-called quantum tomographic cryptography with the source producing entangled photons via an experimental scheme proposed in Phys. Rev. Lett. 92, 37903 (2004). We determine the range of the experimental parameters for which the protocol is secure against the most general incoherent attacks.
We present a crytographic protocol based upon entangled qutrit pairs. We analyse the scheme under a symmetric incoherent attack and plot the region for which the protocol is secure and compare this with the region of violations of certain Bell inequalities.
Intermediate states are known from intercept/resend eavesdropping in the BB84 quantum cryptographic protocol. But they also play fundamental roles in the optimal eavesdropping strategy on BB84 and in the CHSH inequality. We generalize the intermediate states to arbitrary dimension and consider intercept/resend eavesdropping, optimal eavesdropping on the generalized BB84 protocol and present a generalized CHSH inequality for two entangled quNits based on these states.
The quantum key distribution protocol BB84, published by C. H. Bennett and G. Brassard in 1984, describes how two spatially separated parties can generate a random bit string fully known only to them by transmission of single-qubit quantum states. Any attempt to eavesdrop on the protocol introduces disturbance which can be detected by the legitimate parties. In this Master's Thesis a novel modification to the BB84 protocol is analyzed. Instead of sending single particles one-by-one as in BB84, they are grouped and a non-local transformation is applied to each group before transmission. Each pa…
We present a scheme to generate a maximally entangled state of two three-level atoms in a cavity. The success or failure of the generation of the desired entangled state can be determined by detecting the polarization of the photon leaking out of the cavity. With the use of an automatic feedback, the success probability of the scheme can be made to approach unity.
We propose a new cryptographic protocol. It is suggested to encode information in ordinary binary form into many-qubit entangled states with the help of a quantum computer. A state of qubits (realized, e.g., with photons) is transmitted through a quantum channel to the addressee, who applies a quantum computer tuned to realize the inverse unitary transformation decoding of the message. Different ways of eavesdropping are considered, and an estimate of the time needed for determining the secret unitary transformation is given. It is shown that using even small quantum computers can serve as a b…
Multi-photon states from parametric down-conversion can be entangled both in polarization and photon number. Maximal high-dimensional entanglement can be concentrated from these states via photon counting. This makes them natural candidates for quantum key distribution, where the presence of more than one photon per detection interval has up to now been considered as undesirable. We propose a simple multi-photon protocol for the case of low losses and point out the robustness of the entanglement under photon loss.
State-of-the-art quantum key distribution systems are based on the BB84 protocol and single photons generated by lasers. These implementations suffer from range limitations and security loopholes, which require expensive adaptation. The use of polarization entangled photon pairs substantially alleviates the security threads while allowing for basically arbitrary transmission distances when embedded in quantum repeater schemes. Semiconductor quantum dots are capable of emitting highly entangled photon pairs with ultra-low multi-pair emission probability even at maximum brightness. Here we repor…
We study the possible limitations and sources of decoherence in the scheme for the deterministic generation of polarization-entangled photons, recently proposed by Gheri et al. [K. M. Gheri et al., Phys. Rev. A 58, R2627 (1998)], based on an appropriately driven single atom trapped within an optical cavity. We consider in particular the effects of laser intensity fluctuations, photon losses, and atomic motion.
We propose a cavity-QED scheme that can deterministically generate Einstein-Podosky-Rosen polarization-entangled photon pairs. A four-level tripod atom successively couples to two high-Q optical cavities possessing polarization degeneracy, assisted by a classical $π$-polarized pump field. The stimulated Raman adiabatic passage process in the atom-cavity system is used to produce the polarization-entangled photon pairs. The proposal is particularly robust against atomic spontaneous decay, which should have potential applications in quantum information processing.
We demonstrate a prototype-implementation of deterministic information encoding for quantum key distribution (QKD) following the ping-pong coding protocol [K. Bostroem, T. Felbinger, Phys. Rev. Lett. 89 (2002) 187902-1]. Due to the deterministic nature of this protocol the need for post-processing the key is distinctly reduced compared to non-deterministic protocols. In the course of our implementation we analyze the practicability of the protocol and discuss some security aspects of information transfer in such a deterministic scheme.
We propose two deterministic secure quantum communication (DSQC) protocols employing three-qubit GHZ-like states and five-qubit Brown states as quantum channels for secure transmission of information in units of two bits and three bits using multipartite teleportation schemes developed here. In these schemes, the sender's capability in selecting quantum channels and the measuring bases leads to improved qubit efficiency of the protocols.
Quantum Cryptography is on the verge of commercial application. One of its greatest limitations is over long distance - secret key rates are low and the longest fibre over which any key has been exchanged is currently 100 km. We investigate the quantum relay, which can increase the maximum distance at which quantum cryptography is possible. The relay splits the channel into sections, and sends a different photon across each section, increasing the signal to noise ratio. The photons are linked as in teleportation, with entangled photon pairs and Bell measurements. We show that such a scheme cou…
We present two cavity quantum electrodynamics proposals that, sharing the same basic elements, allow for the deterministic generation of entangled photons pairs by means of a three-level atom successively coupled to two single longitudinal mode high-Q optical resonators presenting polarization degeneracy. In the faster proposal, the three-level atom yields a polarization entangled photon pair via two truncated Rabi oscillations, whereas in the adiabatic proposal a counterintuitive Stimulated Raman Adiabatic Passage process is considered. Although slower than the former process, this second met…
The utilization of a $d$-level partially entangled state, shared by two parties wishing to communicate classical information without errors over a noiseless quantum channel, is discussed. We analytically construct deterministic dense coding schemes for certain classes of non-maximally entangled states, and numerically obtain schemes in the general case. We study the dependency of the information capacity of such schemes on the partially entangled state shared by the two parties. Surprisingly, for $d>2$ it is possible to have deterministic dense coding with less than one ebit. In this case the …
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.
We have prepared the internal states of two trapped ions in both the Bell-like singlet and triplet entangled states. In contrast to all other experiments with entangled states of either massive particles or photons, we do this in a deterministic fashion, producing entangled states on demand without selection. The deterministic production of entangled states is a crucial prerequisite for large-scale quantum computation.
Transformations involving only local operations assisted with classical communication are investigated for multipartite entangled pure states having tensor rank 2. All necessary and sufficient conditions for the possibility of deterministically converting truly multipartite, rank-2 states into each other are given. Furthermore, a chain of local operations that successfully achieves the transformation has been identified for all allowed transformations. The identified chains have two nice features: (1) each party needs to carry out at most one local operation and (2) all of these local operatio…
Successful generation of photonic cluster states is the key step in the realization of measurement-based quantum computation and quantum network protocols. Several proposals for the generation of such entangled states from different solid-state emitters have been put forward. Each of these protocols come with their own challenges in terms of both conception and implementation. In this work we propose deterministic generation of these photonic cluster states from a spin-photon interface based on a hole spin qubit hosted in a quantum dot molecule. Our protocol resolves many of the difficulties o…
Sources of entangled electromagnetic radiation are a cornerstone in quantum information processing and offer unique opportunities for the study of quantum many-body physics in a controlled experimental setting. While multi-mode entangled states of radiation have been generated in various platforms, all previous experiments are either probabilistic or restricted to generate specific types of states with a moderate entanglement length. Here, we demonstrate the fully deterministic generation of purely photonic entangled states such as the cluster, GHZ, and W state by sequentially emitting microwa…
Over decades quantum cryptography has been intensively studied for unconditionally secured data transmission in a quantum regime. Due to the quantum loopholes caused by imperfect single photon detectors and/or lossy quantum channels, however, the quantum cryptography is practically inefficient and even vulnerable to eavesdropping. Here, a method of unconditionally secured key distribution potentially compatible with current fiber-optic communications networks is proposed in a classical regime for high-speed optical backbone networks. The unconditional security is due to the quantum superpositi…
We analyze entanglement swapping (ES) of partially entangled pure states with arbitrary Schmidt rank from the perspective of quantum state discrimination. It is shown that the standard deterministic ES protocol is related with an optimal minimum-error strategy. In this case the amount of entanglement of the states resulting from swapping is, in general, lower than the maximum achievable for the quantum channels involved. In this regard, we show that the ES protocol can be probabilistically improved resorting to optimal maximum-confidence (MC) discrimination strategy. Additionally, we show that…
A pulsed source of energy-time entangled photon pairs pumped by a standard laser diode is proposed and demonstrated. The basic states can be distinguished by their time of arrival. This greatly simplifies the realization of 2-photon quantum cryptography, Bell state analyzers, quantum teleportation, dense coding, entanglement swapping, GHZ-states sources, etc. Moreover the entanglement is well protected during photon propagation in telecom optical fibers, opening the door to few-photon applications of quantum communication over long distances.
We propose a general approach for the implementation of the hybrid entangled states consisting of continuous variable (CV) and discrete variable (DV) states. Peculiarities of DV-CV interaction mechanism on the beam splitter with arbitrary parameters is key for the for the birth of the entangled hybridity provided that some measurement event is registered in auxiliary mode. We show that the CV states forming entangled state can consist exclusively of either even or odd Fock states. Various input CV states including Schrodinger cat state (SCSs) are used at the input of the beam splitter where th…
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 propose a deterministic remote state preparation (RSP) scheme for preparing an arbitrary (including pure and mixed) qubit, where a partially entangled state and finite classical communication are used. To our knowledge, our scheme is the first RSP scheme that fits into this category. One other RSP scheme proposed by Berry shares close features, but can only be used to prepare an arbitrary pure qubit. Even so, our scheme saves classical communication by approximate 1 bit per prepared qubit under equal conditions. When using a maximally entangled state, the classical communication for our sch…
Two deterministic secure quantum communication schemes are proposed, one based on pure entangled states and the other on $d$-dimensional single-photon states. In these two schemes, only single-photon measurements are required for the two authorized users, which makes the schemes more convenient than others in practical applications. Although each qubit can be read out after a transmission of additional classical bit, it is unnecessary for the users to transmit qubits double the distance between the sender and the receiver, which will increase their bit rate and their security. The parties use …
The notion of entanglement is the most well-known nonclassical correlation in quantum mechanics and a fundamental resource in quantum information and computation. This correlation, which is displayed by certain classes of quantum states, is of utmost importance when dealing with protocols such as quantum teleportation, cryptography, and quantum key distribution. In this paper, we exploit a classification of tripartite entanglement by introducing the concepts of entangled hypergraph and evolving entangled hypergraph as data structures suitable to model quantum protocols which use entanglement. …
The security of a deterministic quantum scheme for communication, namely the LM05 [1], is studied in presence of a lossy channel under the assumption of imperfect generation and detection of single photons. It is shown that the scheme allows for a rate of distillable secure bits higher than that pertaining to BB84 [2]. We report on a first implementation of LM05 with weak pulses.
For the space of two identical systems of arbitrary dimensions, we introduce a continuous family of bases with the following properties: i) the bases are orthonormal, ii) in each basis, all the states have the same values of entanglement, and iii) they continuously interpolate between the product basis and the maximally entangled basis. The states thus constructed may find applications in many areas related to quantum information science including quantum cryptography, optimal Bell tests and investigation of enhancement of channel capacity due to entanglement.
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.
Investigating a class of models that is familiar in studies of cellular automata, we find that quantum operators can be employed to describe their long distance behavior. These operators span a Hilbert space that appears to turn such a model into a genuine quantum field theory, obeying the usual conditions of locality in terms of its quantum commutators. Entangled states can be constructed exactly as in quantum theories. This raises the question whether such models allow Bell's inequalities to be violated. Being a local, deterministic theory, one would argue that this is impossible, but since …
The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this Letter, we experimentally study how precision measurements can be improved by preparing entangled states immune to the dominant source of decoherence. Using \Ca ions, we explicitly demonstrate the advantage from entanglement on a precision test of local Lorentz invariance for the electron. Reaching the quantum projection noise limit set by quantum mechanics, we observe for bipartite entangled states the expected gain of a factor of two in the precision. Under specific co…
Entangled photon pairs -- discrete light quanta that exhibit non-classical correlations -- play a crucial role in quantum information science (for example in demonstrations of quantum non-locality and quantum cryptography). At the macroscopic optical field level non-classical correlations can also be important, as in the case of squeezed light, entangled light beams and teleportation of continuous quantum variables. Here we use stimulated parametric down-conversion to study entangled states of light that bridge the gap between discrete and macroscopic optical quantum correlations. We demonstra…
Bell's theorem is supposed to exclude all local hidden-variable models of quantum correlations. However, an explicit counterexample shows that a new class of local realistic models, based on generalized arithmetic and calculus, can exactly reconstruct rotationally symmetric quantum probabilities typical of two-electron singlet states. Observable probabilities are consistent with the usual arithmetic employed by macroscopic observers, but counterfactual aspects of Bell's theorem are sensitive to the choice of hidden-variable arithmetic and calculus. The model is classical in the sense of Einste…
We produce two identical keys using, for the first time, entangled trinary quantum systems (qutrits) for quantum key distribution. The advantage of qutrits over the normally used binary quantum systems is an increased coding density and a higher security margin. The qutrits are encoded into the orbital angular momentum of photons, namely Laguerre-Gaussian modes with azimuthal index l +1, 0 and -1, respectively. The orbital angular momentum is controlled with phase holograms. In an Ekert-type protocol the violation of a three-dimensional Bell inequality verifies the security of the generated ke…
We implement experimentally a deterministic method to prepare and measure so called single-photon two-qubit entangled states or single-photon Bell-states, in which the polarization and the spatial modes of a single-photon each represent a quantum bit. All four single-photon Bell-states can be easily prepared and measured deterministically using linear optical elements alone. We also discuss how this method can be used for recently proposed single-photon two-qubit quantum cryptography protocol.
Incomparability of pure bipartite entangled states under deterministic LOCC is a very strange phenomena. We find two possible ways of getting our desired pure entangled state which is incomparable with the given input state, by collective LOCC with certainty. The first one is by providing some pure entanglement through the lower dimensional maximally-entangled states or using further less amount of entanglement and the next one is by collective operation on two pairs which are individually incomparable. It is quite surprising that we are able to achieve maximally entangled states of any Schmid…
We consider a family of continuous variable (CV) states being a superposition of displaced number states with equal modulo but opposite in sign displacement amplitudes. Either an even or odd CV state is mixed with a delocalized photon at a beam splitter with arbitrary transmittance and reflectance coefficients with the subsequent registration of the measurement outcome in an auxiliary mode to deterministically generate hybrid entanglement. We show that at certain values of the experimental parameters maximally entangled states are generated. The considered approach is also applicable to trunca…
We present an efficient method to generate a Greenberger-Horne-Zeilinger (GHZ) entangled state of three cat-state qubits (cqubits) via circuit QED. The GHZ state is prepared with three microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the operation, decoherence caused by the energy relaxation and dephasing of the qutrit is greatly suppressed. The GHZ state is created deterministically because no measurement is involved. Numerical simulations show that high-fidelity generation of a three-cqubit GHZ state is feasible with prese…
In state-of-the-art quantum key distribution (QKD) systems, the main limiting factor in increasing the key generation rate is the timing resolution in detecting photons. Here, we present and experimentally demonstrate a strategy to overcome this limitation, also for high-loss and long-distance implementations. We exploit the intrinsic wavelength correlations of entangled photons using wavelength multiplexing to generate a quantum secure key from polarization entanglement. The presented approach can be integrated into both fiber- and satellite-based quantum-communication schemes, without any ch…
