We consider discrete-alphabet encoding schemes for coherent-state quantum key distribution. The sender encodes the letters of a finite-size alphabet into coherent states whose amplitudes are symmetrically distributed on a circle centered in the origin of the phase space. We study the asymptotic performance of this phase-encoded coherent-state protocol in direct and reverse reconciliation assuming both loss and thermal noise in the communication channel. In particular, we show that using just four phase-shifted coherent states is sufficient for generating secret key rates of the order of $4 \times 10^{-3}$ bits per channel use at about 15 dB loss in the presence of realistic excess noise.
In optical implementations of the phase-encoded BB84 protocol, the bit information is usually encoded in the phase of two consecutive photon pulses generated in a Mach-Zehnder interferometer. In the actual experimental realization, the loss in the arms of the Mach-Zehnder interferometer is not balanced, for example because only one arm contains a lossy phase modulator. Therefore, the amplitudes of the pulses is not balanced, and the structure of the signals and measurements no longer corresponds to the (balanced) ideal BB84 protocol. Hence, the BB84 security analysis no longer applies in this …
High Fidelity Artificial Quantum Thermal State Generation using Encoded Coherent States
Information Sciences Institute, University of Southern California（南加州大学信息科学研究所）；Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California（南加州大学明海希电气与计算机工程系）；Department of Physics and Astronomy, University of Southern California（南加州大学物理与天文学系）
Digital signatures are frequently used in data transfer to prevent impersonation, repudiation and message tampering. Currently used classical digital signature schemes rely on public key encryption techniques, where the complexity of so-called "one-way" mathematical functions is used to provide security over sufficiently long timescales. No mathematical proofs are known for the long-term security of such techniques. Quantum digital signatures offer a means of sending a message which cannot be forged or repudiated, with security verified by information-theoretical limits and quantum mechanics. …
In the context of multiparameter quantum estimation theory, we investigate the construction of linear schemes in order to infer two classical parameters that are encoded in the quadratures of two quantum coherent states. The optimality of the scheme built on two phase-conjugate coherent states is proven with the saturation of the quantum Cramér--Rao bound under some global energy constraint. In a more general setting, we consider and analyze a variety of $n$-mode schemes that can be used to encode $n$ classical parameters into $n$ quantum coherent states and then estimate all parameters optima…
Time-bin encoding is a robust form of optical quantum information, especially for transmission in optical fibers. To read out the information, the separation of the time bins must be larger than the detector time resolution, typically on the order of nanoseconds for photon counters. In the present work, we demonstrate a technique using a nonlinear interaction between chirped entangled time-bin photons and shaped laser pulses to perform projective measurements on arbitrary time-bin states with picosecond-scale separations. We demonstrate a tomographically-complete set of time-bin qubit projecti…
In this work, we study the security of coherent-state quantum key distribution with a strong reference pulse. The consideration is based on a powerful soft filtering attack and uses realistic parameters of the equipment. Our model allows us to relate the secure key generation rate and distance with the energy of signal and reference pulses. We propose a two-pass quantum key distribution phase encoding optical scheme with a strong reference pulse. This simple for realization scheme is experimentally tested showing stable operation. Here we describe the tuning technique and solution for the prob…
We provide a simple description of the most general collective Gaussian attack in continuous-variable quantum cryptography. In the scenario of such general attacks, we analyze the asymptotic secret-key rates which are achievable with coherent states, joint measurements of the quadratures and one-way classical communication.
Entangled multi-qubit states are an essential resource for quantum information and computation. Solid-state emitters can mediate interactions between subsequently emitted photons via their spin, thus offering a route towards generating entangled multi-photon states. However, existing schemes typically rely on the incoherent emission of single photons and suffer from severe practical limitations, for self-assembled quantum dots most notably the limited spin coherence time due to Overhauser magnetic field fluctuations. We here propose an alternative approach of employing spin-flip Raman scatteri…
We investigate the security of continuous-variable (CV) quantum key distribution (QKD) using coherent states in the presence of quadrature excess noise. We consider an eavesdropping attack which uses a linear amplifier and beam splitter. This attack makes a link between beam-splitting attack and intercept-resend attack (classical teleportation attack). We also show how postselection loses its efficiency in a realistic channel.
We prove the unconditional security of a quantum key distribution protocol in which bit values are encoded in the phase of a weak coherent-state pulse relative to a strong reference pulse. In contrast to implementations in which a weak pulse is used as a substitute for a single-photon source, the achievable key rate is found to decrease only linearly with the transmission of the channel.
We apply the techniques introduced in [Kraus et. al., Phys. Rev. Lett. 95, 080501, 2005] to prove security of quantum key distribution (QKD) schemes using two-way classical post-processing as well as QKD schemes based on weak coherent pulses instead of single-photon pulses. As a result, we obtain improved bounds on the secret-key rate of these schemes.
The coherent-state qubit is a promising candidate for optical quantum information processing due to its nearly-deterministic nature of the Bell-state measurement (BSM). However, its non-orthogonality incurs difficulties such as failure of the BSM. One may use a large amplitude ($α$) for the coherent state to minimize the failure probability, but the qubit then becomes more vulnerable to dephasing by photon loss. We propose a hardware-efficient concatenated BSM (CBSM) scheme with modified parity encoding using coherent states with reasonably small amplitudes ($|α| \lessapprox 2$), which simulta…
Weak coherent states as a photon source for quantum cryptography have limit in secure data rate and transmission distance because of the presence of multi-photon events and loss in transmission line. Two-photon events in a coherent state can be taken out by a two-photon interference scheme. We investigate the security issue of utilizing this modified coherent state in quantum cryptography. A 4 dB improvement in secure data rate or a nearly two-fold increase in transmission distance over the coherent state are found. With a recently proposed and improved encoding strategy, further improvement i…
We assess the security of a quantum key distribution protocol relying on the transmission of Gaussian-modulated coherent states and homodyne detection. This protocol is shown to be equivalent to a squeezed state protocol based on a CSS code construction, and is thus provably secure against any eavesdropping strategy. We also briefly show how this protocol can be generalized in order to improve the net key rate.
Graph states are a central resource in measurement-based quantum information processing. In the photonic qubit architecture based on Gottesman-Kitaev-Preskill (GKP) encoding, the generation of high-fidelity graph states composed of realistic, finite-energy approximate GKP-encoded qubits thus constitutes a key task. We consider the finite-energy approximation of GKP qubit states given by a coherent superposition of shifted finite-squeezed vacuum states, where the displacements are Gaussian distributed. We present an exact description of graph states composed of such approximate GKP qubits as a …
Measurement-device-independent quantum key distribution protocol, whose security analysis does not rely on any assumption on the detection system, can immune the attacking against detectors. We give a first composable security analysis for continuous-variable measurement-device-independent quantum key distribution using squeezed states against general coherent attacks. The security analysis is derived based on the entanglement-based scheme considering finite size effect. A version of entropic uncertainty relation is exploited to give a lower bound on the conditional smooth min-entropy by trust…
In this paper, using the full security framework for continuous variable quantum key distribution (CV-QKD), we provide a composable security proof for the CV-QKD system in a realistic implementation. We take into account equipment losses and contributions from various components of excess noise and evaluate performance against collective and coherent attacks assuming trusted hardware noise. The calculation showed that the system remains operable at channel losses up to 10.2 dB in the presence of collective attacks and up to 7.5 dB in the presence of coherent ones.
Security of a continuous-variable quantum key distribution protocol based on noisy coherent states and channel is analyzed. Assuming the noise of coherent states is induced by Fred, a neutral party relative to others, we prove that the prepare and measurement scheme and entanglement-based scheme are equivalent. Then, we show that this protocol is secure against Gaussian collective attacks even if the channel is lossy and noisy, and further, a lower bound to the secure key rate is derived.
We present a rigorous security analysis of Continuous-Variable Measurement-Device Independent Quantum Key Distribution (CV MDI QKD) in a finite size scenario. The security proof is obtained in two steps: by first assessing the security against collective Gaussian attacks, and then extending to the most general class of coherent attacks via the Gaussian de Finetti reduction. Our result combines recent state-of-the-art security proofs for CV QKD with new findings about min-entropy calculus and parameter estimation. In doing so, we improve the finite-size estimate of the secret key rate. Our conc…
We prove the unconditional security of coherent-state-based differential phase shift quantum key distribution protocol (DPSQKD) with block-wise phase randomization. Our proof is based on the conversion of DPSQKD to an equivalent entanglement-distillation protocol where the estimated phase error rate determines the amount of the privacy amplification. The generated final key has a contribution from events where the sender emits two or more photons, indicating the robustness of DPSQKD against photon-number-splitting attacks.
We give the first composable security proof for continuous-variable quantum key distribution with coherent states against collective attacks. Crucially, in the limit of large blocks the secret key rate converges to the usual value computed from the Holevo bound. Combining our proof with either the de Finetti theorem or the Postselection technique then shows the security of the protocol against general attacks, thereby confirming the long-standing conjecture that Gaussian attacks are optimal asymptotically in the composable security framework. We expect that our parameter estimation procedure, …
When a harmonic oscillator is under the influence of a Gaussian process such as linear damping, parametric gain, and linear coupling to a thermal environment, its coherent states are transformed into states with Gaussian Wigner function. Qubit states can be encoded in the |0> and |1> Fock states of a quantum harmonic oscillator, and it is relevant to know the fidelity of the output qubit state after a Gaussian process on the oscillator. In this paper we present a general expression for the average qubit fidelity in terms of the first and second moments of the output from input coherent states …
Recently, the authors [arXiv quant-ph 1209.3706] studied quantum discord for Werner mixed states based on the four entangled coherent states, which are used for quantum teleportation of single qubit information encoded in superposed coherent state and compared it with entanglement of formation. In the present paper, we consider two more general bipartite superposed coherent states and get two quasi-Werner states. We study quantum discord and entanglement of formation for these states and compare them.
We study generation and dynamics of an exchange spin qubit encoded in three coherently coupled quantum dots with three electrons. For two geometries of the system a linear and a triangular one, the creation and coherent control of the qubit states are performed by the Landau--Zener transitions. In the triangular case both the qubit states are equivalent and can be easily generated for particular symmetries of the system. If one of the dots is smaller than the others one can observe Rabi oscillations, that can be used for coherent manipulation of the qubit states. The linear system is easier to…
We develop a quantum learning scheme for binary discrimination of coherent states of light. This is a problem of technological relevance for the reading of information stored in a digital memory. In our setting, a coherent light source is used to illuminate a memory cell and retrieve its encoded bit by determining the quantum state of the reflected signal. We consider a situation where the amplitude of the states produced by the source is not fully known, but instead this information is encoded in a large training set comprising many copies of the same coherent state. We show that an optimal g…
The Differential-Phase-Shift (DPS) and the Coherent-One-Way (COW) are among the most practical protocols for quantum cryptography, and are therefore the object of fast-paced experimental developments. The assessment of their security is also a challenge for theorists: the existing tools, that allow to prove security against the most general attacks, do not apply to these two protocols in any straightforward way. We present new upper bounds for their security in the limit of large distances ($d \gtrsim 50$km with typical values in optical fibers) by considering a large class of collective attac…
Experimental Coherent One-Way Quantum Key Distribution with Simplicity and Practical Security
National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室和物理学院，先进微结构协同创新中心）；School of Physics and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学物理学院与量子态构建与操控教育部重点实验室）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）
In this paper we present finite-key security analysis for quantum key distribution protocol based on weak coherent (in particular phase-coded) states using a fully quantum asymptotic equipartition property technique. This work is the extension of the proof for non-orthogonal states on the coherent states. Below we consider two types of attacks each of them maximizes either Alice-Eve or Eve-Bob mutual information. The cornerstone of this paper is that we do assume the possibility of crucial intercept-resend attack based on errorless unambiguous state discrimination measurement. We demonstrate t…
In this work, we present active and passive linear optical setups for error correction in quantum communication systems that employ polarization of single-photon and mesoscopic coherent states. Applications in quantum communication systems are described.
Present work is an attempt to compare quantum discord and quantum entanglement of Werner states formed with the four bipartite entangled coherent states (ECS) used recently for quantum teleportation of a qubit encoded in superposed coherent state. Out of these, two based on maximally ECS are exactly similar to the perfect Werner state, while the rest two, based on non-maximally ECS, which are called quasi-Werner states behave in somewhat different ways and their quantum discord and entanglement depends on the coherent amplitude and the measurement basis.
Polarizations of single-photon pulses have been controlled with long-term stability of more than 10 hours by using an active feedback technique for auto-compensation of unpredictable polarization scrambling in long-distance fiber. Experimental tests of long-term operations in 50, 75 and 100 km fibers demonstrated that such a single-photon polarization control supported stable polarization encoding in long-distance fibers to facilitate stable one-way fiber system for polarization-encoded quantum key distribution, providing quantum bit error rates below the absolute security threshold.
We propose a scheme for the secure direct communication based on the entangled phase-coherent states, which shows an elevated level of confidentiality. The protocol gives a simultaneous security control for every bit of transferred information. The security-check-per-bit is provided by sending an additional mode to prove the legitimate parties' authenticity. Other benefit include increased transfer rate, since a separate control sequences is unnecessary. We study the security of the scheme for both ideal and realistic quantum channel. The protocol shows a robust security and prepares 50% proba…
Two-way Gaussian protocols have the potential to increase quantum key distribution (QKD) protocols' secret-key rates by orders of magnitudes~[Phys.~Rev.~A {\bf 94}, 012322 (2016)]. Security proofs for two-way protocols, however, are underdeveloped at present. In this paper, we establish a security proof framework for the general coherent attack on two-way Gaussian protocols in the asymptotic regime. We first prove that coherent-attack security can be reduced to collective-attack security for all two-way QKD protocols. Next, we identify two different constraints that each provide intrusion para…
The performance of quantum key distribution (QKD) is severely limited by multi-photon pulses emitted by laser sources due to the photon-number splitting attack. Coherent-one-way (COW) QKD has been introduced as a promising solution to overcome this limitation, and thus extend the achievable distance of practical QKD. Indeed, thanks to its experimental simplicity, the COW protocol is already used in commercial applications. Here, we derive simple upper security bounds on its secret key rate, which demonstrate that it scales at most quadratically with the system's transmittance, thus solving a l…
We investigate the composable security of unidimensional contin- uous variable quantum key distribution (UCVQKD), which is based on the Gaussian modulation of a single quadrature of the coherent-state of light, aiming to provide a simple implementation of key distribution compared to the symmetrically modulated Gaussian coherent-state protocols. This protocol neglects the necessity in one of the quadrature modulation in coherent-states and hence reduces the system complexity. To clarify the influence of finite-size effect and the cost of performance degeneration, we establish the relation- shi…
The work by Christandl, König and Renner [Phys. Rev. Lett. 102, 020504 (2009)] provides in particular the possibility of studying unconditional security in the finite-key regime for all discrete-variable protocols. We spell out this bound from their general formalism. Then we apply it to the study of a recently proposed protocol [Laing et al., Phys. Rev. A 82, 012304 (2010)]. This protocol is meaningful when the alignment of Alice's and Bob's reference frames is not monitored and may vary with time. In this scenario, the notion of asymptotic key rate has hardly any operational meaning, because…
We introduce a ternary quantum key distribution (QKD) protocol and asymptotic security proof based on three coherent states and homodyne detection. Previous work had considered the binary case of two coherent states and here we nontrivially extend this to three. Our motivation is to leverage the practical benefits of both discrete and continuous (Gaussian) encoding schemes creating a best-of-both-worlds approach; namely, the postprocessing of discrete encodings and the hardware benefits of continuous ones. We present a thorough and detailed security proof in the limit of infinite signal states…
Ideal quantum key distribution (QKD) protocols call for a source that emits single photon signals, but the sources used in typical practical realizations emit weak coherent states instead. A weak coherent state may contain more than one photon, which poses a potential security risk. QKD with weak coherent state signals has nevertheless been proven to be secure, but only under the assumption that the phase of each signal is random (and completely unknown to the adversary). Since this assumption need not be fully justified in practice, it is important to know whether phase randomization is reall…
We provide a security analysis for continuous variable quantum key distribution protocols based on the transmission of squeezed vacuum states measured via homodyne detection. We employ a version of the entropic uncertainty relation for smooth entropies to give a lower bound on the number of secret bits which can be extracted from a finite number of runs of the protocol. This bound is valid under general coherent attacks, and gives rise to keys which are composably secure. For comparison, we also give a lower bound valid under the assumption of collective attacks. For both scenarios, we find po…
A precise security analysis of practical quantum key distribution (QKD) systems is an important step for improving their performance. Here we consider a class of quantum soft filtering operations, which generalizes the unambiguous state discrimination (USD) technique. These operations can be applied as a basis for a security analysis of the original coherent one-way (COW) QKD protocol since their application interpolates between beam-splitting (BS) and USD attacks. We demonstrate that a zero-error attack based on quantum soft filtering operations gives a larger amount of the information for Ev…
We investigate the security against collective attacks of a continuous variable quantum key distribution scheme in the asymptotic key limit for a realistic setting. The quantum channel connecting the two honest parties is assumed to be lossy and imposes Gaussian noise on the observed quadrature distributions. Secret key rates are given for direct and reverse reconciliation schemes including postselection in the collective attack scenario. The effect of a non-ideal error correction and two-way communication in the classical post-processing step is also taken into account.
All phase-encoded BB84 implementations have signal states with unbalanced amplitudes in practice. Thus, the original security analyses a priori do not apply to them. Previous security proofs use signal tagging of multi-photon pulses to recover the behaviour of regular BB84. This is overly conservative, as for unbalanced signals, the photon-number splitting attack does not leak full information to Eve. In this work, we exploit the flag-state squashing model to preserve some parts of the multi-photon generated private information in our analysis. Using a numerical proof technique, we obtain sign…
We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the key information is encoded in the relative phase of a coherent-state reference pulse and a weak coherent-state signal pulse, as in some practical implementations of the protocol. In contrast to previous work, our proof applies even if the eavesdropper knows the phase of the reference pulse, provided that this phase is not modulated by the source, and even if the reference pulse is bright. The proof also applies to the case where the key is encoded in the photon polarization of a weak co…
Security of Binary-Modulated Optical Key Distribution Against Quantum-Enhanced Coherent Eavesdropping
Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw（华沙大学新技术中心量子光学技术研究中心）；Faculty of Physics, University of Warsaw（华沙大学物理学院）；Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano（米兰大学阿尔多·庞特罗莫利物理系）；Istituto Nazionale di Fisica Nucleare, Sezione di Milano（意大利国家核物理研究所米兰分部）
Quantum cryptographic protocols based on complementarity are nonsecure against attacks in which complementarity is imitated with classical resources. The Kochen-Specker (KS) theorem provides protection against these attacks, without requiring entanglement or spatially separated composite systems. We analyze the maximum tolerated noise to guarantee the security of a KS-protected cryptographic scheme against these attacks, and describe a photonic realization of this scheme using hybrid ququarts defined by the polarization and orbital angular momentum of single photons.
We propose and demonstrate a quantum key distribution scheme in higher-order $d$-dimensional alphabets using spatial degrees of freedom of photons. Our implementation allows for the transmission of 4.56 bits per sifted photon, while providing improved security: an intercept-resend attack on all photons would induce an error rate of 0.47. Using our system, it should be possible to send more than a byte of information per sifted photon.
We consider the continuous-variable protocol of Pirandola et al. [Nature Photonics 9, 397-402 (2015), see also arXiv.1312.4104] where the secret-key is established by the measurement of an untrusted relay. In this network protocol, two authorized parties are connected to an untrusted relay by insecure quantum links. Secret correlations are generated by a continuous-variable Bell detection performed on incoming coherent states. In the present work we provide a detailed study of the symmetric configuration, where the relay is midway between the parties. We analyze symmetric eavesdropping strateg…
We consider the cloning of sequences of qubits prepared in the states used in the BB84 or 6-state quantum cryptography protocol, and show that the single-qubit fidelity is unaffected even if entire sequences of qubits are prepared in the same basis. This result is of great importance for practical quantum cryptosystems because it reduces the need for high-speed random number generation without impairing on the security against finite-size attacks.
We propose a non-deterministic two-way quantum key distribution in which the quantum correlation is established by transmitting the randomly polarized photon. We analyze the security of the proposed quantum key distribution against photon number splitting, impersonation, and Trojan horse attack and quantify the security bound against mean photon number of the coherent state pulse. Finally, we remark the characteristic features of the protocol.
We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The encryption operations require only rotations in phase space, which commute with computations in the codespace performed via passive linear optics, and with generalized non-linear phase operations that are polynomials of the photon-number operator in the codespace. This encoding scheme can thus be applied to any computation with coherent state inputs, and the computation proceeds via a combination of passive linear optics and generalized non-linear phase operations. An example of s…
To beat PNS attack, decoy state quantum key distribution (QKD) based on coherent state has been studied widely. We present a decoy state QKD protocol with modified coherent state (MCS). By destruction quantum interference, MCS with fewer multi-photon events can be get, which may improve key bit rate and security distance of QKD. Through numerical simulation, we show about 2-dB increment on security distance for BB84 protocol.
Security bounds for key distribution protocols using coherent and squeezed states and homodyne measurements are presented. These bounds refer to (i) general attacks and (ii) collective attacks where Eve interacts individually with the sent states, but delays her measurement until the end of the reconciliation process. For the case of a lossy line and coherent states, it is first proven that a secure key distribution is possible up to 1.9 dB of losses. For the second scenario, the security bounds are the same as for the completely incoherent attack.
