Optical homodyne detection has been widely used in continuous-variable (CV) quantum information processing for measuring field quadrature values. In this paper we explore the possibility of operating a conjugate homodyne detection system in "photon counting" mode to implement discrete-variable (DV) quantum key distribution (QKD) protocols. A conjugate homodyne detection system, which consists of a beam splitter followed by two optical homodyne detectors, can simultaneously measure a pair of conjugate quadratures X and P of the incoming quantum state. In classical electrodynamics, X^2 + P^2 is proportional to the energy (the photon number) of the input light. In quantum optics, X and P do not commute and thus the above photon-number measurement is intrinsically noisy. This suggests that a blind application of the standard security proof could result pessimistic QKD performance. We overcome this obstacle by taking advantage of two special features of the proposed detection scheme. First, the fundamental detection noise associated with vacuum fluctuation cannot be manipulated by an external adversary. Second, the ability to reconstruct the photon number statistics at the receiver's end can place additional constraints on possible attacks from the adversary. As an example, we study the security of the BB84 QKD using conjugate homodyne detection and evaluate its performance through numerical simulations. This study may open the door to a new family of QKD protocols, in complementary to the well-established DV-QKD based on single photon detection and CV-QKD based on coherent detection.
We study the problem of determining the photon number statistics of an unknown quantum state by simultaneously measuring conjugate quadratures with double homodyne detectors. Classically, the sum of the squared outputs of the two homodyne detectors is proportional to the intensity (thus the photon number) of the input light. Quantum mechanically, due to vacuum noise, the above photon number measurement is intrinsically noisy. We quantify the information gain in a single-shot measurement and discuss potential applications of this technology in quantum key distribution. We also show that the pho…
We report an experimental demonstration of optimal measurements of small displacement and tilt of a Gaussian beam - two conjugate variables - involving a homodyne detection with a TEM10 local oscillator. We verify that the standard split detection is only 64% efficient. We also show a displacement measurement beyond the quantum noise limit, using a squeezed vacuum TEM10 mode within the input beam.
We analyze the security against collective attacks for a homodyne-based continuous-variable quantum key distribution protocol using binary coherent states and postselection. We derive a lower bound of the secret key rate in an asymptotic scenario, and numerically optimize it for the case of a symmetric Gaussian channel.
The practical homodyne detector model of continuous-variable quantum key distribution models the inherent imperfections of the practical homodyne detector, namely the limited detection efficiency and the electronic noise, into trusted loss. However, the conventional practical homodyne detector model is valid only when both the imperfections of the practical homodyne detector are calibrated. In this paper, we show a modified practical homodyne detector model that can model the imperfections separately. The phase-sensitive amplifier is further applied to compensate the imperfections of the pract…
We present a QKD system with fainted pulses using self-homodyne coherent detection in optical fibers at 1543nm. BB84 protocol key is encoded in the optical phase using a twoelectrode Mach-Zehnder modulator, producing a QPSK modulation.
We discuss excess noise contributions of a practical balanced homodyne detector in Gaussian-modulated coherent-state (GMCS) quantum key distribution (QKD). We point out the key generated from the original realistic model of GMCS QKD may not be secure. In our refined realistic model, we take into account excess noise due to the finite bandwidth of the homodyne detector and the fluctuation of the local oscillator. A high speed balanced homodyne detector suitable for GMCS QKD in the telecommunication wavelength region is built and experimentally tested. The 3dB bandwidth of the balanced homodyne …
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.
We address binary optical communication channels based on phase-shift keyed coherent signals in the presence of phase diffusion. We prove theoretically and demonstrate experimentally that a discrimination strategy based on homodyne detection is robust against this kind of noise for any value of the channel energy. Moreover, we find that homodyne receiver beats the performance of Kennedy receiver as the signal energy increases, and achieves the Helstrom bound in the limit of large noise.
Discrete-modulated continuous-variable quantum key distribution with homodyne detection is widely recognized for its ease of implementation, efficiency with respect to error correction, and its compatibility with modern optical communication devices. However, recent studies report that the application of homodyne detection obtains poor tolerance to excess noise and insufficient transmission distance, hence seriously restricting the large-scale deployment of quantum secure communication networks. In this paper, we propose a homodyne detection protocol using the quadrature phase shift keying tec…
The role of squeezing in quantum key distribution with continuous variables based on homodyne detection and post-selection is investigated for several specific eavesdropping strategies. It is shown that amplitude squeezing creates strong correlations between the signals of the legitimate receiver and a potential eavesdropper. Post-selection of the received pulses can therefore be used to reduce the eavesdropper's knowledge of the raw key, which increases the secret key rate by orders of magnitude over large distances even for modest amounts of squeezing.
We compare the principles and experimental results of two different QPSK signal detection configurations, photon counting and super homodyning, for applications in fiber-optic Quantum Key Distribution (QKD) systems operating at telecom wavelength, using the BB84 protocol.
We propose a scheme for continuous-variable quantum cloning of coherent states with phase-conjugate input modes using linear optics. The quantum cloning machine yields $M$ identical optimal clones from $N$ replicas of a coherent state and $N$ its replicas of phase conjugate. This scheme can be straightforwardly implemented with the setup accessible at present since its optical implementation only employs simple linear optical elements and homodyne detection. Compared with the original scheme for continuous variables quantum cloning with phase-conjugate input modes proposed by Cerf and Iblisdir…
We propose an improved two-way continuous-variable quantum key distribution (CV QKD) protocol by adding proper random noise on the receiver's homodyne detection, the security of which is analysed against general collective attacks. The simulation result under the collective entangling cloner attack indicates that despite the correlation between two-way channels decreasing the secret key rate relative to the uncorrelated channels slightly, the performance of the two-way protocol is still far beyond that of the one-way protocols. Importantly, the added noise in detection is beneficial for the se…
Imperfect devices in commercial quantum key distribution systems open security loopholes that an eavesdropper may exploit. An example of one such imperfection is the wavelength dependent coupling ratio of the fiber beam splitter. Utilizing this loophole, the eavesdropper can vary the transmittances of the fiber beam splitter at the receiver's side by inserting lights with wavelengths different from what is normally used. Here, we propose a wavelength attack on a practical continuous-variable quantum key distribution system using homodyne detection. By inserting light pulses at different wavele…
Most quantum key distribution (QKD) protocols can be classified as either a discrete-variable (DV) protocol or continuous-variable (CV) protocol, based on how classical information is being encoded. We propose a protocol that combines the best of both worlds -- the simplicity of quantum state preparation in DV-QKD together with the cost-effective and high-bandwidth of homodyne detectors used in CV-QKD. Our proposed protocol has two highly practical features: (1) it does not require the honest parties to share the same reference phase (as required in CV-QKD) and (2) the selection of decoding ba…
Secure quantum key distribution with multimode Gaussian entangled states and multimode homodyne detectors is proposed. In general the multimode character of both the sources of entanglement and the homodyne detectors can cause a security break even for a perfect channel when trusted parties are unaware of the detection structure. Taking into account the multimode structure and potential leakage of information from a homodyne detector reduces the loss of security to some extent. We suggest the symmetrization of the multimode sources of entanglement as an efficient method allowing us to fully re…
We introduce a formalism of nonlinear canonical transformations for general systems of multiphoton quantum optics. For single-mode systems the transformations depend on a tunable free parameter, the homodyne local oscillator angle; for n-mode systems they depend on n heterodyne mixing angles. The canonical formalism realizes nontrivial mixings of pairs of conjugate quadratures of the electromagnetic field in terms of homodyne variables for single-mode systems; and in terms of heterodyne variables for multimode systems. In the first instance the transformations yield nonquadratic model Hamilton…
In this paper, we propose to use the decoy-state technique to improve the security of the quantum key distribution (QKD) systems based on homodyne detection against the photon number splitting (PNS) attack. The decoy-state technique is a powerful tool that can significantly boost the secure transmission range of the QKD systems. However it has not yet been applied to the systems that use coherent detection. After adapting this theory to the systems based on homodyne detection, we quantify the secure performance and transmission range of the resulting system.
In this paper we investigate the security of a quantum cryptographic scheme which utilizes balanced homodyne detection and weak coherent pulse (WCP). The performance of the system is mainly characterized by the intensity of the WCP and postselected threshold. Two of the simplest intercept/resend eavesdropping attacks are analyzed. The secure key gain for a given loss is also discussed in terms of the pulse intensity and threshold.
Asymmetry effects in homodyne and heterodyne measurements: Positive operator-valued measures and asymptotic security of Gaussian-continuous-variable quantum key distribution
ITMO University（伊托夫大学）；Laboratory for Quantum Communications, ITMO University（伊托夫大学量子通信实验室）；Laboratory of Quantum Processes and Measurements, ITMO University（伊托夫大学量子过程与测量实验室）
We propose an efficient strategy to attack a continuous-variable quantum key distribution (CV-QKD) system, that we call homodyne detector blinding. This attack strategy takes advantage of a generic vulnerability of homodyne receivers: a bright light pulse sent on the signal port can lead to a saturation of the detector electronics. While detector saturation has already been proposed to attack CV-QKD, the attack we study in this paper has the additional advantage of not requiring an eavesdropper to be phase locked with the homodyne receiver. We show that under certain conditions, an attacker ca…
We report an experimental quantum key distribution that utilizes balanced homodyne detection, instead of photon counting, to detect weak pulses of coherent light. Although our scheme inherently has a finite error rate, it allows high-efficiency detection and quantum state measurement of the transmitted light using only conventional devices at room temperature. When the average photon number was 0.1, an error rate of 0.08 and "effective" quantum efficiency of 0.76 were obtained.
We put forward a hybrid quantum key distribution protocol based on coherent states, Gaussian modulation, and photon-number-resolving (PNR) detectors, and show that it may enhance the secret key generation rate (KGR) compared to homodyne-based schemes. Improvement in the KGR may be traced back to the dependence of the two-dimensional discrete output variable on both the input quadratures, thus overcoming the limitations of the original protocol. When reverse reconciliation is considered, the scheme based on PNR detectors outperforms the homodyne one both for individual and collective attacks. I…
Low-noise, efficient, phase-sensitive time-domain optical detection is essential for foundational tests of quantum physics based on optical quantum states and the realization of numerous applications ranging from quantum key distribution to coherent classical telecommunications. Stability, bandwidth, efficiency, and signal-to-noise ratio are crucial performance parameters for effective detector operation. Here we present a high-bandwidth, low-noise, ultra-stable time-domain coherent measurement scheme based on balanced homodyne detection ideally suited to characterization of quantum and classi…
Quantum states of light having a Wigner function with negative values represent a key resource in quantum communication and quantum information processing. Here, we present the generation of such a state at the telecommunication wavelength of 1550nm. The state is generated by means of photon subtraction from a weakly squeezed vacuum state and is heralded by the `click' of a single photon counter. Balanced homodyne detection is applied to reconstruct the Wigner function, also yielding the state's photon number distribution. The heralding photons are frequency up-converted to 532nm to allow for …
The homodyne detection is one of the most basic tools for identifying the quantum state of light. It has been used to detect useful non-local properties, such as entanglement for the quantum teleportation and distillability of a secret key in quantum key distribution. In so doing, the detection scheme employs a bright optical pulse, called the local oscillator (LO) pulse, and the LO pulse is usually transmitted along with the signal pulses. The LO pulse is presumed to be a coherent state with an infinite intensity. However, it is difficult in practice to hold this presumption owing to noise in…
In this paper, we study the feasibility of conducting quantum key distribution (QKD) together with classical communication through the same optical fiber by employing dense-wavelength-division-multiplexing (DWDM) technology at telecom wavelength. The impact of the classical channels to the quantum channel has been investigated for both QKD based on single photon detection and QKD based on homodyne detection. Our studies show that the latter can tolerate a much higher level of contamination from the classical channels than the former. This is because the local oscillator used in the homodyne de…
Continuous-variable quantum key distribution (CV-QKD) has many practical advantages including compatibility with current optical communication technology. Implementation using heterodyne measurements is particularly attractive since it eliminates the need for active phase locking of the remote pair of local oscillators, but the full security of CV QKD with discrete modulation was only proved for a protocol using homodyne measurements. Here we propose an all-heterodyne CV-QKD protocol with binary modulation and prove its security against general attacks in the finite-key regime. Although replac…
Optical downconversion is a key resource for generating nonclassical states. Very recently, direct nondegenerate triple-photon spontaneous downconversion (NTPSD) with bright photon triplets and strong third-order correlations has been demonstrated in a superconducting device (2020 Phys. Rev. X 10 011011). Besides, linear and nonlinear tripartite entanglement in this process have also been predicted (2018 Phys. Rev. Lett. 120 043601; 2020 Phys. Rev. Lett. 125 020502). In this paper, we consider the generation of nonclassical optical quantum superpositions and investigate nonlinear quantum steer…
We identify and study a new security loophole in continuous-variable quantum key distribution (CV-QKD) implementations, related to the imperfect linearity of the homodyne detector. By exploiting this loophole, we propose an active side-channel attack on the Gaussian-modulated coherent state CV-QKD protocol combining an intercept-resend attack with an induced saturation of the homodyne detection on the receiver side (Bob). We show that an attacker can bias the excess noise estimation by displacing the quadratures of the coherent states received by Bob. We propose a saturation model that matches…
We present several quantum public-key encryption (QPKE) protocols designed with conjugate coding single-photon string, thus may be realized in laboratory with nowadays techniques. Two of these schemes are orienting one-bit message, and are extended to two kinds of QPKE schemes orienting multi-bits. The novel structure of these protocols ensures they are information-theoretically secure with, probably, a bound greater than any given polynomial of $n$. Finally, we describe a way to conceal the classical part of the public key with quantum state, this idea is expected to enhance a scheme to be in…
We expand the recently discussed continuous-variable quantum key distribution scheme of Heid and Luetkenhaus (2006) to qudits with a lossy but noiseless quantum channel. Postselection methods are used. Secret key rates are calculated in the presence of loss for the direct and the reverse reconciliation method. In the case of reverse reconciliation the secret key rate increases with higher dimensions, in the case of direct reconciliation the result is reverse. Several ways of optimising the amplitude are discussed. In a next step the used states are generalised to squeezed states. Again secret …
We present a quantum probabilistic encryption algorithm for a private-key encryption scheme based on conjugate coding of the qubit string. A probabilistic encryption algorithm is generally adopted in public-key encryption protocols. Here we consider the way it increases the unicity distance of both classical and quantum private-key encryption schemes. The security of quantum probabilistic private-key encryption schemes against two kinds of attacks is analyzed. By using the no-signalling postulate, we show that the scheme can resist attack to the key. The scheme's security against plaintext att…
We present the wavelength attack on a practical continuous-variable quantum-key-distribution system with a heterodyne protocol, in which the transmittance of beam splitters at Bob's station is wavelength-dependent. Our strategy is proposed independent of but analogous to that of Huang et al. [arXiv: 1206.6550v1 [quant-ph]], but in that paper the shot noise of the two beams that Eve sends to Bob, transmitting after the homodyne detector, is unconsidered. However, shot noise is the main contribution to the deviation of Bob's measurements from Eve's when implementing the wavelength attack, so it …
We present the integration of the optical and electronic subsystems of a BB84-QKD fiber link. A highspeed FPGA MODEM generates the random QPSK sequences for a fiber-optic delayed self-homodyne scheme using APD detectors.
We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon number resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, proof to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.
We give an achievable secret key rate of a binary modulated continuous variable quantum key distribution schemes in the collective attack scenario considering quantum channels that impose arbitrary noise on the exchanged signals. Bob performs homodyne measurements on the received states and the two honest parties employ a reverse reconciliation procedure in the classical post-processing step of the protocol.
Balanced homodyne detector (BHD) that can measure the field quadratures of coherent states has been widely used in a range of quantum information technologies. Generally, the BHD tends to suffer from narrow bands and an expanding bandwidth behavior usually traps into a compromise with the gain, electronic noise, and quantum to classical noise ratio, etc. In this paper, we design and construct a wideband BHD based on radio frequency and integrated circuit technology. Our BHD shows bandwidth behavior up to 1.2 GHz and its quantum to classical noise ratio is around 18 dB. Simultaneously, the BHD …
The continuous-variable quantum key distribution with entanglement in the middle, a semi-device-independent protocol, places the source at the untrusted third party between Alice and Bob, and thus has the advantage of high levels of security with the purpose of eliminating the assumptions about the source device. However, previous works considered the collective-attack analysis, which inevitably assumes that the states of the source has an identical and independently distributed (i.i.d) structure, and limits the application of the protocol. To solve this problem, we modify the original protoco…
We analyze homodyne detection of macroscopically bright multimode nonclassical states of light and propose their application in quantum communication. We observe that the homodyne detection is sensitive to a mode-matching of the bright light to the highly intense local oscillator. Unmatched bright modes of light result in additional noise which technically limits detection of Gaussian entanglement at macroscopic level. When the mode-matching is sufficient, we show that multimode quantum key distribution with bright beams is feasible. It finally merges the quantum communication with classical o…
In the Gaussian-modulated coherent states (GMCS) quantum key distribution (QKD) protocol, Alice prepares quantum states \emph{actively}: for each transmission, Alice generates a pair of Gaussian-distributed random numbers, encodes them on a weak coherent pulse using optical amplitude and phase modulators, and then transmits the Gaussian-modulated weak coherent pulse to Bob. Here we propose a \emph{passive} state preparation scheme using a thermal source. In our scheme, Alice splits the output of a thermal source into two spatial modes using a beam splitter. She measures one mode locally using …
Quantum key distribution with continuous variables already uses advantageous high-speed single-mode homodyne detection with low electronic noise at room temperature. Together with continuous-variable information encoding to nonclassical states, the distance for secure key transmission through lossy channels can approach 300 km in current optical fibers. Such protocols tolerate higher channel noise and also limited data processing efficiency compared to coherent-state protocols. The secret key rate can be further increased by increasing the system clock rates, and, further, by a suitable freque…
We show how to implement the optimal Gaussian $N$-to-$M$ cloning with linear optics and homodyne detection. We also show that the Gaussian $N$-to-$M$ cloning of known-phase coherent states can be performed with the fidelity $\sqrt \frac{2 M N}{2M N+M -N}$ by linear optics and homodyne detection, and with $\frac{2}{\sqrt{1+\frac{1}{N}}+\sqrt {1-\frac{1}{M}}}$ by utilizing quadrature squeezing. From the classical limit of the cloning (1-to-$\infty$ cloning), a necessary condition of continuous variable quantum key distribution using known-phase coherent states is provided.
Most continuous-variable quantum key distribution schemes are based on the Gaussian modulation of coherent states followed by continuous quadrature detection using homodyne detectors. In all previous schemes, the Gaussian modulation has been carried out in conjugate quadratures thus requiring two independent modulators for their implementations. Here, we propose and experimentally test a largely simplified scheme in which the Gaussian modulation is performed in a single quadrature. The scheme is shown to be asymptotically secure against collective attacks, and considers asymmetric preparation …
We examine different methods to implement coherent detection in the subcarrier wave quantum key distribution (SCW QKD) systems. For classical wavefields, we present the models describing homodyne-type and heterodyne-type coherent detection schemes needed to extract information from the quadrature phase-coded multimode signals used in SCW QKD. Practical feasibility of the proposed schemes is corroborated by the experiments.
We propose a new upper bound for the eavesdropper's information in the direct and reverse reconciliated coherent states quantum key distribution protocols with heterodyne detection. This bound is derived by maximizing the leaked information over the symplectic group of transformations that spans every physical Gaussian attack on individual pulses. We exhibit four different attacks that reach this bound, which shows that this bound is tight. Finally, we compare the secret key rate obtained with this new bound to the homodyne rate.
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.
