Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is a novel protocol which eliminates all possible attacks on detector side and necessity of reference-frame alignment in source sides. However, its performance may degrade notably due to statistical fluctuations, since more parameters, e.g. yields and error rates for mismatched-basis events, must be accumulated to monitor the security. In this work, we find that the original decoy-states method estimates these yields over pessimistically since it ignores the potential relations between different bases. Through processing parameters of different bases jointly, the performance of RFI-MDI-QKD is greatly improved in terms of secret key rate and achievable distance when statistical fluctuations are considered. Our results pave an avenue towards practical RFI-MDI-QKD.
Without actively aligning the reference frames, the reference-frame-independent quantum key distribution (RFI-QKD) can generate secure keys even when the reference frames drift slowly. Here, we propose a new scheme on the decoy-state RFI-QKD, where the basis assignments of two legitimate parties are biased, reducing the fraction of mismatched-basis data. When accounting for statistical fluctuations under different misalignments of reference frames, we investigate the performance of biased decoy-state RFI-QKD with full parameter optimization. We also make a clear comparison between the new sche…
In this work, we incorporate decoy-state analysis into a well-established numerical framework for key rate calculation, and apply the numerical framework to decoy-state BB84 and measurement-device-independent (MDI) QKD protocols as examples. Additionally, we combine with these decoy-state protocols what is called "fine-grained statistics", which is a variation of existing QKD protocols that makes use of originally discarded data to get a better key rate. We show that such variations can grant protocols resilience against any unknown and slowly changing rotation along one axis, similar to refer…
To the active basis choice decoy state quantum key distribution systems with detector efficiency mismatch, we present a modified attack strategy, which is based on faked states attack, with quantum nondemolition measurement ability to restress the threat of detector efficiency mismatch. Considering that perfect quantum nondemolition measurement ability dose not exist in real life, we also propose a practical attack strategy using photon number resolving detectors. Theoretical analysis and numerical simulation results show that, without changing the channel, our attack strategies are serious th…
Twin-field quantum key distribution (TF-QKD) and its variants can overcome the fundamental rate-distance limit of QKD which has been demonstrated in the laboratory and field while their physical implementations with side channels remains to be further researched. We find the external modulation of different intensity states through the test, required in those TF-QKD with post-phase compensation, shows a side channel in frequency domain. Based on this, we propose a complete and undetected eavesdropping attack, named passive frequency shift attack, on sending or not-sending (SNS) TF-QKD protocol…
Decoy state method quantum key distribution (QKD) is one of the promising practical solutions to BB84 QKD with coherent light pulses. In the real world, however, statistical fluctuations with the finite code length cannot be negligible, and the securities of theoretical and experimental researches of the decoy method state QKD so far are based on the asymptotic GLLP's formula which guarantees only that the limit of eavesdropper's information becomes zero as the code length approaches infinity. In this paper, we propose a substantially improved decoy state QKD in the framework of the finite cod…
The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines the key-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making an number of heuristic assump…
Quantum key distribution (QKD) promises provably secure communications. In order to improve the secret key rate, combining a biased basis choice with the decoy-state method is proposed. Concomitantly, there is a basis-independent detection efficiency condition, which usually cannot be satisfied in a practical system, such as the time-phase encoding. Fortunately, this flaw has been recently removed theoretically and experimentally using the fact that the expected yields of single-photon states prepared in two bases stay the same for a given measurement basis. However, the security proofs do not…
Reference-Frame-Independent quantum key distribution (RFI-QKD) is known to be robust against slowly varying reference frames. However, other QKD protocols such as BB84 can also provide secrete keys if the speed of the relative motion of the reference frames is slow enough. While there has been a few studies to quantify the speed of the relative motion of the reference frames in RFI- QKD, it is not yet clear if RFI-QKD provides better performance than other QKD protocols under this condition. Here, we analyze and compare the security of RFI-QKD and BB84 protocol in the presence of the relative …
We have demonstrated a proof-of-principle experiment of reference-frame-independent phase coding quantum key distribution (RFI-QKD) over an 80-km optical fiber. After considering the finite-key bound, we still achieve a distance of 50 km. In this scenario, the phases of the basis states are related by a slowly time-varying transformation. Furthermore, we developed and realized a new decoy state method for RFI-QKD systems with weak coherent sources to counteract the photon-number-splitting attack. With the help of a reference-frame-independent protocol and a Michelson interferometer with Farada…
A novel protocol - measurement-device-independent quantum key distribution (MDI-QKD) - removes all attacks from the detection system, the most vulnerable part in QKD implementations. In this paper, we present an analysis for practical aspects of MDI-QKD. To evaluate its performance, we study various error sources by developing a general system model. We find that MDI-QKD is highly practical and thus can be easily implemented with standard optical devices. Moreover, we present a simple analytical method with only two (general) decoy states for the finite decoy-state analysis. This method can be…
We introduce a novel form of decoy-state technique to make the single-photon Bennett 1992 protocol robust against losses and noise of a communication channel. Two uninformative states are prepared by the transmitter in order to prevent the unambiguous state discrimination attack and improve the phase-error rate estimation. The presented method does not require strong reference pulses, additional electronics or extra detectors for its implementation.
Secure quantum key distribution can be achieved with an imperfect single-photon source through implementing the decoy-state method. However, security of all those theoretical results of decoy-state method based on the original framework raised by Hwang needs monitoring the source state very carefully, because the elementary proposition that the counting rates of the same state from different sources are equal does not hold in general when the source is unstable. Source intensity monitoring greatly decreases the system efficiency. Here without using Hwang's proposition for stable source, we pre…
Measurement-device-independent quantum key distribution (MDI-QKD) is proved to be able to eliminate all potential detector side channel attacks. Combining with the reference frame independent (RFI) scheme, the complexity of practical system can be reduced because of the unnecessary alignment for reference frame. Here, based on polarization multiplexing, we propose a time-bin encoding structure, and experimentally demonstrate the RFI-MDI-QKD protocol. Thanks to this, two of the four Bell states can be distinguished, whereas only one is used to generate the secure key in previous RFI-MDI-QKD exp…
Measurement-device-independent quantum key distribution (MDI-QKD) can remove all detection side-channels from quantum communication systems. The security proofs require, however, that certain assumptions on the sources are satisfied. This includes, for instance, the requirement that there is no information leakage from the transmitters of the senders, which unfortunately is very difficult to guarantee in practice. In this paper we relax this unrealistic assumption by presenting a general formalism to prove the security of MDI-QKD with leaky sources. With this formalism, we analyze the finite-k…
The security of a passive plug-and-play QKD arrangement in the case of finite (resources) key lengths is analysed. It is assumed that the eavesdropper has full access to the channel so an unknown and untrusted source is assumed. To take into account the security of the BB84 protocol under collective attacks within the framework of quantum adversaries, a full treatment provides the well-known equations for the secure key rate. A numerical simulation keeping a minimum number of initial parameters constant as the total error sought and the number of pulses is carried out. The remaining parameters…
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…
Decoy-state quantum key distribution (QKD) has convincingly been shown the core solution to secure key exchange. While standard BB84 protocol needs to prepare and measure all states of two complementary bases, which seriously restricts its real life applications in photonic integration and high speed system. Fortunately, a simplified BB84, only sending and receiving three states, achieves the same asymptotic secret key rate compared with standard BB84 under coherent attacks. In this work, by skillfully exploiting uncertainty relation for smooth entropies, we provide the finite-key security bou…
Decoy-state quantum key distribution (QKD) is a standard technique in current quantum cryptographic implementations. Unfortunately, existing experiments have two important drawbacks: the state preparation is assumed to be perfect without errors and the employed security proofs do not fully consider the finite-key effects for general attacks. These two drawbacks mean that existing experiments are not guaranteed to be secure in practice. Here, we perform an experiment that for the first time shows secure QKD with imperfect state preparations over long distances and achieves rigorous finite-key s…
We investigate the transformation rule of a single particle wave-function under a change of reference frame. A postulate is raised, and some fundamental aspects regarding the reference-frame independence of quantum probabilities are explored.
Any quantum communication task requires a common reference frame (i.e. phase, coordinate system). In particular, Quantum Key Distribution requires different bases for preparation and measurements of states which are obviously based on the existence of a common frame of reference. Here we show how QKD can be achieved in the absence of any common frame of reference. We study the coordinate reference frame, where the two parties do not even share a single direction, but the method can be generalized to other general frames of reference, pertaining to other groups of transformations.
Quantum metrology studies quantum strategies which enable us to outperform their classical counterparts. In this framework, the existence of perfect classical reference frames is usually assumed. However, such ideal reference frames might not always be available. The reference frames required in metrology strategies can either degrade or become misaligned during the estimation process. We investigate how the imperfectness of reference frames leads to noise which in general affects the ultimate precision limits in measurement of physical parameters. Moreover, since quantum parameter estimation …
We present two new schemes for quantum teleportation between parties whose local reference frames are misaligned by the action of a compact Lie group G. These schemes require no prior alignment of reference frames and are unaffected by arbitrary changes in reference frame alignment during execution, suiting them to situations of rapid reference frame drift. Our tight scheme yields improved purity compared to standard teleportation, in some cases substantially --- this includes the case of qubit teleportation under arbitrary SU(2) reference frame uncertainty--- while communicating no informatio…
We show that communication without a shared reference frame is possible using entangled states. Both classical and quantum information can be communicated with perfect fidelity without a shared reference frame at a rate that asymptotically approaches one classical bit or one encoded qubit per transmitted qubit. We present an optical scheme to communicate classical bits without a shared reference frame using entangled photon pairs and linear optical Bell state measurements.
We define a new quantity called refbit, which allows one to quantify the resource of sharing a reference frame in quantum communication protocols. By considering both asymptotic and nonasymptotic protocols we find relations between refbits and other communication resources. We also consider the same resources in encoded, reference-frame independent, form. This allows one to rephrase and unify previous work on phase references, reference frames, and superselection rules.
A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described. By introducing a relational formalism which identifies coordinate systems with elements of a symmetry group $G$, we define a general operator for reversibly changing between quantum reference frames associated to a group $G$. This generalises the known operator for translations and boosts to arbitrary finite and locally compact groups, including non-Abelian groups. We show under which conditio…
A simple procedure to derive the transformation of a wavefunction under a change of reference frame is applied to some examples and its relation with the transformation of the Hamilton principal function is studied.
In order to communicate information in a quantum network effectively, all network nodes should share a common reference frame. Here, we propose to study how well m nodes in a quantum network can establish a common reference frame from scratch, even though t of them may be arbitrarily faulty. We present a protocol that allows all correctly functioning nodes to agree on a common reference frame as long as not more than t < m/3 nodes are faulty. Our protocol furthermore has the appealing property that it allows any existing two-party protocol for reference frame agreement to be lifted to a protoc…
Quantum experiments usually assume the existence of perfect, classical, reference frames, which allow for the specification of measurement settings (e.g. orientation of the Stern Gerlach magnet in spin measurements) with arbitrary precision. If the reference frames are "bounded" (i.e. quantum systems themselves, having a finite number of degrees of freedom), only limited precision can be attained. Using spin coherent states as bounded reference frames we have found their minimal size needed to violate local realism for entangled spin systems. For composite systems of spin-1/2 particles referen…
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox "absolute" quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a long-standing…
In a recent Letter [G. Chiribella et al., Phys. Rev. Lett. 98, 120501 (2007)], four protocols were proposed to secretly transmit a reference frame. Here We point out that in these protocols an eavesdropper can change the transmitted reference frame without being detected, which means the consistency of the shared reference frames should be reexamined. The way to check the above consistency is discussed. It is shown that this problem is quite different from that in previous protocols of quantum cryptography.
We investigate the degradation of reference frames, treated as dynamical quantum systems, and quantify their longevity as a resource for performing tasks in quantum information processing. We adopt an operational measure of a reference frame's longevity, namely, the number of measurements that can be made against it with a certain error tolerance. We investigate two distinct types of reference frame: a reference direction, realized by a spin-j system, and a phase reference, realized by an oscillator mode with bounded energy. For both cases, we show that our measure of longevity increases quadr…
Quantum communication without a shared reference frame or the construction of a relational quantum theory requires the notion of a quantum reference frame. We analyze aspects of quantum reference frames associated with non-compact groups, specifically the group of spatial translations and Galilean boosts. We begin by demonstrating how the usually employed group average, used to dispense of the notion of an external reference frame, leads to unphysical states when applied to reference frames associated with non-compact groups. However, we show that this average does lead naturally to a reduced …
We generalize a quantum communication protocol introduced by Bartlett et al. [New. J. Phys. 11, 063013 (2009)] in which two parties communicating do not share a classical reference frame, to the case where changes of their reference frames form a one-dimensional noncompact Lie group. Alice sends to Bob the state $ρ_R \otimes ρ_S$, where $ρ_S$ is the state of the system Alice wishes to communicate and $ρ_R$ is the state of an ancillary system serving as a token of her reference frame. Because Bob is ignorant of the relationship between his reference frame and Alice's, he will describe the state…
A transition of focus from state space to frames of reference and their transformations is argued as being the appropriate setup for ensuring the covariance of physical laws. Such an approach can not only simplify and clarify aspects of General Relativity, but can possibly help in the development of a Grand Unified Theory as well.
Quantum Darwinism describes objectivity of quantum systems via their correlations with their environment--information that hypothetical observers can recover by measuring the environments. However, observations are done with respect to a frame of reference. Here, we take the formalism of [Giacomini, Castro-Ruiz, & Brukner. Nat Commun 10, 494 (2019)], and consider the repercussions on objectivity when changing quantum reference frames. We find that objectivity depends on non-degenerative relative separations, conditional state localisation, and environment macro-fractions. There is different ob…
We propose a covariant protocol for transmitting reference frames encoded on $N$ spins, achieving sensitivity $N^{-2}$ without the need of a pre-established reference frame and without using entanglement between sender and receiver. The protocol exploits the use of equivalent representations, which were overlooked in the previous literature.
The optimal N qubit states featuring highest sensitivity to small misalignment of cartesian reference frames are found using the Quantum Cramer-Rao bound. It is shown that the optimal states are supported on the symmetric subspace and hence are mathematically equivalent to a single spin J=N/2. Majorana representation of spin states is used to reveal a beautiful connection between the states optimal for aligning reference frames and the platonic solids.
We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communication model.
In quantum communication protocols the existence of a shared reference frame between two spatially separated parties is normally presumed. However, in many practical situations we are faced with the problem of misaligned reference frames. In this paper, we study communication between two inertial observers who have partial knowledge about the Lorentz transformation that relates their frames of reference. Since every Lorentz transformation can be decomposed into a pure boost followed by a rotation, we begin by analysing the effects on communication when the parties have partial knowledge about …
