In this article we present a new prepare and measure quantum key distribution protocol that uses an experimentally accessible measure of single qubit contextuality to warranty the security of the quantum channel. The definition of contextuality used is that due to Spekkens in which any underlying hidden variable model of the physical system is noncontextual if the probability distribution of the model's hidden variables is independent of the preparation and measurement context. Under this more general definition of noncontextuality the measurement outcomes of a single qubit can be shown to require a contextual model in order to reproduce the results of some non-projective, positive operator valued measurements (POVMs). The proposed protocol utilizes a particular set of POVMs to exhibit the degree of contextuality of the qubits exiting the QKD system's quantum channel. The contextuality measure is defined in terms of the weak values of a set of projective measurements that are implemented as POVMs using weak measurements. The resulting QKD protocol should have a key rate that is equal to or greater than BB84 since none of the sifted key is used to test for the presence of an eavesdropper. Additionally, the new protocol is shown to be immune to detector based attacks.
In this article we present a new prepare and measure quantum key distribution protocol that uses an experimentally accessible measure of single qubit contextuality to warranty the security of the quantum channel. The definition of contextuality used is that due to Spekkens in which any underlying hidden variable model of the physical system is noncontextual if the probability distribution of the model's hidden variables is independent of the preparation and measurement context. Under this more general definition of noncontextuality the measurement outcomes of a single qubit can be shown to require a contextual model in order to reproduce the results of some non-projective, positive operator valued measurements (POVMs). The proposed protocol utilizes a particular set of POVMs to exhibit the degree of contextuality of the qubits exiting the QKD system's quantum channel. The contextuality measure is defined in terms of the weak values of a set of projective measurements that are implemented as POVMs using weak measurements. The resulting QKD protocol should have a key rate that is equal to or greater than BB84 since none of the sifted key is used to test for the presence of an eavesdropper. Additionally, the new protocol is shown to be immune to detector based attacks.
Bell nonlocality allows secret key to be certified without trusting the internal operation of the devices, and even against eavesdroppers constrained only by the no-signaling principle. We ask whether generalized contextuality, a notion of nonclassicality available in prepare-and-measure experiments on a single system, can play an analogous role. In our approach, Alice and Bob first establish operational equivalences among their local preparation and measurement procedures, which are then treated as theory-independent constraints that any physical intervention on the communication channel, including that of an adversary, must respect. Eve is otherwise unrestricted, that is, her intervention on the transmitted system is not assumed to be described by quantum theory. Within this adversarial model, we show that Eve's optimal guessing probability against individual attacks is the solution of a finite linear program, and hence that a worst-case asymptotic key rate follows from the observed statistics and the operational equivalences alone. We prove that contextuality is necessary for a positive key rate. However, we also show that it is not sufficient. Concretely, the (3,2)-parity-oblivious random access code, known to yield secret key against a quantum eavesdropper, yields none certifiable key rate against a post-quantum one. Conversely, operational equivalences with no analogue among no-signaling constraints can strictly increase the asymptotic key rate. We illustrate this with the prepare-and-measure version of the standard CHSH protocol with an aligned key-generating setting.
In this article we present a new prepare and measure quantum key distribution protocol that decouples the necessary quantum channel error estimation from its dependency on sifting, or otherwise post-selecting, the detection outcomes. Rather than estimating Eve's coupling to the quantum channel from the statistics of the sifted key, we infer this information from weak measurements made equally on all of the received photons immediately prior to post-selection by the photon detectors. We prove that the accuracy of the weak measurement parameter estimation is robust to reasonable device imperfections, even in an adversarial environment, and hence the asymptotic security of this protocol can be inferred from the security analysis of BB84. In addition to eliminating detector basis-dependent attacks, such as detector blinding, we demonstrate that this new prepared and measure QKD protocol is immune to a very powerful class of measurement-side device attacks that also allow an adversary control of the weak measurement outcomes given two modest requirements placed on the measurement-side devices. Finally, we compare the asymptotically achievable secure key rate of a decoy state version of the weak measurement protocol and show it is essentially equal to that of BB84 with decoy states and significantly higher than MDI-QKD for realistic system parameters.
Every quantum key distribution (QKD) protocol must limit the information available outside the users' laboratories. In device-independent QKD this is essentially the only assumption made on the devices. In a prepare-and-measure setting it cannot be imposed strictly, since the sender's device must emit a signal that depends on her private input. The natural replacement, and a minimal one, is a leakage bound: a bound on how much information about the input leaves the sender's laboratory, through the intended signal or through any side channel. We ask how far this unavoidable requirement can replace a detailed model of the source. We show that this single bound, quantified by the probability of guessing the input from everything the source emits, suffices to prove security against collective attacks. In our analysis, nothing is assumed about the precise form of the emitted states, their dimension, energy or purity, nor about the receiver's measurement device, beyond the standard requirement that it does not leak Bob's data. The standard B92 and BB84 protocols do not certify any key under this minimal leakage bound assumption. But closely related protocols can and, in the ideal limit, achieve one secret bit per key round. For noisy implementations, we compute key rates using semidefinite programming relaxations. Our best protocols tolerate visibilities down to 0.84, corresponding to an 8% quantum bit error rate, compared with the 11% threshold of standard device-dependent BB84.
The prepare-and-measure quantum key distribution (QKD) has the merits of fast speed, high key generation rate, and easy implementation. However, the detector side channel attacks greatly undermine the security of the key bits. The eavesdropper, Eve, exploits the flaws of the detectors to obtain illegal information without violating quantum principles. It means that she can intervene in the communication without being detected. A prepare-and-measure Bell test protocol will be proposed. By randomly carrying out Bell test at the side of the information receiver, Bob, Eve's illegal information gain within the detector side channel attack can be well bounded. This protocol does not require any improvement on the detectors used in available prepare-and-measure QKD. Though we only illustrate its application in the BB84 protocol, it is applicable for any prepare-and-measure QKD.
The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios, including contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations, we demonstrate monogamy of preparation contextuality in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.
Quantum key distribution (QKD) allows two spatially separated parties to securely generate a cryptographic key. The first QKD protocol, published by C. H. Bennett and G. Brassard in 1984 (BB84), describes how this is achieved by transmitting individual qubits and exchanging classical authenticated information. Any attempt to eavesdrop on the protocol introduces errors detectable by the legitimate parties. This Licentiate Thesis studies the recently introduced EEQKD protocol which builds on BB84. In EEQKD, the qubits sent individually in BB84 are entangled and thus not directly available to an eavesdropper who is, in this protocol, provided only one-by-one access to the transmission. The maximal information an eavesdropper can gain using a straightforward intercept-resend (IR) attack, is obtained for a given error rate. The secure key generation rate of EEQKD is estimated in practical scenarios including qubit loss and quantum channel noise. In addition, an exquisite vulnerability is exposed: For a particular setting of qubit entanglement, paradoxically proving most useful in the face of an IR attack, EEQKD reduces to BB84. Part of this research has been published in O. Ahonen et al., Physical Review A 78, 032314 (2008).