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arXiv:1412.6870 · Scientific Reports

Gaussian private quantum channel with squeezed coherent states

Kabgyun Jeong, Jaewan Kim, Su-Yong Lee

Published Sep 14, 2015• 10 citations
arXivHTMLPDF

Abstract

While the objective of conventional quantum key distribution (QKD) is to secretly generate and share the classical bits concealed in the form of maximally mixed quantum states, that of private quantum channel (PQC) is to secretly transmit individual quantum states concealed in the form of maximally mixed states using shared one-time pad and it is called Gaussian private quantum channel (GPQC) when the scheme is in the regime of continuous variables. We propose a GPQC enhanced with squeezed coherent states (GPQCwSC), which is a generalization of GPQC with coherent states only (GPQCo) [Phys. Rev. A 72, 042313 (2005)]. We show that GPQCwSC beats the GPQCo for the upper bound on accessible information. As a subsidiary example, it is shown that the squeezed states take an advantage over the coherent states against a beam splitting attack in a continuous variable QKD. It is also shown that a squeezing operation can be approximated as a superposition of two different displacement operations in the small squeezing regime.

DOI
10.1038/srep13974

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While the objective of conventional quantum key distribution (QKD) is to secretly generate and share the classical bits concealed in the form of maximally mixed quantum states, that of private quantum channel (PQC) is to secretly transmit individual quantum states concealed in the form of maximally mixed states using shared one-time pad and it is called Gaussian private quantum channel (GPQC) when the scheme is in the regime of continuous variables. We propose a GPQC enhanced with squeezed coherent states (GPQCwSC), which is a generalization of GPQC with coherent states only (GPQCo) [Phys. Rev. A 72, 042313 (2005)]. We show that GPQCwSC beats the GPQCo for the upper bound on accessible information. As a subsidiary example, it is shown that the squeezed states take an advantage over the coherent states against a beam splitting attack in a continuous variable QKD. It is also shown that a squeezing operation can be approximated as a superposition of two different displacement operations in the small squeezing regime.
In this paper we introduce the concept of quantum private channel within the continuous variables framework (CVPQC) and investigate its properties. In terms of CVPQC we naturally define a ``maximally'' mixed state in phase space together with its explicit construction and show that for increasing number of encryption operations (which sets the length of a shared key between Alice and Bob) the encrypted state is arbitrarily close to the maximally mixed state in the sense of the Hilbert-Schmidt distance. We bring the exact solution for the distance dependence and give also a rough estimate of the necessary number of bits of the shared secret key (i.e., how much classical resources are needed for an approximate encryption of a generally unknown continuous-variable state). The definition of the CVPQC is analyzed from the Holevo bound point of view which determines an upper bound of information about an incoming state an eavesdropper is able to get from his optimal measurement.
Continuous-variable quantum key distribution (CV-QKD) has gathered significant interest for its potential to achieve high secret key rates and seamless integration with existing optical communication infrastructure. State-of-the-art CV-QKD systems primarily use coherent states for simplicity. However, squeezed states of light have been theoretically shown to offer significant advantages, including higher secret key rates, greater resilience to excess noise, and reduced requirements on information reconciliation efficiency. In this work, we experimentally verify these theoretical predictions and propose and demonstrate a practical squeezed-state CV-QKD system based on modern local-local oscillator and digital signal processing techniques. Operating over fiber channels and considering finite-size security against collective attacks, we show the advantages of our system over its coherent-state counterpart. Our work paves the way for squeezed states to become practical resources for quantum key distribution and other quantum information protocols.
The discrete modulation of quantum states as in BB84 stems fairly naturally from the need to produce zeroes and ones for the final secret key. But since secret-key distillation can also process continuous key elements, there is no reason not to investigate the continuous modulation of quantum states. In fact, continuous-variable protocols are fairly elegant alternatives to their discrete counterparts and allow for high secret key rates. In this chapter, I describe two important QKD protocols involving continuous variables: first a protocol involving the Gaussian modulation of squeezed states and then a protocol with coherent states. These QKD protocols must be seen as a source of Gaussian key elements, from which we can extract a secret key. Finally, I detail the implementation of the protocol with coherent states. From discrete to continuous variables In the scope of continuous-variable QKD, we focus on quantum states that are represented in a continuous Hilbert space, of which their most notable examples are the coherent and squeezed states. The BB84 protocol was designed with single photon states in mind. The coherent states, much easier to produce, are used only as an approximation of single photon states.
We extend the formalism of cluster-state quantum secret sharing, as presented by Markham and Sanders [Phys. Rev. A 78, 042309 (2008)] and Keet et al. [Phys. Rev. A 82, 062315 (2010)], to the continuous-variable regime. We show that both classical and quantum information can be shared by distributing continuous-variable cluster states through either public or private channels. We find that the adversary structure is completely denied from the secret if the cluster state is infinitely squeezed, but some secret information would be leaked if a realistic finitely squeezed state is employed. We suggest benchmarks to evaluate the security in the finitely squeezed cases. For the sharing of classical secrets, we borrow techniques from the continuous-variable quantum key distribution to compute the secret-sharing rate. For the sharing of quantum states, we estimate the amount of entanglement distilled for teleportation from each cluster state.
In this paper we investigate the security of continuous variable BB84 quantum key distribution protocol using single photon added then subtracted squeezed coherent state SPASSCS. It's found that the SPASSCS is a non-Gaussian and nonclassical state. Its non-Gaussianity and non-classicality are exhibited via the Wigner function. It's shown that the proposed state is generally robust against the eavesdropping strategies, such as intercept-resend attack and superior channel attack. Further, a comparative study has proved the strong efficiency of the proposed state over coherent state, squeezed coherent state and photon added then subtracted coherent state. Our analysis employs bit error rate, mutual information, and secure key gain.
Quantum key distribution (QKD) protocols allow two trusted parties to distribute a cryptographic key which they can further use for the unconditionally secure classical communication. During the last decades the field has grown mature with the commercial prototypes being available. They mostly rely on the faint laser pulses implementing the protocols on the basis of single qubits and qubit pairs. Alternatively, the continuous-variable (CV) protocols based on the multi-photon states of light were developed recently. They are typically built using the quadrature modulation of the coherent or squeezed states and subsequent homodyne detection. In the case of Gaussian modulation the security of the protocols is based on the extremality of Gaussian states, which allows estimating bounds on the leaked information. The Gaussian CV QKD protocols were shown secure for any degree of channel attenuation, but are restricted by the channel noise. Moreover, the applicability of Gaussian CV QKD protocols is limited by the effectiveness of classical post-processing algorithms, used by the trusted parties to process the measured data and distill the cryptographic key. On the other hand, the squeezedstate CV QKD protocols were previously considered ineffective under limited degrees of squeezing, while strong squeezing remains experimentally challenging. In the present work we distinguish between the classical and quantum resources in the Gaussian CV QKD and address the role of nonclassicality in the Gaussian protocols. We demonstrate, that by properly combining squeezed resource and coherent modulation, trusted parties are able to decouple eavesdropper from the channel, thus being able to establish the secure key from any amount of the classical mutual information. Our result shows a very promising path towards the long-distance CV QKD.