Design and Analysis of Communication Protocols using Quantum Resources
Mitali Sisodia
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Ph.D. Thesis. Optimal quantum communication schemes with proof of principle experiments on IBM quantum experience and optical designs of quantum cryptographic schemes. Based on arXiv:1610.02514, arXiv:1705.00670, arXiv:1704.05294, arXiv:1804.01776
This thesis is focused on the design and analysis of quantum communication protocols. Several schemes for quantum communication have been introduced in the recent past. For example, quantum teleportation, dense coding, quantum key distribution, quantum secure direct communication, etc., have been rigorously studied in the last 2-3 decades. Specifically, a specific attention of the present thesis is to study the quantum teleportation schemes with entangled orthogonal and nonorthogonal states and their experimental realization, but not limited to it. We have also studied some aspects of quantum cryptography.
We present an one-time-pad key communication protocol that allows secure direct communication with entanglement. Alice can send message to Bob in a deterministic manner by using local measurements and public communication. The theoretical efficiency of this protocol is double compared with BB84 protocol. We show this protocol is unconditional secure under arbitrary quantum attack. And we discuss that this protocol can be perfectly implemented with current technologies.
We provide a quantum key distribution protocol based on the correlations of the Greenburger-Horne-Zeilinger(GHZ) state. No classical communication is needed in the process of the establishment of the key. Our protocol is useful when an unjammable classical communication channel is unavailable. We prove that the protocol is secure.
We propose a W state-based protocol for anonymously transmitting quantum messages in a quantum network. Different from the existing protocols [A. Unnikrishnan, et al., Phys. Rev. Lett. 122, 240501 (2019)], the proposed protocol can be effectively implemented in the network only equipped with quantum channels and regular broadcast channels. Throughout the design procedure, we develop three sub-protocols using the W state, including the quantum collision detection protocol and the quantum notification protocol. Moreover, together with the conventional anonymous entanglement protocol, the whole a…
In this letter a deterministic secure direct bidirectional communication protocol is proposed by using the quantum entanglement and local unitary operations on one photon of the Einstein-Podolsky-Rosen (EPR) photon pair.
We show a deterministic secure direct communication protocol using single qubit in mixed state. The security of this protocol is based on the security proof of BB84 protocol. It can be realized with current technologies.
The crucial issue of quantum communication protocol is its security. In this paper, we show that all the deterministic and direct two-way quantum communication protocols, sometimes called ping-pong (PP) protocols, are insecure when an eavesdropper uses the invisible photon to eavesdrop on the communication. With our invisible photon eavesdropping (IPE) scheme, the eavesdropper can obtain full information of the communication with zero risk of being detected. We show that this IPE scheme can be implemented experimentally with current technology. Finally, a possible improvement of PP communicati…
I argue that recent "Protocol for Direct Counterfactual Quantum Communication" by Salih et al. [PRL 110, 170502 (2013), arXiv:1206.2042] is counterfactual only for one type of the information bit.
Recently, Hassanpour and Houshmand have proposed a protocol of controlled deterministic secure quantum communication (Quant. Info. Process, DOI 10.1007/s11128-014-0866-z (2014)). The authors compared the efficiency of their protocol with that of two other existing protocols and claimed that their protocol is efficient. Here, we have shown that the efficiency of Hassanpour Houshmand (HH) protocol is not high, and there exist several approaches through which more efficient protocols for the same task can be designed. To establish this point, we have proposed an efficient protocol of controlled d…
In light of Deng-Long-Liu's two-step secret direct communication protocol using the Einstein-Podolsky-Rosen pair block [Phys. Rev. A {\bf 68}, 042317 (2003)], by introducing additional local operations for encoding, we propose a brand-new secure direct communication protocol, in which two legitimate users can simultaneously transmit their different secret messages to each other in a set of quantum communication device.
The proposed eavesdropping scheme reveals that the quantum communication protocol recently presented by Bostrom and Felbinger [Phys. Rev. Lett. 89, 187902 (2002)] is not secure as far as quantum channel losses are taken into account.
We discuss the robustness of two-way quantum communication protocols against Trojan horse attack and introduce a novel attack, delay-photon Trojan horse attack. Moreover, we present a practical way for two-way quantum communication protocols to prevent the eavesdropper from stealing the information transmitted with Trojan horse attacks. It means that two-way quantum communication protocols is also secure in a practical application.
Counterfactual communication, i.e., communication without particle travelling in the transmission channel, is a bizarre quantum effect. Starting from interaction-free measurements many protocols achieving various tasks from counterfactual cryptogrphy to counterfactual transfer of quantum states were proposed and implemented in experiments. However, the meaning of conterfactuality in various protocols remained a controversial topic. A simple error-free counterfactual protocol is proposed. This protocol and its modification are used as a test bed for analysis of meaning of counterfactuality to c…
The unique features of quantum walk, such as the possibility of the walker to be in superposition ofthe position space and get entangled with the position space, provides inherent advantages that canbe captured to design highly secure quantum communication protocols. Here we propose two quan-tum direct communication protocols, a Quantum Secure Direct Communication (QSDC) protocoland a Controlled Quantum Dialogue (CQD) protocol using discrete-time quantum walk on a cycle.The proposed protocols are unconditionally secure against various attacks such as the intercept-resend attack, the denial of …
The effect of noise on various protocols of secure quantum communication has been studied. Specifically, we have investigated the effect of amplitude damping, phase damping, squeezed generalized amplitude damping, Pauli type as well as various collective noise models on the protocols of quantum key distribution, quantum key agreement,quantum secure direct quantum communication and quantum dialogue. From each type of protocol of secure quantum communication, we have chosen two protocols for our comparative study; one based on single qubit states and the other one on entangled states. The compar…
Recently, Hwang et al. [Eur. Phys. J. D. 61, 785 (2011)] and Yuan et al. [Int. J. Theo. Phys. 50, 2403 (2011)] have proposed two efficient protocols of secure quantum communication using 3-qubit and 4-qubit symmetric W state respectively. These two dense coding based protocols are generalized and their efficiencies are considerably improved. Simple bounds on the qubit efficiency of deterministic secure quantum communication (DSQC) and quantum secure direct communication (QSDC) protocols are obtained and it is shown that dense coding is not essential for designing of maximally efficient DSQC an…
This paper presents a new formal method for verification of quantum communication protocols. By extending the symbolic system of Petri nets, we can define quantum pure states in Petri-net settings. Therefore, it is possible to emerge a framework from formalizing basic quantum phenomena, which are utilized to achieve communication tasks. We also present an example of applying this framework to the modeling and analyzing quantum communication protocols to show how it works.
The communication cost of a classical protocol is typically measured in terms of the number of bits communicated for this determines the time required for communication during the protocol. Similarly, for quantum communication protocols, which use finite-dimensional quantum states, the communication cost is measured in terms of the number of qubits communicated. However, in quantum physics, one can also use infinite-dimensional states, like optical quantum states, for communication protocols. Communication cost measures based on counting the (equivalent) number of qubits transmitted during com…
We present a quantum secure direct communication protocol and a multiparty quantum secret sharing protocol based on Einstein-Podolsky-Rosen pairs and entanglement swapping. The present quantum secure direct communication protocol makes use of the ideal of block transmission. We also point out that the sender can encode his or her secret message without ensuring the security of the quantum channel firstly. In the multiparty quantum secret sharing protocol, the communication parties adopt checking mode or encoding mode with a certain probability. It is not necessary for the protocol to perform l…
We show an eavesdropping scheme on Bostr\UNICODE{0xf6}m-Felbinger communication protocol (called ping-pong protocol) [Phys. Rev. Lett. 89, 187902 (2002)] in an ideal quantum channel. A measurement attack can be perfectly used to eavesdrop Alice's information instead of a most general quantum operation attack. In a noisy quantum channel, the direct communication is forbidden. We present a quantum key distribution protocol based on the ping-pong protocol, which can be used in a low noisy quantum channel. And we give a weak upper bound on the bit-error ratio that the detection probability $d$ sho…
We analyze the security of a quantum secure direct communication protocol equipped with authentication. We first propose a specifc attack on the protocol by which, an adversary can break the secret already shared between Alice and Bob, when he (adversary) runs the protocol few times. The attack shows that there is a gap in authentication procedure of the protocol, and by doing so the adversary can obtain the key without remaining any trace. We then give the modification of the protocol and analyze the security of it, and show how the modified protocol can close the gap.
We propose a class of quantum no-key protocols for private communication of classical message based on quantum computing of random Boolean permutations, and demonstrate that they are information-theoretic secure. These protocols are designed to resist middleman attack for two parties preshared authentication key, and achieve perfect mutual data origin authentication which ensures the permanent reusing of authentication key. Finally, we simplify the protocol to a 4-round one, and show that any protocol with 3 or less rounds cannot achieve perfect security without consuming preshared key.
Semi-quantum protocols that allow some of the users to remain classical are proposed for a large class of problems associated with secure communication and secure multiparty computation. Specifically, first time semi-quantum protocols are proposed for key agreement, controlled deterministic secure communication and dialogue, and it is shown that the semi-quantum protocols for controlled deterministic secure communication and dialogue can be reduced to semi-quantum protocols for e-commerce and private comparison (socialist millionaire problem), respectively. Complementing with the earlier propo…
We propose two deterministic secure quantum communication (DSQC) protocols employing three-qubit GHZ-like states and five-qubit Brown states as quantum channels for secure transmission of information in units of two bits and three bits using multipartite teleportation schemes developed here. In these schemes, the sender's capability in selecting quantum channels and the measuring bases leads to improved qubit efficiency of the protocols.
In reply to Vaidman's Comment [arXiv:1304.6689], we show that his claim that our Protocol for Direct Counterfactual Quantum Communication [PRL 110, 170502 (2013), arXiv:1206.2042] is counterfactual only for one type of information bit is wrong.
In this letter we propose a theoretical deterministic secure direct bidirectional quantum communication protocol by using swapping quantum entanglement and local unitary operations, in which the quantum channel for photon transmission can be discarded, hence any attack with or without eavesdropping or even the destructive attack without scruple is impossible.
I show that a simple multi-party communication task can be performed more efficiently with quantum communication than with classical communication, even with low detection efficiency $η$. The task is a communication complexity problem in which distant parties need to compute a function of the distributed inputs, while minimizing the amount of communication between them. A realistic quantum optical setup is suggested that can demonstrate a five-party quantum protocol with higher-than-classical performance, provided $η>0.33$ .
We propose an information reconciliation protocol that uses two-way classical communication. In the case of the BB84 protocol and the six-state protocol, the key rates of the quantum key distribution (QKD) protocols that use our proposed information reconciliation protocol are higher than previously known protocols for wide range of error rates. We also clarify the relation between the proposed protocol and known QKD protocols, and the relation between the proposed protocol and entanglement distillation protocols (EDPs).
We formulate a two-party communication complexity problem and present its quantum solution that exploits the entanglement between two qutrits. We prove that for a broad class of protocols the entangled state can enhance the efficiency of solving the problem in the quantum protocol over any classical one if and only if the state violates Bell's inequality for two qutrits.
We consider using a secret key and a noisy quantum channel to generate noiseless public communication and noiseless private communication. The optimal protocol for this setting is the publicly-enhanced private father protocol. This protocol exploits random coding techniques and "piggybacking" of public information along with secret-key-assisted private codes. The publicly-enhanced private father protocol is a generalization of the secret-key-assisted protocol of Hsieh, Luo, and Brun and a generelization of a protocol for simultaneous communication of public and private information suggested by…
Consider a function where its entries are distributed among many parties. Suppose each party is allowed to transmit only a limited amount of information to a net. One can use a classical protocol to guess the value of the global function. Is there a quantum protocol improving the results of all classical protocols? Brukner et. al. showed the deep connection between such problems and the theory of Bell's inequalities. Here we generalize the theory to trits. There the best classical protocol fails whereas the quantum protocol yields the correct answer.
Two protocols for deterministic secure quantum communication (DSQC) using GHZ-like states have been proposed. It is shown that one of these protocols can be modified to an equivalent but more efficient protocol of quantum secure direct communication (QSDC). Security and efficiency of the proposed protocols are analyzed in detail and are critically compared with the existing protocols. It is shown that the proposed protocols are highly efficient. It is also shown that all the physical systems where dense coding is possible can be used to design maximally efficient protocol of DSQC and QSDC. Fur…
We introduce a general mapping for encoding quantum communication protocols involving pure states of multiple qubits, unitary transformations, and projective measurements into another set of protocols that employ coherent states of light in a superposition of optical modes, linear optics transformations and measurements with single-photon threshold detectors. This provides a general framework for transforming protocols in quantum communication into a form in which they can be implemented with current technology. We explore the similarity between properties of the original qubit protocols and t…
Quantum entanglement distillation protocols are LOCC protocols between Alice and Bob that convert imperfect EPR pairs, or, in general, partially entangled bipartite states into perfect or near-perfect EPR pairs. The classical communication complexity of these protocols is the minimal amount of classical communication needed for the conversion. In this paper, we focus on the communication complexity of protocols that operate with incomplete information, i.e., where the inputs are mixed states and/or prepared adversarially. We study 3 models of imperfect EPR pairs. In the measure-r model, r out …
Based on the two-step protocol [Phys. Rev. A68(03)042317], we propose a $(n,n)$-threshold multiparty quantum secret sharing protocol of secure direct communication. In our protocol only all the sharers collaborate can the sender's secure direct communication message be extracted. We show a variant version of this protocol based on the variant two-step protocol. This variant version can considerably reduce the realization difficulty in experiment. In contrast to the use of multi-particle GHZ states in the case that the sharer number is larger than 3, the use and identification of Bell states ar…
Communication security with quantum key distribution has been one of the important features of quantum information theory. A novel concept of secured direct communication has been the next step forward without the need to establish any shared secret key. The present paper is based on the ping-pong protocol with three particle GHZ state as the initial state where the receiver can simultaneously receive information from two parties. Possible eavesdropping on the travelling particle has been examined.
Quantum information science breaks limitations of conventional information transfer, cryptography and computation by using quantum superpositions or entanglement as resources for information processing. Here, we report on the experimental realization of three-party quantum communication protocols using single three-level quantum system (qutrit) communication: secret sharing, detectable Byzantine agreement, and communication complexity reduction for a three-valued function. We have implemented these three schemes using the same optical fiber interferometric setup. Our realization is easily scal…
It is shown that maximally efficient protocols for secure direct quantum communications can be constructed using any arbitrary orthogonal basis. This establishes that no set of quantum states (e.g. GHZ states, W states, Brown states or Cluster states) has an advantage over the others, barring the relative difficulty in physical implementation. The work provides a wide choice of states for experimental realization of direct secure quantum communication protocols. We have also shown that this protocol can be generalized to a completely orthogonal state based protocol of Goldenberg-Vaidman (GV) t…
We speculate what quantum information protocols can be implemented between two accelerating observers using the vacuum. Whether it is in principle possible or not to implement a protocol depends on whether the aim is to end up with classical information or quantum information. Thus, unconditionally secure coin flipping seems possible but not teleportation.
Kak's three-stage protocol for quantum key distribution is revisited with special focus on its hitherto unknown strengths and weaknesses. It is shown that this protocol can be used for secure direct quantum communication. Further, the implementability of this protocol in the realistic situation is analyzed by considering various Markovian noise models. It is found that the Kak's protocol and its variants in their original form can be implemented only in a restricted class of noisy channels, where the protocols can be transformed to corresponding protocols based on logical qubits in decoherence…
We analyze how the performance of a quantum-repeater network depends on the protocol employed to distribute entanglement, and we find that the choice of repeater-to-repeater link protocol has a profound impact on communication rate as a function of hardware parameters. We develop numerical simulations of quantum networks using different protocols, where the repeater hardware is modeled in terms of key performance parameters, such as photon generation rate and collection efficiency. These parameters are motivated by recent experimental demonstrations in quantum dots, trapped ions, and nitrogen-…
We present a quantum hyperdense coding protocol with hyperentanglement in polarization and spatial-mode degrees of freedom of photons first and then give the details for a quantum secure direct communication (QSDC) protocol based on this quantum hyperdense coding protocol. This QSDC protocol has the advantage of having a higher capacity than the quantum communication protocols with a qubit system. Compared with the QSDC protocol based on superdense coding with $d$-dimensional systems, this QSDC protocol is more feasible as the preparation of a high-dimension quantum system is more difficult th…
I present a simple two-party quantum communication complexity protocol with higher success rate than the best possible classical protocol for the same task. The quantum protocol is shown to be equivalent to a quantum non-locality test, except that it is not necessary to close the locality loophole. I derive bounds for the detector efficiency and background count rates necessary for an experimental implementation and show that they are close to what can be currently achieved using ion trap technology. I also analyze the requirements for a three-party protocol and show that they are less demandi…
The simulation of quantum correlations with alternative nonlocal resources, such as classical communication, gives a natural way to quantify their nonlocality. While multipartite nonlocal correlations appear to be useful resources, very little is known on how to simulate multipartite quantum correlations. We present the first known protocol that reproduces 3-partite GHZ correlations with bounded communication: 3 bits in total turn out to be sufficient to simulate all equatorial Von Neumann measurements on the 3-partite GHZ state.
We present a family of entanglement purification protocols that generalize four previous methods, namely the recurrence method, the modified recurrence method, and the two methods proposed by Maneva-Smolin and Leung-Shor. We will show that this family of protocols have improved yields over a wide range of initial fidelities F, and hence imply new lower bounds on the quantum capacity assisted by two-way classical communication of the quantum depolarizing channel. In particular, the yields of these protocols are higher than the yield of universal hashing for F less than 0.993 and as F goes to 1.
The direct counterfactual quantum communication protocol involving double chained Mach-Zehnder interferometers requires a single photon input. Here, we show that even with multiphoton light sources, including a strong coherent light source as inputs, the counterfactual communication can be achieved with success probability approaching unity in the ideal asymptotic limit. The path evolution of multiple photons is non-locally controlled. Thus, information is transmitted without any photons, or any other auxiliary information carriers, appearing in the public transmission channel. The effect is q…
We recall several cryptographic protocols based on entanglement alone and also on entanglement swapping. We make an exposition in terms of the geometrical aspects of the involved Hilbert spaces, and we concentrate on the formal nature of the used transformations.
In all existing protocols of private communication with encryption and decryption, the pre-shared key can be used for only one time. We give a deterministic quantum key expansion protocol where the pre-shared key can be recycled. Our protocol is exponentially secure. Our protocol costs less qubits and almost zero classical communications with authentication steps being included. Since our protocol can distribute the deterministic bits, it can also be used for direct communication.
We show an improved ping-pong protocol which is based on the protocol showed by Kim Bostrom and Timo Felbinger [Phys. Rev. Lett. 89, 187902 (2002); quant-ph/0209040]. We show that our protocol is asymptotically secure key distribution and quasisecure direct communication using a single photon resource. And this protocol can be can be carried out with great efficiency and speed using today's technology.
This study presents the first two authenticated semi-quantum direct communication (ASQDC) protocols without using any classical channel. By pre-sharing the master secret key between two communicants, a sender with advanced quantum devices can transmit a secret message to a receiver who can only perform classical operations without any information leakage. The receiver is then capable of verifying the message up to the single qubit level, i.e., a one-qubit modification of the transmitted quantum sequence can be detected with a probability close to 1. Moreover, the proposed protocols are resista…
Two protocols of quantum direct communication with authentication [Phys. Rev. A {\bf 73}, 042305 (2006)] are recently proposed by Lee, Lim and Yang. In this paper we will show that in the two protocols the authenticator Trent should be prevented from knowing the secret message of communication. The first protocol can be eavesdropped by Trent using the the intercept-measure-resend attack, while the second protocol can be eavesdropped by Trent using single-qubit measurement. To fix these leaks, I revise the original versions of the protocols by using the Pauli-Z operation $σ_z$ instead of the or…
In this paper, we consider a quantum key distribution protocol (QKD) with two-way classical communication that is assisted by one-time pad encryption. We propose a two-way preprocessing that uses one-time pad encryption by previously shared secret key, and the net key rate of the QKD with proposed preprocessing exceeds the key rate of the QKD without it. The preprocessing is reduced to the entanglement distillation protocol with two-way classical communication and previously shared EPR pairs (two-way breeding protocol), and the security of QKD with the preprocessing is guaranteed in the same w…
We present Authenticated Multiuser Quantum Direct Communication(MQDC) protocols using entanglement swapping. Quantum direct communication is believed to be a safe way to send a secret message without quantum key distribution. The authentication process in our protocol allows only proper users to participate in communication. In the communication stage after the authentication, any two authorized users among n users can communicate each other even though there is no quantum communication channels between them. For this protocol, we need only n quantum communication channels between the authenti…
By how much must the communication complexity of a function increase if we demand that the parties not only correctly compute the function but also return all registers (other than the one containing the answer) to their initial states at the end of the communication protocol? Protocols that achieve this are referred to as clean and the associated cost as the clean communication complexity. Here we present clean protocols for calculating the Inner Product of two $n$-bit strings, showing that (in the absence of pre-shared entanglement) at most $n+3$ qubits or $n+O(\sqrt{n})$ bits of communicati…
We propose a protocol for Alice to implement a multiqubit quantum operation from the restricted sets on distant qubits possessed by Bob, and then we investigate the communication complexity of the task in different communication scenarios. By comparing with the previous work, our protocol works without prior sharing of entanglement, and requires less communication resources than the previous protocol in the qubit-transmission scenario. Furthermore, we generalize our protocol to $d$-dimensional operations.
We present two protocols for the single-photon entanglement concentration. With the help of the 50:50 beam splitter, variable beam splitter and an auxiliary photon, we can concentrate a less-entangled single-photon state into a maximally single-photon entangled state with some probability. The first protocol is implemented with linear optics and the second protocol is implemented with the cross-Kerr nonlinearity. Our two protocols do not need two pairs of entangled states shared by the two parties, which makes our protocols more economic. Especially, in the second protocol, with the help of th…
Possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, was known for quarter of a century. The protocols of full communication, including transmitting unknown quantum states were proposed only few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace larger than the trace left by a single particle passing through t…
The local hidden variable assumption was repeatedly proved unable to explain results of experiments in which contextuality is involved. Then, the correlated results of measurements of entangled particles, began to be attributed to a communication between particles through so-called "signals". These "signals" need to possess superluminal velocity or move backward in time. No object that has a rest-mass, not even the photons whose rest mass is zero, behave this way. Still, as the nature of the presumed "sinals" is not known, people don't reject the idea, despite the conflict with the theory of r…
We provide the first example of a communication model and a distributed task, for which there exists a realistic quantum protocol which is asymptotically more efficient than any classical protocol, both in the communication and the information resources. For this, we extend a recently proposed coherent state mapping for quantum communication protocols, introduce the notion of multiplexed coherent state fingerprints and show how to use them to design an efficient quantum protocol for estimating the Euclidean distance of two real vectors within a constant factor.
