This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions: namely, the probability of an identification error, the Kolmogorov distance, the Bhattacharyya coefficient, and the Shannon distinguishability (as defined through mutual information). These measures have a long history of use in statistical pattern recognition and classical cryptography. We obtain several inequalities that relate the quantum distinguishability measures to each other, one of which may be crucial for proving the security of quantum cryptographic key distribution. In another vein, these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states. This is a tool that may prove useful in the analysis of various quantum cryptographic protocols.
Relativistic quantum field theory imposes additional fundamental restrictions on the distinguishability of quantum states. Because of the unavoidable delocalization of the quantum field states in the Minkowski space-time, the reliable (with unit probability) distinguishability of orthogonal states formally requires infinite time. For the cryptographic protocols which are finite in time the latter means that the effective ``noise'' is present even in the ideal communication channel because of the non-localizability of the quantum field states.
A family of quantum measures like the Shannon distinguishability is presented. These measures are defined over the two classes of POVM measurements and related to separate parts in the expression for mutual information. Changes of Ky Fan's norms and the partitioned trace distances under the operation of partial trace are discussed. Upper and lower bounds on the introduced quantities are obtained in terms of partitioned trace distances and Uhlmann's partial fidelities. These inequalities provide a kind of generalization of the well-known bounds on the Shannon distinguishability. The notion of c…
Erasing quantum-mechanical distinguishability is of fundamental interest and also of practical importance, particularly in subject areas related to quantum information processing. We demonstrate a method applicable to optical systems in which single-mode filtering is used with only linear optical instruments to achieve quantum indistinguishability. Through "heralded" Hong-Ou-Mandel interference experiments we measure and quantify the improvement of indistinguishability between single photons generated via spontaneous four-wave mixing in optical fibers. The experimental results are in excellent…
In the context of the quantum mechanical modelling of a measurement process using the Stern-Gerlach setup, we critically examine the relationship between the notion of `distinguishability' of apparatus states defined in terms of the inner product and spatial separation among the emerging wave packets. We show that, in general, the mutual orthogonality of these wave packets does not necessarily imply their unambiguous spatial separation even in the asymptotic limit. A testable scheme is formulated to quantify such departures from `idealness' for a range of relevant parameters.
A cryptographic algorithm is proposed based on fully quantum mechanical keys and ciphers. Encryption and decryption are carried out via an appropriate measurement process on entangled states as governed by a quantum mechanical, asymmetrical and dynamical public key distribution. The use of public keys leads to a high availability of our scheme, while their quantum nature is shown to ensure unconditional security of the proposed algorithm.
Oblivious transfer protocol is a basic building block in cryptography and is used to transfer information from a sender to a receiver in such a way that, at the end of the protocol, the sender does not know if the receiver got the message or not. Since Shor's quantum algorithm appeared, the security of most of classical cryptographic schemes has been compromised, as they rely on the fact that factoring is unfeasible. To overcome this, quantum mechanics has been used intensively in the past decades, and alternatives resistant to quantum attacks have been developed in order to fulfill the (poten…
Partial polarization is the manifestation of the correlation between two mutually orthogonal transverse field components associated with a light beam. We show both theoretically and experimentally that the origin of this correlation can be purely quantum mechanical. We perform a two-path first-order (single photon) interference experiment and demonstrate that the degree of polarization of the light emerging from the output of the interferometer depends on path distinguishability. We use two independent methods to control the distinguishability of the photon paths. While the distinguishability …
The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical statistical mechanics. In particular, the Gibbs paradox has sometimes been interpreted as a sign of the untenability of the classical concept of a particle and as a premonition that quantum theory is needed. This idea of a quantum connection stubbornly persists in the literature, even though it has also been criticized frequently. Here we shall argue that although thi…
Cryptographic security of quantum key distribution is currently based on a trace distance criterion. The widespread misinterpretation of the criterion as failure probability and also its actual scope have been discussed previously. Recently its distinguishability advantage interpretation is re-emphasized as an operational guarantee, and the failure probability misinterpretation is maintained with a further failure probability per bit interpretation. In this paper we explain the basic perpetuating error as a confusion on the correspondence between mathematics and reality. We note that the assig…
Quantum mechanical wave-particle duality is quantified in terms of a trade-off relation between the fringe visibility and the which-way distinguishability in an interference experiment. This relation is recently generalized by Banaszek et. al., (Nature Communications 4, 2594, 2013) when the particle is equipped with an internal degree of freedom such as spin. Here, we extend the visibility-distinguishability trade-off relation to quantum interference of a particle possessing an internal degree of freedom, when the which-way detector state is entangled with an ancillary system. We introduce an …
In a recent paper, [Phys. Rev. A 65, 052326 (2002)], Mihara presented several cryptographic protocols that were claimed to be quantum mechanical in nature. In this comment it is pointed out that these protocols can be described in purely classical terms. Hence, the security of these schemes does not rely on the usage of entanglement or any other quantum mechanical property.
We establish a method of directly measuring and estimating non-classicality - operationally defined in terms of the distinguishability of a given state from one with a positive Wigner function. It allows to certify non-classicality, based on possibly much fewer measurement settings than necessary for obtaining complete tomographic knowledge, and is at the same time equipped with a full certificate. We find that even from measuring two conjugate variables alone, one may infer the non-classicality of quantum mechanical modes. This method also provides a practical tool to eventually certify such …
This paper provides a simple variation of the basic ideas of the BB84 quantum cryptographic scheme leading to a method of key expansion. A secure random sequence (the bases sequence) determines the encoding bases in a proposed scheme. Using the bases sequence repeatedly is proven to be safe by quantum mechanical laws.
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum algorithms perform a select set of tasks vastly more efficiently than any classical algorithm, but for many tasks it has been proved that quantum algorithms provide no advantage. The breadth of quantum computing applications is still being explored. Major application areas include security and the many fields that would benefit from efficient quantum simula…
Quantum key distribution (QKD) promises secure key agreement by using quantum mechanical systems. We argue that QKD will be an important part of future cryptographic infrastructures. It can provide long-term confidentiality for encrypted information without reliance on computational assumptions. Although QKD still requires authentication to prevent man-in-the-middle attacks, it can make use of either information-theoretically secure symmetric key authentication or computationally secure public key authentication: even when using public key authentication, we argue that QKD still offers stronge…
Quantum mechanical effects have enabled the construction of cryptographic primitives that are impossible classically. For example, quantum copy-protection allows for a program to be encoded in a quantum state in such a way that the program can be evaluated, but not copied. Many of these cryptographic primitives are two-party protocols, where one party, Bob, has full quantum computational capabilities, and the other party, Alice, is only required to send random BB84 states to Bob. In this work, we show how such protocols can generically be converted to ones where Alice is fully classical, assum…
The effect of measurement attributes (quantum level of precision, finite duration) on the classical and quantum correlations is analysed for a pair of qubits immersed in a common reservoir. We show that the quantum discord is enhanced as the precision of the measuring instrument is increased, and both the classical correlation and the quantum discord experience noticeable changes during finite-time measurements performed on a neighboring partition of the entangled system. The implications of these results on the "information-disturbance relationship" are examined, with critical analysis of the…
Quantum key distribution (QKD) uniquely allows distribution of cryptographic keys with security verified by quantum mechanical limits. Both protocol execution and subsequent applications require the assistance of classical data communication channels. While using separate fibers is one option, it is economically more viable if data and quantum signals are simultaneously transmitted through a single fiber. However, noise-photon contamination arising from the intense data signal has severely restricted both the QKD distances and secure key rates. Here, we exploit a novel temporal-filtering effec…
Distributing cryptographic keys over public channels in a way that can provide information-theoretic security is the holy grail for secure communication. This can be achieved by exploiting quantum mechanical principles in so-called quantum key distribution (QKD). Continuous-variable (CV) QKD based on coherent states, in particular, is an attractive scheme for secure communication since it requires only standard telecommunication technology that can operate at room temperature. However, a recently discovered side-channel created in the process of state preparation leads to a leakage of informat…
The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap between quantum mechanical and statistical mechanical descriptions of isolated quantum systems. Here, we define unbiased measures for how well the ETH works in various regimes, by mapping general interacting quantum systems on regular lattices onto a single particle living on a high-dimensional graph. By numerically analyzing deviations from ETH behavior in the non-integrable Ising model, we propose a quantity that we call the $n$-$weight$ to democratically characterize the average deviations for all operators residing o…
Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notio…
The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and information are grounded in classical mechanics, but the physics underlying our world is quantum. In the early 80s researchers began to ask how computation would change if we adopted a quantum mechanical, instead of a classical mechanical, view of computation. Slowly, a new picture of computation arose, one that gave rise to a variety of faster algorithms, n…
Field-Trial Quantum Key Distribution with Qubit-Based Frame Synchronization
Guangxi University（广西大学）；The 34th Research Institute of China Electronics Technology Group Corporation（中国电子科技集团公司第三十四研究所）；Ji Hua Laboratory（季华实验室）；Guangxi Zhuang Autonomous Region Information Center（广西壮族自治区信息中心）
One-time memories (OTM's) are simple tamper-resistant cryptographic devices, which can be used to implement one-time programs, a very general form of software protection and program obfuscation. Here we investigate the possibility of building OTM's using quantum mechanical devices. It is known that OTM's cannot exist in a fully-quantum world or in a fully-classical world. Instead, we propose a new model based on "isolated qubits" -- qubits that can only be accessed using local operations and classical communication (LOCC). This model combines a quantum resource (single-qubit measurements) with…
