Unambiguous State Discrimination Research Articles

General measurements with limited resources and their application to quantum unambiguous state discrimination

In this report, we present a framework for implementing an arbitrary n-outcome generalized quantum measurement (POVM) on an m-qubit register as a sequence of two-outcome measurements requiring only single ancillary qubit. Our procedure offers a particular construction for the two-outcome partial measurements which can be composed into a full implementation of the measurement on any gate architecture. This implementation in general requires classical feedback; we present specific cases when this is not the case. We apply this framework on the unambiguous state discrimination and analyze possible strategies. In the simplest case, it gives the same construction as is known, if we opt for performing conclusiveness measurement first. However, it also offers possibility of performing measurement for one of the state outcomes first, leaving conclusiveness measurement for later. This shows flexibility of presented framework and opens possibilities for further optimization. We present discussion also on biased qubit case as well as general case of unambiguous quantum state discrimination in higher dimension.

Hacking coherent-one-way quantum key distribution with present-day technology

Recent results have shown that the secret-key rate of coherent-one-way (COW) quantum key distribution (QKD) scales quadratically with the system’s transmittance, thus rendering this protocol unsuitable for long-distance transmission. This was proven by using a so-called zero-error attack, which relies on an unambiguous state discrimination (USD) measurement. This type of attack allows the eavesdropper to learn the whole secret key without introducing any error. Here, we investigate the feasibility and effectiveness of zero-error attacks against COW QKD with present-day technology. For this, we introduce two practical USD receivers that can be realized with linear passive optical elements, phase-space displacement operations and threshold single-photon detectors. The first receiver is optimal with respect to its success probability, while the second one can impose stronger restrictions on the protocol’s performance with faulty eavesdropping equipment. Our findings suggest that zero-error attacks could break the security of COW QKD even assuming realistic experimental conditions.

Qudit quantum state tomography

In this study, we present a new procedure for quantum state reconstruction of qudit quantum state based on unambiguous state discrimination (USD) measurement. In our recent paper (Karimi et al., 2022), we considered the reconstruction of a single-qubit state via USD measurement. In this paper, we extend this method to the reconstruction of the qudit quantum state.

Discrimination of coherent states via atom–field interaction without rotation wave approximation

Quantum state discrimination is an important part of quantum information processing. We investigate the discrimination of coherent states through a Jaynes–Cummings (JC) model interaction between the field and the ancilla without rotation wave approximation (RWA). We show that the minimum failure probability can be reduced as RWA is eliminated from the JC model and the non-RWA terms accompanied by the quantum effects of fields (e.g. the virtual-photon process in the JC model without RWA) can enhance the state discrimination. The JC model without RWA for unambiguous state discrimination is superior to ambiguous state discrimination, particularly when the number of sequential measurements increases. Unambiguous state discrimination implemented via the non-RWA JC model is beneficial to saving resource costs.

Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination

Coherent states of the quantum electromagnetic field, the quantum description of ideal laser light, are prime candidates as information carriers for optical communications. A large body of literature exists on their quantum-limited estimation and discrimination. However, very little is known about the practical realizations of receivers for unambiguous state discrimination (USD) of coherent states. Here we fill this gap and outline a theory of USD with receivers that are allowed to employ: passive multimode linear optics, phase-space displacements, auxiliary vacuum modes, and on-off photon detection. Our results indicate that, in some regimes, these currently-available optical components are typically sufficient to achieve near-optimal unambiguous discrimination of multiple, multimode coherent states.

Quantum Bit Commitment Without Quantum Memory

Abstract Commitment scheme is a fundamental cryptographic primitive that serve as building blocks for many other two-party protocols. In this paper, we propose a novel quantum bit commitment scheme, which is secure and does not require quantum memory. Our scheme processes the quantum information using coherent states and unambiguous state discrimination (USD) measurements, which can be experimentally realized by linear optics and photon detectors. We ensure the unconditionally hiding and binding property by preventing both Alice and Bob from obtaining complete information about the commitment in committing stage, and eliminate the requirement for quantum memory by performing USD measurements and phase shifts immediately after receiving the coherent states.

Reconstructing quantum states via unambiguous state discrimination

Abstract In this paper, we introduce an analytical framework for the reconstruction of quantum states. The reconstruction of an unknown quantum state requires the information of a complete set of observables, obtained through experimental measurements of Hermitian operators usually defined as positive-operator-valued measures (POVMs). The scheme involves a single-qubit unambiguous state discrimination POVM, which can be generalized to perform n-qubit measurements. We also use maximum likelihood estimation as a method in the reconstruction of the density matrix from experimental data and show that the expected value of the cleaner is independent of the parameter of the density operator.

Experimental certification of nonprojective quantum measurements under a minimum overlap assumption.

Certifying quantum measurements is increasingly important for foundational insights in quantum information science. Here, we report an experimental certification of unknown quantum measurements in a semi-device-independent setting. For the first time, we experimentally demonstrate that genuine three-outcome positive operator-valued measures (POVMs) can be certified under the assumption of a limited overlap between the prepared quantum states. The generalized quantum measurements are realized through discrete-time quantum walk and our experimental results clearly show that three-outcome POVMs can be certified even in the presence of noise. Finally, we experimentally investigate that optimal POVMs for performing unambiguous state discrimination can be self-tested. Our work opens new avenues for robust certification of quantum systems in the prepare-and-measure scenario.

Threshold switching strategy for unambiguous state discrimination of quadrature phase-shift-keying coherent states under thermal noise.

Quantum-enhanced measurement technologies can unambiguously discriminate coherent states with accuracy beyond the classical heterodyne measurement. However, typical quantum-enhanced measurement scheme is vulnerable to the thermal noise, which will change the photon counting statistics of the coherent state. This paper presents a threshold-switching strategy that can discriminate quadrature phase-shift-keying coherent states with performance surpassing the typical quantum-enhanced scheme. In our scheme, photon number resolving detectors are used to switch the value of the threshold, which can mitigate the influence of thermal noise and other imperfections. Simulation results show that our scheme unambiguously discriminates the signal states with higher correct probability and the same error ratio compared with the typical scheme. Besides, this scheme can reduce the error ratio simultaneously for thermal noise N ≤ 0.2. The paper demonstrations that quantum-enhanced measurement with the threshold-switching strategy can adapt to different thermal noises by switching the value of the threshold under situations of different thermal noises and signal states.

Quantum state discrimination in a PT -symmetric system

Nonorthogonal quantum state discrimination (QSD) plays an important role in quantum information and quantum communication. In addition, compared to Hermitian quantum systems, parity-time-($\mathcal{PT}$-)symmetric non-Hermitian quantum systems exhibit novel phenomena and have attracted considerable attention. Here, we experimentally demonstrate QSD in a $\mathcal{PT}$-symmetric system (i.e., $\mathcal{PT}$-symmetric QSD), by having quantum states evolve under a $\mathcal{PT}$-symmetric Hamiltonian in a lossy linear optical setup. We observe that two initially nonorthogonal states can rapidly evolve into orthogonal states, and the required evolution time can even be vanishing provided the matrix elements of the Hamiltonian become sufficiently large. We also observe that the cost of such a discrimination is a dissipation of quantum states into the environment. Furthermore, by comparing $\mathcal{PT}$-symmetric QSD with optimal strategies in Hermitian systems, we find that at the critical value, $\mathcal{PT}$-symmetric QSD is equivalent to the optimal unambiguous state discrimination in Hermitian systems. We also extend the $\mathcal{PT}$-symmetric QSD to the case of discriminating three nonorthogonal states. The QSD in a $\mathcal{PT}$-symmetric system opens a new door for quantum state discrimination, which has important applications in quantum computing, quantum cryptography, and quantum communication.

Multi-Access Channel Based on Quantum Detection in Wireless Optical Communication.

In this paper, we propose a novel multi-user access in wireless optical communication based on the quantum detection of the coherent state. In this case, the coherent states are used as the signal carrier and a technique of quantum detection is applied to distinguish between signals from different users. To accomplish this task, two main quantum measurement methods are introduced; one is minimum error discrimination (MED), and the other is unambiguous state discrimination (USD). The theoretical derivation implies that the two methods can both distinguish between the signals from different users efficiently when the average photon number is large enough. Typically, the numerical result shows that in the two-user case, the channel capacity will approach the theoretical maximum limit when the average photon number is greater than 2.5 for MED and 5 for USD in the absence of noise. The MED gains more channel capacity than the USD at the same average photon number. However, the USD wins the error-correction scene with its free-error capability. Furthermore, the detection error probability and channel capacity for the USD with the thermal noise are examined. The result shows that increasing the signal average photon number can continue the USD’s advantage of error-free detection even if in the presence of thermal noise. In addition, compared with non-orthogonal multiple access (NOMA), the bit error rate (BER) against signal-to-noise rate (SNR) performance of USD has been improved.

Quantum vs Noncontextual Semi-Device-Independent Randomness Certification.

We compare the power of quantum and classical physics in terms of randomness certification from devices which are only partially characterized. We study randomness certification based on state discrimination and take noncontextuality as the notion of classicality. A contextual advantage was recently shown to exist for state discrimination. Here, we develop quantum and noncontextual semi-device independent protocols for random-number generation based on maximum-confidence discrimination, which generalizes unambiguous and minimum-error state discrimination. We show that, for quantum eavesdroppers, quantum devices can certify more randomness than noncontextual ones whenever none of the input states are unambiguously identified. That is, a quantum-over-classical advantage exists.

Unextendible entangled bases and more nonlocality with less entanglement

We consider a general version of the phenomenon of more nonlocality with less entanglement, within the framework of the unambiguous (i.e., conclusive) quantum state discrimination problem under local quantum operations and classical communication. We show that although the phenomenon was obtained before for two qutrits, it can also be observed for two qubits, while still being at the single-copy level. We establish that the phenomenon is intrinsically connected to the concept of unextendible entangled bases, in the two-qubit case. In the process, we demonstrate a hierarchy of nonlocality among sets of two-qubit orthogonal pure states, where the "nonlocality" is in the sense of a difference between global and local abilities of quantum state discrimination. We present a complete characterization of two-qubit pure orthogonal state sets of cardinality three with respect to their nonlocality in terms of unambiguous local distinguishability, the status for other cardinalities being already known. The results are potentially useful for secure quantum communication technologies with an optimal amount of resources.

Qutrit state tomography via optimal unambiguous state discrimination and mutually unbiased measurements

We propose an efficient scheme for qutrit state tomography based on optimal unambiguous discrimination of three nonorthogonal pure qutrit states. In our scheme, we first introduce an ancillary qubit initially prepared in a known state and apply a joint unitary transformation on the whole system composed of a qutrit state and an ancillary qubit state. Afterwards, we make a local von Neumann measurement (VNM) on the ancillary qubit. If it is projected onto the state |0〉, we finally perform mutually unbiased measurements (MUMs) on the collapsed qutrit state arbitrarily chosen from a complete set of four mutually unbiased bases (MUBs). With only six properly-chosen projectors, the real and imaginary parts of non-diagonal elements can be entirely obtained. Together with the diagonal elements obtained directly from one VNM in the computational bases, the density matrix of an arbitrary unknown qutrit state can be fully determined. Compared with the previous work (R. Salazar and A. Delgado 2012), our scheme consumes much less resources. In comparison with MUBs-based tomography scheme (H. Yuan, et al., 2016), our scheme requires more measurements and less projectors, but pays the price of a loss of certain fraction identically prepared states. Our proposal can be extended to the case of other d-dimensional quantum states if their d MUBs are exactly known.

Quantum postselective measurements: Sufficient condition for overcoming the Holevo bound and the role of max-relative entropy

The operation of unambiguous state discrimination (USD) plays an important role in quantum information theory. Here, we study the generalization for this operation which can be applied where USD is not available, including the case of completely coinciding supports. We demonstrate the effect of overcoming the Holevo bound after postselective measurements, which works for a class of ensembles, including two arbitrary noncommuting quantum states. We also discuss the role of max-relative entropy in postselective measurements and give an alternative operational interpretation for this function.

Unambiguous State Discrimination with Intrinsic Coherence.

We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the mixed states. We prove that under the equal-fidelity condition, the pure-pure state discrimination scheme is superior to the pure-mixed (mixed-mixed) one. With respect to quantum filtering, the coherence exists only in one pure state and is detrimental to the state discrimination for lower dimensional systems; while it is the opposite for the mixed-mixed case with symmetrically distributed coherence. Making an extension to infinite-dimensional systems, we find that the coherence which is detrimental to state discrimination may become helpful and vice versa.

Unambiguous state discrimination and joint measurement attacks on passive side channel of the light source in BB84 decoy-state protocol

Quantum key distribution (QKD) has a promise of unconditionally secure communication between the remote sides. The real-world QKD implementations, however, have numerous loopholes, both of engeneering and physical origin, and compromise the security promise. In this work, we investigate two attack strategies on the passive side channel of the light source along with the optimal cloning attack on the BB84 protocol with decoy-states. We calculate an upper bound of a secret key rate for these situations and show that the joint measurement attack on the signal and side channel degree of freedom is more effective to the adversary.

Unambiguous State Discrimination Attack on the B92 Protocol of Quantum Key Distribution with Single Photons

We consider an unambiguous state discrimination attack on the B92 protocol of quantum key distribution, realized on the basis of polarization encoding of photons produced by a single-photon source. We calculate the secure key rate and the maximal tolerable loss for various overlaps between two signal states employed in this protocol. We make also a comparison with a physically impossible attack of perfect quantum cloning, and show that the unambiguous state discrimination is much more dangerous for the B92 protocol, than this attack, demonstrating thus, that the security of quantum key distribution is not always based on the no-cloning theorem.

Vulnerabilities of quantum cryptography on geometrically uniform coherent states

It is shown that the quantum cryptography protocol on geometrically uniform coherent states, which uses the restriction for unambiguous discrimination of a set of symmetric coherent states and allows resisting an unambiguous state discrimination attack (USD attack), is not secure to a number of other attacks. The key length formula from the work of ] and the key generation rate for a number of constructive attacks of the eavesdropper are compared and it is shown that the key generation rate in this work is significantly overestimated. This leads to the fact that the distributed key is not secret.

Protocol for unambiguous quantum state discrimination using quantum coherence

Roa et al. showed that quantum state discrimination between two nonorthogonal quantum states does not require quantum entanglement but quantum dissonance only. We find that quantum coherence can also be utilized for unambiguous quantum state discrimination. We present a protocol and quantify the required coherence for this task. We discuss the optimal unambiguous quantum state discrimination strategy in some cases. In particular, our work illustrates an avenue to find the optimal strategy for discriminating two nonorthogonal quantum states by measuring quantum coherence.