Unambiguous Quantum 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.

Unambiguous correct discrimination of real quantum states

ABSTRACT We investigate the unambiguous correct discrimination strategy of a set of linearly independent equidistant real quantum states and three sets of three linearly independent states. The measurement operators include the success and correct operators, and can gain more information about the input states than by using the conventional unambiguous discrimination strategy. Five examples are given to demonstrate the efficiency of the unambiguous correct discrimination strategy.

Bound on optimal local discrimination of multipartite quantum states

We consider the unambiguous discrimination of multipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition to realize the upper bound. We further establish a necessary and sufficient condition for this upper bound to be saturated. Finally, we illustrate our results using examples in multidimensional multipartite quantum systems.

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.

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.

Optimal unambiguous discrimination of pure quantum states using SDP method

In the present paper, an exact analytic solution for the optimal unambiguous state discrimination(OPUSD) problem involving an arbitrary number of pure linearly independent quantum states with real and complex inner product is presented. Using semidefinite programming and Karush-Kuhn-Tucker convex optimization method, we derive an analytical formula which shows the relation between optimal solution of unambiguous state discrimination problem and an arbitrary number of pure linearly independent quantum states.

Understanding of Various Type of Unambiguous Discrimination in View of Coherence Distribution.

Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states.

Operational Restrictions in General Probabilistic Theories

The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular.

Coherence and path information

Complementarity, or more specifically, the wave-particle duality, and quantum coherence are two fundamental concepts in quantum mechanics. Recently, motivated by the progress of the quantification of quantum coherence, the complementary relation between coherence and path information is investigated by many authors, and various duality relations between them are established. Such relations not only provide insights into fundamental problems of quantum mechanics, such as the understanding of quantum coherence and wave-particle duality; but also are important in applications of quantum technologies. In this paper, based on the Bures distance and unambiguous quantum state discrimination, systematic analysis of the complementarity between the quantum coherence and path information in two path interferometers is carried out. Similarly as other related works, the wave aspect, or the visibility of the interferometer, is quantified by the <i>l</i><sub>1</sub>-norm measure of quantum coherence, and the path information is considered via unambiguous quantum state discrimination. In this way, a novel duality relation in two path interferometers is obtained. Compared with known results, our work considers mixed states as well as pure states; considers the path predictability resulting from the intrinsic path asymmetry of the quantum state, as well as the path distinguishability resulting from the use of a which-path detector. Therefore, our work systematically generalizes known results in two path interferometers by removing all the unnecessary restrictions. Specifically, the most general form of quantum states in two path interferometers is considered and the duality relation between quantum coherence and path information is proved based on the positivity property of density matrices. The cases of path predictability and path distinguishability are considered separately. For path predictability, the proof is straightforward; whereas some advanced mathematical techniques, such as the Schur-Weyl inequality, properties of the fidelity and properties of positive matrices, are required in order to give a rigorous proof of the duality relation between coherence and path distinguishability. Concrete examples are provided to illustrate the abstract method and results. Our work concerns about two path interferometers exclusively and depends heavily that the dimensionality is two, therefore it would be an interesting task to generalize the results in this paper to <i>n</i>-path interferometers.

Unambiguous discrimination of nonorthogonal entangled quantum states in cavity QED

In this work we propose a scheme in the context of superconducting cavities to unambiguously discriminate non-orthogonal quantum field states when one of them is one of the four Bell states. The present work, which generalizes an earlier proposal [1] dealing with non-entangled states, also makes use of a single high Q cavity, a sample of three-level atoms, Ramsey zones and selective detectors, thus consisting of an oversimplification from the experimental view.

Equiprobable unambiguous discrimination of quantum states by symmetric orthogonalisation

We show that the maximal probability of equiprobable unambiguous discrimination of a set of pure quantum states is given by the minimal eigenvalue of the Gram matrix of this set. We illustrate this result with several examples important for the protocols of quantum key distribution realized with weak coherent states of light.

Unambiguous discrimination of nonorthogonal quantum states in cavity QED

We propose an oversimplified scheme to unambiguously discriminate nonorthogonal quantum field states inside high-Q cavities. Our scheme, which is based on positive operator-valued measures (POVM) technique, uses a single three-level atom interacting resonantly with a single mode of a cavity-field and selective atomic state detectors. While the single three-level atom takes the role of the ancilla, the single cavity mode field represents the system we want to obtain information. The efficiency of our proposal is analyzed considering the nowadays achievements in the context of cavity QED. We also analyze the effect of a thermal environment to discrimination of nonorthogonal states.

Megahertz-Rate Semi-Device-Independent Quantum Random Number Generators Based on Unambiguous State Discrimination

An approach to quantum random number generation based on unambiguous quantum state discrimination (USD) is developed. We consider a prepare-and-measure protocol, where two non-orthogonal quantum states can be prepared, and a measurement device aims at unambiguously discriminating between them. Because the states are non-orthogonal, this necessarily leads to a minimal rate of inconclusive events whose occurrence must be genuinely random and which provide the randomness source that we exploit. Our protocol is semi-device-independent in the sense that the output entropy can be lower bounded based on experimental data and few general assumptions about the setup alone. It is also practically relevant, which we demonstrate by realising a simple optical implementation achieving rates of 16.5 Mbits/s. Combining ease of implementation, high rate, and real-time entropy estimation, our protocol represents a promising approach intermediate between fully device-independent protocols and commercial QRNGs.

Three-slit interference: A duality relation: Fig. 1.

The issue of interference and which-way information is addressed in the context of 3-slit interference experiments. A new path distinguishability ${\mathcal D_Q}$ is introduced, based on Unambiguous Quantum State Discrimination (UQSD). An inequality connecting the interference visibility and path distinguishability, ${\mathcal V} + {2{\mathcal D_Q}\over 3- {\mathcal D_Q}} \le 1$, is derived which puts a bound on how much fringe visibility and which-way information can be simultaneously obtained. It is argued that this bound is tight. For 2-slit interference, we derive a new duality relation which reduces to Englert's duality relation and Greenberger-Yasin's duality relation, in different limits.

Duality of quantum coherence and path distinguishability

We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.

Extended necessary condition for local operations and classical communication: Tight bound for all measurements

We give a necessary condition that a separable measurement can be implemented by local quantum operations and classical communication (LOCC) in any finite number of rounds of communication, generalizing and strengthening a result obtained previously. That earlier result involved a bound that is tight when the number of measurement operators defining the measurement is relatively small. The present results generalize that bound to one that is tight for any finite number of measurement operators, and we also provide an extension which holds when that number is infinite. We apply these results to the famous example on a $3\ifmmode\times\else\texttimes\fi{}3$ system known as ``domino states,'' which were the first demonstration of nonlocality without entanglement. Our extended necessary condition provides another way of showing that these states cannot be perfectly distinguished by (finite-round) LOCC. It directly shows that this conclusion also holds for their related rotated domino states. We also introduce a class of problems involving the unambiguous discrimination of quantum states, each of which is an example where the states can be optimally discriminated by a separable measurement, but according to our condition, cannot be optimally discriminated by LOCC. These examples nicely illustrate the usefulness of the present results, since our earlier necessary condition, which the present result generalizes, is not strong enough to reach a conclusion in any of these cases.

Class of unambiguous state discrimination problems achievable by separable measurements but impossible by local operations and classical communication

We consider an infinite class of unambiguous quantum state discrimination problems on multipartite systems, described by Hilbert space $\cal{H}$, of any number of parties. Restricting consideration to measurements that act only on $\cal{H}$, we find the optimal global measurement for each element of this class, achieving the maximum possible success probability of $1/2$ in all cases. This measurement turns out to be both separable and unique, and by our recently discovered necessary condition for local quantum operations and classical communication (LOCC), it is easily shown to be impossible by any finite-round LOCC protocol. We also show that, quite generally, if the input state is restricted to lie in $\cal{H}$, then any LOCC measurement on an enlarged Hilbert space is effectively identical to an LOCC measurement on $\cal{H}$. Therefore, our necessary condition for LOCC demonstrates directly that a higher success probability is attainable for each of these problems using general separable measurements as compared to that which is possible with any finite-round LOCC protocol.

Unambiguous state discrimination in high dimensions

We propose methods for the unambiguous discrimination of quantum states encoded in the spatial profile of light modes, in particular in the orbital angular momentum of light. Perfect discrimination between quantum states is possible only between orthogonal states of a known basis system. Generalised measurement strategies have been developed for the distinction between non-orthogonal states in a two-dimensional state space, e.g. the polarisation of light. Here we consider information encoded in superpositions of orbital angular momentum states of light, defined within an infinite-dimensional state space. Generalised measurements will be an important addition to quantum communication in high-dimensional spaces.

Dissonance is Required for Assisted Optimal State Discrimination

The roles of quantum correlations, entanglement, discord, and dissonance needed for performing unambiguous quantum state discrimination assisted by an auxiliary system are studied. In general, this procedure for conclusive recognition between two nonorthogonal states relies on the availability of entanglement and discord. However, we find that there exist special cases for which the procedure can be successfully achieved without entanglement. In particular, we show that the optimal case for discriminating between two nonorthogonal states prepared with equal a priori probabilities does not require entanglement but quantum dissonance only.

A Simplified Quantum Logic Network for Unambiguous Discrimination of Two Nonlocal and Unknown Pure Qubit States

Two nonlocal and unknown pure qubit states can, with a certain probability of success, be discriminated unambiguously with the aid of local operations, classical communication, and shared entanglements (LOCCSE). We present a scheme for such kind of nonlocal unambiguous quantum state discrimination. This scheme consists of a nonlocal positive operator valued measurement (POVM). This nonlocal POVM can be realized by performing nonlocal unitary operations on initial system and ancillary qubits, and local von Neumann projective measurements on the ancilla plus initial system. By utilizing the degrees of freedom of the original system Hilbert space, we need far more simpler operations than those required by the original Neumark approach. We construct a quantum logic network to implement the required nonlocal POVM.