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Janos A. Bergou

Publications and source records attributed to Janos A. Bergou.

At least 19 recordsLinked to original sources
arXiv2023

Broadcasting single-qubit and multi-qubit-entangled states: authentication, cryptography, and distributed quantum computation

Quantum entanglement assisted with measurements provides various pathways to communicate information to parties within a network. In this work, we generalize a previous broadcasting protocol and present schemes to broadcast product and multi-partite entangled quantum states, where in the latter case the sender can remotely add phase gates or abort distributing the states. We first focus on the broadcasting of product quantum states in a network, and generalize the basic protocol to include an arbitrary basis rotation and allow for multiple receivers and senders. We show how to add and delete senders from the network. The generalization also includes the case where a phase to be applied to the broadcast states is not known in advance but is provided to a sender encoded in another quantum state. Applications of broadcasting product states include authentication and three-state quantum cryptography. In the second part, we study the distribution of a single multi-qubit state shared among several receivers entangled with multi-qubit phase gates, which includes the graph states as an example. We show that by coordinating with the sender, the receivers can assist in performing remote, distributed measurement-based quantum computation with the Pauli X basis measurement alone. As another application of this, we discuss the distribution of the multi-qubit Greenberger-Horne-Zeilinger state.

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arXiv2021

Optimal linear optical discrimination of Bell-like states

Quantum information processing using linear optics is challenging due to the limited set of deterministic operations achievable without using complicated resource-intensive methods. While techniques such as the use of ancillary photons can enhance the information processing capabilities of linear optical systems they are technologically demanding. Therefore, determining the constraints posed by linear optics and optimizing linear optical operations for specific tasks under those constraints, without the use of ancillas, can facilitate their potential implementation. Here, we consider the task of unambiguously discriminating between Bell-like states without the use of ancillary photons. This is a basic problem relevant in diverse settings, for example, in the measurement of the output of an entangling quantum circuit or for entanglement swapping at a quantum repeater station. While it is known that exact Bell states of two qubits can be discriminated with an optimal success probability of 50% we find, surprisingly, that for Bell-like states the optimal probability can be only 25%. We analyze a set of Bell-like states in terms of their distinguishability, entanglement as measured by concurrence, and parameters of the beam-splitter network used for unambiguous discrimination. Further, we provide the linear optical configuration comprised of single photon detectors and beam splitters with input state-dependent parameters that achieves optimal discrimination in the Bell-like case.

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arXiv2020

Wave-particle duality relations based on entropic bounds for which-way information

We present wave-particle duality relations involving the relative entropy coherence measure, which plays a prominent role in the resource theory of coherence. The main input in these relations is an entropic bound for the which-way information, which we derive in this letter. We show that this latter crucially depends on the choice of the measurement strategy to obtain the path information. In particular, we present results for two strategies: zero-error identification of the path-detector states, which never produces an error but sometimes fails to return a conclusive answer, and a mixed strategy where both errors and failure are allowed.

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arXiv2018

A quantum controlled quantum eraser

We show that the protocol known as quantum state separation can be used to transfer information between the phase and path of a particle in an interferometer. When applied to a quantum eraser, this allows us to erase some, but not all, of the path information. We can control how much path information we wish to erase.

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arXiv2018

A generalized wave-particle duality relation for finite groups

Wave-particle duality relations express the fact that knowledge about the path a particle took suppresses information about its wave-like properties, in particular, its ability to generate an interference pattern. Recently, duality relations in which the wave-like properties are quantified by using measures of quantum coherence have been proposed. Quantum coherence can be generalized to a property called group asymmetry. Here we derive a generalized duality relation involving group asymmetry, which is closely related to the success probability of discriminating between the actions of the elements of a group. The second quantity in the duality relation, the one generalizing which-path information, is related to information about the irreducible representations that make up the group representation.

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arXiv2017

Duality games and operational duality relations

We give operational meaning to wave-particle duality in terms of discrimination games. Duality arises as a constraint on the probability of winning these games. The games are played with the aid of an n-port interferometer, and involve 3 parties, Alice and Bob, who cooperate, and the House, who supervises the game. In one game called ways they attempt to determine the path of a particle in the interferometer. In another, called phases, they attempt to determine which set of known phases have been applied to the different paths. The House determines which game is to be played by flipping a coin. We find a tight wave-particle duality relation that allows us to relate the probabilities of winning these games, and use it to find an upper bound on the probability of winning the combined game. This procedure allows us to describe wave-particle duality in terms of discrimination probabilities.

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arXiv2015

Relations between coherence and path information

We find two relations between coherence and path-information in a multi-path interferometer. The first builds on earlier results for the two-path interferometer, which used minimum-error state discrimination between detector states to provide the path information. For visibility, which was used in the two-path case, we substitute a recently defined $l_{1}$ measure of quantum coherence. The second is an entropic relation in which the path information is characterized by the mutual information between the detector states and the outcome of the measurement performed on them, and the coherence measure is one based on relative entropy.

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arXiv2015

A generalized unknown qubit discriminator

We discuss a state discriminator that unambiguously distinguishes between two quantum registers prepared with multiple copies of two unknown qubits. This device achieves the optimal performance by von Neumann measurement and general POVM in different ranges of the input preparation probabilities, respectively, and in the limit of very large program registers the optimal measurement reduces to only von Neumann measurements.

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arXiv2015

A Geometric Approach to Quantum State Separation

Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure states in the general case where the known states have arbitrary a priori probabilities. The problem is formulated from a geometric perspective and shown to be equivalent to the problem of finding tangent curves within two families of conics that represent the unitarity constraints and the objective functions to be optimized, respectively. We present the corresponding analytical solutions in various forms. In the limit of perfect state separation, which is equivalent to unambiguous state discrimination, the solution exhibits a phenomenon analogous to a second order symmetry breaking phase transition. We also propose a linear optics implementation of separation which is based on the dual rail representation of qubits and single-photon multiport interferometry.

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arXiv2015

Probabilistically Perfect Cloning of Two Pure States: A Geometric Approach

We solve the long-standing problem of making n perfect clones from m copies of one of two known pure states with minimum failure probability in the general case where the known states have arbitrary a priori probabilities. The solution emerges from a geometric formulation of the problem. This formulation also reveals a deeper connection between cloning and state discrimination. The convergence of cloning to state discrimination as the number of clones goes to infinity exhibits a phenomenon analogous to a second order symmetry breaking phase transition.

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arXiv2009

Universal entangler with photon pairs in arbitrary states

We propose a setup that transforms a photon pair in arbitrary rank-four mixed state, which could also be unknown, to a Bell state. The setup involves two linear optical circuits processing the individual photons and a parity gate working with weak cross-Kerr nonlinearity. By the photon number resolving detection on one of the output quantum bus or communication beams, the setup will realize a near deterministic transformation to a Bell state for every entangling attempt. With the simple threshold detectors, on the other hand, the system can still reach a considerable success probability of 0.5 per try. The decoherence effect caused by photon absorption losses in the operation is also discussed.

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arXiv2009

Quantum key distribution using vacuum-one-photon qubits: maximum number of transferable bits per particle

Quantum key distribution schemes which employ encoding on vacuum-one-photon qubits are capable of transferring more information bits per particle than the standard schemes employing polarization or phase coding. We calculate the maximum number of classical bits per particle that can be securely transferred when the key distribution is performed with the BB84 and B92 protocols, respectively, using the vacuum-one-photon qubits. In particular, we show that for a generalized B92 protocol with the vacuum-one-photon qubits, a maximum of two bits per particle can be securely transferred. We also demonstrate the advantage brought about by performing a generalized measurement that is optimized for unambiguous discrimination of the encoded states: the parameter range where the transfer of two bits per particle can be achieved is dramatically enhanced as compared to the corresponding parameter range of projective measurements.

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arXiv2009

Creation of high-quality long-distance entanglement with flexible resources

We present a quantum repeater protocol that generates the elementary segments of entangled photons through the communication of qubus in coherent states. The input photons at the repeater stations can be in arbitrary states to save the local state preparation time for the operations. The flexibility of the scheme accelerates the generation of the elementary segments (close to the exact Bell states) to a high rate for practical quantum communications. The entanglement connection to long distances is simplified and sped up, possibly realizing an entangled pair of high quality within the time in the order of that for classical communication between two far-away locations.

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arXiv2008

Optimum unambiguous identification of d unknown pure qudit states

We address the problem of unambiguously identifying the state of a probe qudit with the state of one of d reference qudits. The reference states are assumed pure and linearly independent but we have no knowledge of them. The state of the probe qudit is assumed to coincide equally likely with either one of the d unknown reference states. We derive the optimum measurement strategy that maximizes the success probability of unambiguous identification and find that the optimum strategy is a generalized measurement. We give both the measurement operators and the optimum success probability explicitly. Technically, the problem we solve amounts to the optimum unambiguous discrimination of d known mixed quantum states.

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arXiv2007

Universal discriminator for completely unknown optical qubits

We propose an experimental setup that is capable of unambiguously discriminating any pair of linearly independent single photon polarization qubits, about which we don't have any knowledge except that an extra pair of these unknown states are provided as the reference. This setup, which is constructed with optical CNOT gates, weak cross Kerr non-linearities, Bell state analysers and other linear optical elements, transforms the unknown triple photon input states to the corresponding single photon states to be deterministically processed by linear optics circuit. The optimal discrimination of the unknown states is achieved by this setup.

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arXiv2006

Optimal unambiguous discrimination of two subspaces as a case in mixed state discrimination

We show how to optimally unambiguously discriminate between two subspaces of a Hilbert space. In particular we suppose that we are given a quantum system in either the state ψ_{1}, where ψ_{1} can be any state in the subspace S_{1}, or ψ_{2}, where ψ_{2} can be any state in the subspace S_{2}, and our task is to determine in which of the subspaces the state of our quantum system lies. We do not want to make a mistake, which means that our procedure will sometimes fail if the subspaces are not orthogonal. This is a special case of the unambiguous discrimination of mixed states. We present the POVM that solves this problem and several applications of this procedure, including the discrimination of multipartite states without classical communication.

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arXiv2006

Programmable quantum state discriminators with simple programs

We describe a class of programmable devices that can discriminate between two quantum states. We consider two cases. In the first, both states are unknown. One copy of each of the unknown states is provided as input, or program, for the two program registers, and the data state, which is guaranteed to be prepared in one of the program states, is fed into the data register of the device. This device will then tell us, in an optimal way, which of the templates stored in the program registers the data state matches. In the second case, we know one of the states while the other is unknown. One copy of the unknown state is fed into the single program register, and the data state which is guaranteed to be prepared in either the program state or the known state, is fed into the data register. The device will then tell us, again optimally, whether the data state matches the template or is the known state. We determine two types of optimal devices. The first performs discrimination with minimum error, the second performs optimal unambiguous discrimination. In all cases we first treat the simpler problem of only one copy of the data state and then generalize the treatment to n copies. In comparison to other works we find that providing n > 1 copies of the data state yields higher success probabilities than providing n > 1 copies of the program states.

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