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Register a new userLinear-Optical Implementation of Perfect Discrimination between Single-bit Unitary Operations
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Discrimination of unitary operations is a fundamental quantum information processing task. Assisted with linear optical elements, we experimentally demonstrate perfect discrimination between single-bit unitary operations using two methods--sequential scheme and parallel scheme. The complexity and resource consumed in these two schemes are analyzed and compared.
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Retrieving classical information encoded in optical modes is at the heart of many quantum information processing tasks, especially in the field of quantum communication and sensing. Yet, despite its importance, the fundamental limits of optical mode discrimination have been studied only in few specific examples. Here we present a toolbox to find the optimal discrimination of any set of optical modes. The toolbox uses linear and semi-definite programming techniques, which provide rigorous (not heuristic) bounds, and which can be efficiently solved on standard computers. We study both probabilistic and unambiguous single-shot discrimination in two scenarios: the channel-discrimination scenario, typical of metrology, in which the verifier holds the light source and can set up a reference frame for the phase; and the source-discrimination scenario, more frequent in cryptography, in which the verifier only sees states that are diagonal in the photon-number basis. Our techniques are illustrated with several examples. Among the results, we find that, for many sets of modes, the optimal state for mode discrimination is a superposition or mixture of at most two number states; but this is not general, and we also exhibit counter-examples.
Unconditionally secure quantum bit commitment (QBC) was widely believed to be impossible for more than two decades. But recently, basing on an anomalous behavior found in quantum steering, we proposed a QBC protocol which can be unconditionally secure in principle. The protocol requires the use of infinite-dimensional systems, thus it may seem less feasible at first glance. Here we show that such infinite-dimensional systems can be implemented with quantum optical methods, and propose an experimental scheme using Mach-Zehnder interferometer.
Discrimination of unitary operations is fundamental in quantum computation and information. A lot of quantum algorithms including the well-known Deutsch-Jozsa algorithm, Simon algorithm, and Grover algorithm can essentially be regarded as discriminating among individual, or sets of unitary operations (oracle operators). The problem of discriminating between two unitary operations $U$ and $V$ can be described as: Given $Xin{U, V}$, determine which one $X$ is. If $X$ is given with multiple copies, then one can design an adaptive procedure that takes multiple queries to $X$ to output the identification result of $X$. In this paper, we consider the problem: How many queries are required for achieving a desired failure probability $epsilon$ of discrimination between $U$ and $V$. We prove in a uniform framework: (i) if $U$ and $V$ are discriminated with bound error $epsilon$ , then the number of queries $T$ must satisfy $Tgeq leftlceilfrac{2sqrt{1-4epsilon(1-epsilon)}}{Theta (U^dagger V)}rightrceil$, and (ii) if they are discriminated with one-sided error $epsilon$, then there is $Tgeq leftlceilfrac{2sqrt{1-epsilon}}{Theta (U^dagger V)}rightrceil$, where $Theta(W)$ denotes the length of the smallest arc containing all the eigenvalues of $W$ on the unit circle.
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
We study the possibility for a global unitary applied on an arbitrary number of qubits to be decomposed in a sequential unitary procedure, where an ancillary system is allowed to interact only once with each qubit. We prove that sequential unitary decompositions are in general impossible for genuine entangling operations, even with an infinite-dimensional ancilla, being the controlled-NOT gate a paradigmatic example. Nevertheless, we find particular nontrivial operations in quantum information that can be performed in a sequential unitary manner, as is the case of quantum error correction and quantum cloning.
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