Related papers: Decision problems with quantum black boxes
Discrimination of unitary operations is fundamental in quantum computation and information. A lot of quantum algorithms including the well-known Deutsch-Jozsa algorithm, Simon's algorithm, and Grover's algorithm can essentially be regarded…
In the problem of quantum channel discrimination, one distinguishes between a given number of quantum channels, which is done by sending an input state through a channel and measuring the output state. This work studies applications of…
A bipartite state which is secretly chosen from a finite set of known entangled pure states cannot be immediately useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown…
Modern programming relies on our ability to treat preprogrammed functions as black boxes - we can invoke them as subroutines without knowing their physical implementation. Here we show it is generally impossible to execute an unknown…
State transformation problems such as compressing quantum information or breaking quantum commitments are fundamental quantum tasks. However, their computational difficulty cannot easily be characterized using traditional complexity theory,…
The need of discriminating between different quantum states is a fundamental issue in Quantum Information and Communication. The actual realization of generally optimal strategies in this task is often limited by the need of supplemental…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
We investigate the extent to which we can establish whether or not two quantum systems have been prepared in the same state. We investigate the possibility of universal unambiguous state comparison. We show that it is impossible to…
Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on…
Accurate control of quantum states is crucial for quantum computing and other quantum technologies. In the basic scenario, the task is to steer a quantum system towards a target state through a sequence of control operations. Determining…
Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is, rather than what it is not. Apart…
This paper explores the role of a priori knowledge in the optimization of quantum information processing by investigating optimum unambiguous discrimination problems for both the qubit and qutrit states. In general, a priori knowledge in…
We discuss the problem of designing unambiguous programmable discriminators for any $n$ unknown quantum states in an $m$-dimensional Hilbert space. The discriminator is a fixed measurement which has two kinds of input registers: the program…
Unitary operations are a fundamental component of quantum algorithms, but they seem to be far more useful if given with a "quantum control" as a controlled unitary operation. However, quantum operations are not limited to unitary…
Tasks involving black boxes appear frequently in quantum computer science. An example that has been deeply studied is quantum channel discrimination. In this work, we study the discrimination between two quantum unitary channels in the…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
We model a quantum sensor network using techniques from quantum state discrimination. The interaction between a qubit detector and the environment is described by a unitary operator, and we will assume that at most one detector does…
We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states…
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As…