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Sequential measurements on qubits by multiple observers: Joint Best Guess strategy

机译：多个观察者对量子位的顺序测量：联合最佳猜测策略

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We study sequential state discrimination measurements performed on the same qubit by subsequent observers. Specifically, we focus on the case when the observers perform a kind of a minimum-error type state discriminating measurement where the goal of the observers is to maximize their joint probability of successfully guessing the state that the qubit was initially prepared in. We call this the Joint Best Guess strategy. In this scheme, Alice prepares a qubit in one of two possible states. The qubit is first sent to Bob, who measures it, and then on to Charlie, and so on to altogether N consecutive receivers who all perform measurements on it. The goal for all observers is to determine which state Alice sent. In the Joint Best Guess strategy, every time a system is received the observer is required to make a guess, aided by the measurement, about its state. The price to pay for this requirement is that errors must be permitted, the guess can be correct or in error. There is a nonzero probability for all the receivers to successfully identify the initially prepared state, and we maximize this joint probability of success. This work is a step toward developing a theory of nondestructive sequential quantum measurements and could be useful in multiparty quantum communication schemes based on communicating with single qubits, particularly in schemes employing continuous variable states. It also represents a case where subsequent observers can probabilistically and optimally get around both the collapse postulate and the no-broadcasting theorem.
机译：我们研究由后续观察者在相同的量子位上执行的顺序状态鉴别测量。具体来说，我们关注观察者执行一种最小错误类型状态区分度量的情况，其中观察者的目标是最大程度地提高他们成功猜测qubit最初处于何种状态的联合概率。联合最佳猜测策略。在此方案中，爱丽丝准备处于两种可能状态之一的量子比特。首先将量子比特发送给Bob进行测量，然后再将其发送给Charlie，依次类推至总共N个连续的接收器，所有接收器都对其进行测量。所有观察者的目标是确定爱丽丝发送的状态。在“联合最佳猜想”策略中，每次接收到一个系统时，都要求观察者对自己的状态进行猜测，并借助测量。为此要求付出的代价是必须允许错误，猜测可以是正确的或错误的。所有接收者成功识别初始准备状态的概率不为零，我们将这种联合成功概率最大化。这项工作是朝着发展非破坏性顺序量子测量理论迈出的一步，并且可能在基于与单量子位通信的多方量子通信方案中很有用，特别是在采用连续可变状态的方案中。这也代表了随后的观察者可以概率性地且最佳地避开崩溃假设和无广播定理的情况。

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