Based on nonlocal two-level controlled-rotation gates, the maximum-confident discrimination among N linearly dependent symmetric d-level quantum states implemented by two remote parters could be realized (N>d). We present a scheme for such kind of nonlocal maximum-confident quantum state discrimination. In this scheme, the sequential nonlocal positive operator valued measurements (POVMs) lies at the heart. We construct the required optimal POVMs, in which each POVM has only two remote detection operators. We also report on the quantitative relations between the success probability of discrimination, entanglement and classical communication resources required in the implementation. The fact that the two-outcome nonlocal 2m×2m POVM could be realized using only (m-1) two-level maximally entangled pairs is notable. This scheme is feasible for current experimental technology.
Based on nonlocal two-level controlled-rotation gates, the maximum-confident discrimination among N linearly dependent symmetric d-level quantum states implemented by two remote parters could be realized (N>d). We present a scheme for such kind of nonlocal maximum-confident quantum state discrimination. In this scheme, the sequential nonlocal positive operator valued measurements (POVMs) lies at the heart. We construct the required optimal POVMs, in which each POVM has only two remote detection operators. We also report on the quantitative relations between the success probability of discrimination, entanglement and classical communication resources required in the implementation. The fact that the two-outcome nonlocal 2m×2m POVM could be realized using only (m-1) two-level maximally entangled pairs is notable. This scheme is feasible for current experimental technology.
A set of linearly independent nonorthogonal symmetric d -level quantum states can be discriminated remotely and unambiguously with the aid of two-level Einstein–Podolsky–Rosen (EPR) states. We present a scheme for such a kind of remote unambiguous quantum state discrimination (UD). The probability of discrimination is in agreement with the optimal probability for local unambiguous discrimination among d symmetric states (Chefles and Barnettt 1998 Phys. Lett. A 250 223). This scheme consists of a remote generalized measurement described by a positive operator valued measurement (POVM). This remote POVM can be realized by performing a nonlocal 2 d × 2 d unitary operation on two spatially separated systems, one is the qudit which is encoded by one of the d symmetric nonorthogonal states to be distinguished and the other is an ancillary qubit, and a conventional local von Neumann orthogonal measurement on the ancilla. By decomposing the evolution process from the initial state to the final state, we construct a quantum network for realizing the remote POVM with a set of two-level nonlocal controlled-rotation gates, and thus provide a feasible physical means to realize the remote UD. A two-level nonlocal controlled-rotation gate can be implemented by using a two-level EPR pair in addition to local operations and classical communications (LOCCs).
Remote quantum-state discrimination is a critical step for the implementation of quantum communication network and distributed quantum computation. We present a protocol for remotely implementing the unambiguous discrimination between nonorthogonal states using quantum entanglements, local operations, and classical communications. This protocol consists of a remote generalized measurement described by a positive operator valued measurement (POVM). We explicitly construct the required remote POVM. The remote POVM can be realized by performing a nonlocal controlled-rotation operation on two spatially separated qubits, one is an ancillary qubit and the other is the qubit which is encoded by two nonorthogonal states to be distinguished, and a conventional local Von Neumann orthogonal measurement on the ancilla. The particular pair of states that can be remotely and unambiguously distinguished is specified by the state of the ancilla. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subset it can be very close to an optimal value in an ordinary local POVM.
We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure (POVM) that maximizes our confidence in identifying each state in the set and minimizes the probability of obtaining inconclusive results. The physical realization of this POVM is completely determined and it is shown that after an inconclusive outcome, the input states may be mapped into a new set of equiprobable symmetric states, restricted, however, to a subspace of the original qudit Hilbert space. By applying the MC measurement again onto this new set, we can still gain some information about the input states, although with less confidence than before. This leads us to introduce the concept of sequential maximum-confidence (SMC) measurements, where the optimized MC strategy is iterated in as many stages as allowed by the input set, until no further information can be extracted from an inconclusive result. Within each stage of this measurement our confidence in identifying the input states is the highest possible, although it decreases from one stage to the next. In addition, the more stages we accomplish within the maximum allowed, the higher will be the probability of correct identification. We will discuss an explicit example of the optimal SMC measurement applied in the discrimination among four symmetric qutrit states and propose an optical network to implement it.
Sequential quantum information processing may lie in the peaceful coexistence of no-go theorems on quantum operations, such as the no-cloning theorem, the monogamy of correlations, and the no-signalling principle. In this work, we investigate a sequential scenario of quantum state discrimination with maximum confidence, called maximum-confidence discrimination, which generalizes other strategies such as minimum-error and unambiguous discrimination. We show that sequential discrimination with equally high confidence can be realized if and only if positive-operator-valued measure elements for a maximum-confidence measurement can be unambiguously discriminated, i.e., linearly independent; otherwise, a party will have strictly less confidence in measurement outcomes than the previous one. We investigate the tradeoff between state disturbance and information gain in sequential state discrimination and show that the less guessing probability there is from conclusive outcomes for each party, the more parties can participate in the sequential scenario.
Sequential quantum information processing may lie in the peaceful coexistence of no-go theorems on quantum operations, such as the no-cloning theorem, the monogamy of correlations, and the no-signalling principle. In this work, we investigate a sequential scenario of quantum state discrimination with maximum confidence, called maximum-confidence discrimination, which generalizes other strategies including minimum-error and unambiguous state discrimination. We show that sequential state discrimination with equally high confidence can be realized only when positive-operator-valued measure elements for a maximum-confidence measurement are linearly independent; otherwise, a party will have strictly less confidence in measurement outcomes than the previous one. We establish a tradeoff between the disturbance of states and information gain in sequential state discrimination, namely, that the less a party learn in state discrimination in terms of a guessing probability, the more parties can participate in the sequential scenario.
Alice, Cindy, and Bob are three remote parties. We present a scheme which allows Alice and Cindy to transform probabilistically and conclusively Bob's unknown d-level quantum (qudit) state into another. In this scheme, the remote positive operator valued measurements (POVM) lies at the heart. Based on the knowledge of probability amplitudes and phase factors of Bob's original state and target state, Alice and Cindy could construct jointly the required optimal POVM, which acts remotely on Bob's (2d-1)-dimensional direct sum space. We construct a quantum network for realizing the remote POVM with 2(d-1) remote two-level unitary rotations, and thus provide a feasible physical means to realize the remote POVM. The fact that the remote POVM could be realized using only 2(d-1) two-level Bell states (ebits) and 3(d-1) two-level classical communications (cbits) is notable. This scheme can be generalized to implement conclusively the (N+2)-party remote qudit state transformation via (d-1) (N+1)-body two-level GHZ states, in which the phase factors of Bob's original state and target state are shared jointly by N agents. The success probability of implementing this remote state transformation is also investigated. This scheme is simpler but conclusive, and more efficient but with less resource, which will make it more feasible with the current experimental technology and more suitable for large-scale quantum network.