Optimal measurements for symmetric quantum states with applications to optical quantum communication

2014 ◽  
Author(s):  
Hari Krovi ◽  
Saikat Guha ◽  
Zachary Dutton ◽  
Marcus P. da Silva
Keyword(s):  
Quantum Communication ◽  
Quantum States ◽  
Symmetric Quantum ◽  
Optimal Measurements

scholarly journals Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

2021 ◽  
Author(s):  
Miguel Ángel Solís-Prosser ◽  
Omar Jiménez ◽  
Aldo Delgado ◽  
Leonardo Neves
Keyword(s):  
Hilbert Spaces ◽  
Quantum Communication ◽  
Success Probability ◽  
Quantum States ◽  
High Dimensional ◽  
Full Potential ◽  
The Core ◽  
Photonic States ◽  
Optimal Measurements ◽  
Measurement Strategies

Abstract The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors, while demanding certainty leads to some inconclusiveness. One of the most fundamental strategies developed for this task is the optimal unambiguous measurement. It encompasses conclusive results, which allow for error-free state retrodictions with the maximum success probability, and inconclusive results, which are discarded for not allowing perfect identifications. Interestingly, in high-dimensional Hilbert spaces the inconclusive results may contain valuable information about the input states. Here, we theoretically describe and experimentally demonstrate the discrimination of nonorthogonal states from both conclusive and inconclusive results in the optimal unambiguous strategy, by concatenating a minimum-error measurement at its inconclusive space. Our implementation comprises 4- and 9-dimensional spatially encoded photonic states. By accessing the inconclusive space to retrieve the information that is wasted in the conventional protocol, we achieve significant increases of up to a factor of 2.07 and 3.73, respectively, in the overall probabilities of correct retrodictions. The concept of concatenated optimal measurements demonstrated here can be extended to other strategies and will enable one to explore the full potential of high-dimensional nonorthogonal states for quantum communication with larger alphabets.

scholarly journals Path-encoded high-dimensional quantum communication over a 2-km multicore fiber

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Beatrice Da Lio ◽  
Daniele Cozzolino ◽  
Nicola Biagi ◽  
Yunhong Ding ◽  
Karsten Rottwitt ◽  
...  
Keyword(s):  
Quantum Key Distribution ◽  
Quantum Communication ◽  
Error Rates ◽  
Quantum States ◽  
High Dimensional ◽  
Secret Key ◽  
System A ◽  
Reliable Transmission ◽  
Multicore Fiber ◽  
Interferometric Detection

AbstractQuantum key distribution (QKD) protocols based on high-dimensional quantum states have shown the route to increase the key rate generation while benefiting of enhanced error tolerance, thus overcoming the limitations of two-dimensional QKD protocols. Nonetheless, the reliable transmission through fiber links of high-dimensional quantum states remains an open challenge that must be addressed to boost their application. Here, we demonstrate the reliable transmission over a 2-km-long multicore fiber of path-encoded high-dimensional quantum states. Leveraging on a phase-locked loop system, a stable interferometric detection is guaranteed, allowing for low error rates and the generation of 6.3 Mbit/s of a secret key rate.

Optimal ambiguous discrimination between states given by two projections

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Krzysztof Kaniowski
Keyword(s):  
Hilbert Space ◽  
Quantum States ◽  
Prior Probabilities ◽  
Optimal Measurements

AbstractLet P 0 and P 1 be projections in a Hilbert space H. We shall construct a class of optimal measurements for the problem of discrimination between quantum states $$\rho _i = \tfrac{1} {{\dim P_i }}P_i$$, with prior probabilities π 0 and π 1. The probabilities of failure for such measurements will also be derived.

Long distance two-party quantum crypto made simple

2012 ◽  
Vol 12 (5&6) ◽  
pp. 448-460
Author(s):  
Iordanis Kerenidis ◽  
Stephanie Wehner
Keyword(s):  
Quantum Communication ◽  
Oblivious Transfer ◽  
Difficult Problem ◽  
Entanglement Swapping ◽  
Quantum States ◽  
Large Network ◽  
Long Distance ◽  
Computational Problem ◽  
Cryptographic Primitive

Any two-party cryptographic primitive can be implemented using quantum communication under the assumption that it is difficult to store a large number of quantum states perfectly. However, achieving reliable quantum communication over long distances remains a difficult problem. Here, we consider a large network of nodes with only neighboring quantum links. We exploit properties of this cloud of nodes to enable any two nodes to achieve security even if they are not directly connected. Our results are based on techniques from classical cryptography and do not resort to technologically difficult procedures like entanglement swapping. More precisely, we show that oblivious transfer can be achieved in such a network if and only if there exists a path in the network between the sender and the receiver along which all nodes are honest. Finally, we show that useful notions of security can still be achieved when we relax the assumption of an honest path. For example, we show that we can combine our protocol for oblivious transfer with computational assumptions such that we obtain security if either there exists an honest path, or, as a backup, at least the adversary cannot solve a computational problem.

scholarly journals Efficient optimal minimum error discrimination of symmetric quantum states

2010 ◽  
Vol 81 (1) ◽  
Author(s):  
Antonio Assalini ◽  
Gianfranco Cariolaro ◽  
Gianfranco Pierobon
Keyword(s):  
Quantum States ◽  
Minimum Error ◽  
Symmetric Quantum

Optimum measurements for discrimination among symmetric quantum states and parameter estimation

1997 ◽  
Vol 36 (6) ◽  
pp. 1269-1288 ◽  
Author(s):  
Masashi Ban ◽  
Keiko Kurokawa ◽  
Rei Momose ◽  
Osamu Hirota
Keyword(s):  
Parameter Estimation ◽  
Quantum States ◽  
Symmetric Quantum

NONLOCAL MEASUREMENTS IN THE TIME-SYMMETRIC QUANTUM MECHANICS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1528-1535 ◽  
Author(s):  
LEV VAIDMAN ◽  
IZHAR NEVO
Keyword(s):  
Quantum Mechanics ◽  
Quantum Systems ◽  
Quantum Measurements ◽  
Quantum States ◽  
Standard Quantum ◽  
Time Direction ◽  
Quantum Formalism ◽  
Symmetric Quantum ◽  
Time Symmetric Quantum Mechanics

Although for some nonlocal variables the standard quantum measurements which are reliable, instantaneous, and nondemolition, are impossible, demolition reliable instantaneous measurements of all variables are possible. It is shown that this is correct also in the framework of the time-symmetric quantum formalism, i.e. nonlocal variables of composite quantum systems with quantum states evolving both forward and backward in time are measurable in a demolition way. The result follows from the possibility to reverse with certainty the time direction of backward evolving quantum states.

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